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Journal of Medicine and Pharmacy","Tạp chí Y Dược học Cần Thơ",{"EN":487,"VI":488},"\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">04\u002F10\u002F2015 Ministry of Information and Communications allowed Can Tho journal of medicine and pharmacy to operate (102 \u002FGP-BTTTT)\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">07\u002F16\u002F2015 Can Tho journal of medicine and pharmacy is internationally recognized: ISSN 2354-1210\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">In 2016, The journal has been included in the list of medical science journals by The State Council for professorship which is awarded a work score of 0-0.5 points for a published article.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Can Tho Journal of Medicine and Pharmacy welcome original works that haven’t been submitted or published in other medical journals. Posts must contain content related to one of the journal’s categories.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">The content published\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">The journal is divided into 3 categories:\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">- Scientific research article: are valuable scientific works, which have been researched and accepted.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">- Overview of medicine, biology and pharmacy: serving the objective of continuing training in the fields of medicine, biology and pharmacy; to systematize classical and modern knowledge.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">- Update information on new knowledge about medicine, biology, pharmacy in the country and in the world.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Scope\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">- Publication and introduction of scientific research in the fields:\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">+ Medicine (internal medicine, surgery, pediatrics, obstetrics and gynecology, odonto-stomatology, laboratory, oncology, traditional medicine, nursing).\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">+ Biology (genetics, biotechnology).\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">+ Pharmacology (pharmaceutics, drug quality analysis-control, synthetic pharmaceutical chemistry, biochemistry, pharmacognosy, botany, clinical pharmacy).\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">- To enhance the quality of undergraduate, postgraduate education, scientifically researching and meet the necessary treatment in hospital.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">- Introducing the updated domestic and oversea information about science technology to promote scientific research and exchanging technology in local, other universities.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">- Exchanging pharmaceutical and medical information for social health developing in the Mekong Delta and Vietnam.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">The object\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Postgraduate students, student of Can Tho University of Medicine and Pharmacy, scientists from schools, research institutes, hospitals, health centers, pharmaceutical companies of the Mekong Delta; other provinces and regions in Vietnam and other country.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Address\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Headquarters of Can Tho Journal of Medicine and Pharmacy, located Scientific Research and International Cooperation Office: 179 Nguyen Van Cu Street, An Khanh Ward, Ninh Kieu District, Can Tho City, Vietnam.\u003C\u002Fspan>\u003C\u002Fp>","\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Ngày 16\u002F7\u002F2015, Tạp chí Y Dược học Cần Thơ được cấp chỉ số quốc tế: ISSN 2354-1210.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Từ tháng 4\u002F2016, Tạp chí đã được Hội đồng Giáo sư ngành Y đưa vào danh sách các tạp chí khoa học Y học được tính điểm công trình 0-0,5 điểm cho một bài báo đăng.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Năm 2020 Tạp chí Y Dược học Cần Thơ đã được phê duyệt vào danh mục của các Hội đồng Giáo sư ngành Dược học được tính điểm công trình 0-0,5 điểm cho một bài báo đăng.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tạp chí Y Dược học Cần Thơ ra 12 số\u002Fnăm, 180-200 trang\u002Fsố.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Từ tháng 12\u002F2022 Tạp chí Y Dược học Cần Thơ là thành viên của hệ thống Crossref và từ tháng 01\u002F2023 tạp chí thực hiện bình duyệt online kín 2 chiều nhằm tăng tính minh bạch, tin cậy của các công trình nghiên cứu khoa học và đảm bảo tốt nhất chất lượng khoa học của bài viết.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tôn chỉ, mục đích và phạm vi của tạp chí\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tôn chỉ và mục đích hoạt động của tạp chí: xuất bản nhằm mục đích phổ biến kết quả từ các đề tài nghiên cứu khoa học; giao lưu trao đổi khoa học, chia sẻ kinh nghiệm, học tập, đồng thời cập nhật thông tin khoa học mới trong các lĩnh vực y, sinh, dược học trong và ngoài nước.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Phạm vi của tạp chí: Tạp chí xuất bản được chia thành 3 chuyên mục: (i) Bài báo nghiên cứu khoa học là kết quả công trình nghiên cứu khoa học có giá trị đã được triển khai nghiên cứu, (ii) Bài tổng quan y, sinh, dược học: phục vụ mục tiêu đào tạo liên tục trong lĩnh vực y, sinh, dược học; nhằm hệ thống hóa những kiến thức kinh điển và hiện đại; (iii) Thông tin cập nhật kiến thức mới về y, sinh, dược học trong nước và trên thế giới.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Chính sách truy cập mở\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tạp chí Y Dược học Cần Thơ áp dụng chính sách truy cập mở đối với các bài báo đã xuất bản đến với độc giả, nhằm mở rộng cơ hội tiếp cận các kết quả nghiên cứu chất lượng cao và tăng cường trao đổi kiến thức. Tạp chí đăng tải trực tuyến (miễn phí) toàn văn các bài báo được công bố trên website của Tạp chí (https:\u002F\u002Ftapchi.ctump.edu.vn).\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Đạo đức xuất bản\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tạp chí Y Dược học Cần Thơ cam kết tuân thủ đạo đức xuất bản phù hợp với các hướng dẫn và tiêu chuẩn của the Committee on Publication Ethics (COPE), tuân thủ các nguyên tắc của COPE’s Core Practices, Best Practices Guidelines for Journal Editors và Guidelines on Good Publication Practices.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Bản thảo bài báo chỉ được chấp nhận khi được tác giả chịu trách nhiệm chính cam kết các nội dung sau: Các nội dung của bản thảo chưa được đăng tải toàn bộ hoặc một phần ở các tạp chí khác; Tất cả các tác giả đều có đóng góp một cách đáng kể vào quá trình nghiên cứu hoặc chuẩn bị bản thảo và cùng chịu trách nhiệm về các nội dung của bản thảo; Tuân thủ các biện pháp đảm bảo đạo đức nghiên cứu (ví dụ thỏa thuận đồng ý tham gia nghiên cứu).\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Cam kết bảo mật\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tạp chí cam kết thực hiện và tuân thủ các quy định của luật và các văn bản hướng dẫn liên quan đến bảo mật thông tin cá nhân trên không gian mạng. Các thông tin mà người dùng (tác giả, độc giả, biên tập viên, người phản biện) nhập vào các biểu mẫu trên Hệ thống Quản lý xuất bản trực tuyến của tạp chí chỉ được sử dụng vào các mục đích đã được tuyên bố rõ ràng và sẽ không được cung cấp cho bất kỳ bên thứ ba nào khác, hay dùng vào bất kỳ mục đích nào khác.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Phí gửi bài\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Lệ phí gửi đăng bài: 1.000.000đ\u002Fbài báo\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Lệ phí gửi đăng nhanh: 1.500.000đ\u002Fbài báo\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Đối với tác giả là cán bộ viên chức thuộc Trường Đại học Y Dược Cần Thơ thì được hỗ trợ 50% lệ phí gửi đăng bài.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Đối với sinh viên thực hiện đề tài nghiên cứu khoa học cấp trường được hỗ trợ 100% lệ phí đăng bài ( Tác giả gửi đính kèm “ Quyết định về việc giao tổ chức thực hiện đề tài nghiên cứu khoa học cấp Trường của sinh viên”).\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Hình thức nộp lệ phí:\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">1. Tiền mặt:\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Nộp trực tiếp tại Phòng Tài chính - Kế toán, Trường Đại học Y Dược Cần Thơ, số 179 Nguyễn Văn Cừ, P. An Khánh, Q. Ninh Kiều, thành phố Cần Thơ.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">2. Chuyển khoản:\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tên Tài khoản: Trường ĐHYD Cần Thơ, Số TK: 0111000115668, tại ngân hàng Vietcombank chi nhánh Cần Thơ.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Thời gian: Áp dụng từ ngày 01\u002F02\u002F2023.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">* Phí gửi bài không được hoàn trả khi bài viết bị từ chối hoặc tác giả xin rút bài viết.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Quy trình phản biện bài báo\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tạp chí Y Dược học Cần Thơ thực hiện quy trình phản biện kín hai chiều nghiêm ngặt. Danh tính của những người phản biện không được tiết lộ cho các tác giả và ngược lại. Quy trình thẩm định bài báo đăng gồm các bước sau:\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tiếp nhận bản thảo\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Tác giả liên hệ gửi bản thảo đến Tạp chí qua hệ thống trực tuyến tại website: https:\u002F\u002Ftapchi.ctump.edu.vn. Hướng dẫn về cách đăng ký, gửi bài và chuẩn bị bản thảo được cung cấp trên website của Tạp chí.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Sàng lọc sơ bộ\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Sau khi Tòa soạn nhận được bài báo của tác giả, Ban Thư ký sẽ tiến hành kiểm tra sơ bộ bài báo (các yêu cầu về nội dung và hình thức). Những bài báo không đúng quy cách hoặc có nội dung không phù hợp hoặc vi phạm bản quyền sẽ bị từ chối (Ban Thư ký thông báo phản hồi đến tác giả trong vòng 1 tuần). Những bài báo đủ điều kiện, được Ban Thư ký tòa soạn chuyển đến Ban Biên tập có cùng chuyên môn với nội dung bài báo để đề xuất người phản biện. Thời gian kể từ khi Ban Biên tập nhận bài báo đến khi đề xuất người phản biện bài báo chậm nhất là 5 ngày.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Vòng phản biện\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">1. Ban Thư ký gửi bài và yêu cầu phản biện đến 02 phản biện độc lập.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">2. Các phản biện gởi nhận xét cho Ban Thư ký. Thời gian từ khi gửi bài cho phản biện đến khi nhận ý kiến của phản biện tối đa là 20 ngày.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Xử ký kết quả phản biện\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">1. Nếu ý kiến đồng ý cho đăng và không cần chỉnh sửa, Ban Thư ký tiếp tục đăng bài theo qui trình.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">2. Nếu ý kiến đồng ý đăng và cần chỉnh sửa, Ban Thư ký sẽ thông tin đến tác giả chỉnh sửa theo yêu cầu của người phản biện. Thời gian chỉnh sửa và gửi lại kéo dài không quá 2 tuần, từ khi tác giả bài báo nhận được thông tin (Quá trình này có thể lặp lại tối đa 2 lần\u002F1 bài báo). Khi có sự thống nhất, đồng ý của người phản biện; bài báo được tiếp tục đăng theo qui trình.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">3. Những bài báo có chất lượng không đạt yêu cầu, cả 2 phản biện không đồng ý cho đăng sẽ bị Tòa soạn từ chối đăng.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">Xuất bản\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">1. Ban Thư ký tổng hợp các bản thảo đã được tác giả hoàn thiện sau thẩm định trình Ban Biên tập xem xét, Tổng Biên tập phê duyệt, quyết định bài đăng theo các tiêu chí: sự phù hợp nội dung với tôn chỉ và mục đích, thể loại bài viết (ưu tiên các bài có bài có nghiên cứu chuyên sâu, hàm lượng khoa học cao), đóng góp mới bài báo, bài báo được ưu tiên đăng trong số gần nhất của Tạp chí theo thứ tự: tính thời sự, chất lượng bài báo và thời gian gửi bài.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">2. Ban Biên tập và Ban Thư ký biên tập bản thảo, chế bản, đọc rà soát lỗi. Thời gian hoàn thành từ 10-15 ngày.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">3. Ban Thư ký có trách nhiệm thông báo cho tác giả bài báo (bằng e-mail) về tình hình phê duyệt bài báo, thời gian, số kỳ, tập xuất bản bài báo theo qui định.\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(0, 0, 0);\">4. Danh sách bài báo theo số Tạp chí được in ấn và phát hành trong năm định kỳ được công bố chính thức trên website: https:\u002F\u002Ftapchi.ctump.edu.vn\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cbr>\u003C\u002Fp>",{"VOID":490},"wcQ1uqwAAAAJ","2023-05-30T08:17:21.868+00:00",[],[494],{"id":495,"createTime":28,"updateTime":28,"relativeEntities":496,"slug":28,"properties":497,"entityType":28,"verifyStatus":28,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":28,"url":507,"parentIds":508,"statistic":28},"6413896b-eca9-442b-a73f-182a58a0ce40",[],{"title":498,"address":501,"country":504,"abbreviation":505},{"EN":499,"VI":500},"Can Tho University of Medicine and Pharmacy","Trường Đại học Y Dược Cần Thơ",{"EN":502,"VI":503},"No 179, Nguyen Van Cu street, An Khanh ward, Ninh Kieu district, Can Tho city, Vietnam","Số 179, đường Nguyễn Văn Cừ, phường An Khánh, quận Ninh Kiều, thành phố Cần Thơ, Việt Nam",{"VOID":15},{"VOID":506},"ctump","http:\u002F\u002Fwww.ctump.edu.vn\u002F",[],[],"https:\u002F\u002Ftapchi.ctump.edu.vn\u002Findex.php\u002Fctump",{"impactFactor":32,"impactFactorByYear":512,"i10Index":32,"i10IndexLast5Year":32,"totalPublication":514,"totalPublicationByYear":515,"totalCitation":520,"totalCitationByYear":521,"totalCitationPerPublication":108,"totalCitationPerPublicationByYear":523,"hindexLast5Year":45,"hindex":45},{"2022":513,"2023":111,"2024":106},0.01,1556,{"2020":47,"2021":516,"2022":517,"2023":518,"2024":519,"2025":122},57,306,801,358,161,{"2021":146,"2022":280,"2023":522},99,{"2021":524,"2022":318,"2023":104},0.23,{"impactFactor":28,"impactFactorByYear":28,"i10Index":123,"i10IndexLast5Year":123,"totalPublication":526,"totalPublicationByYear":527,"totalCitation":526,"totalCitationByYear":528,"totalCitationPerPublication":40,"totalCitationPerPublicationByYear":531,"hindexLast5Year":49,"hindex":49},476,{"0":205,"2019":123,"2021":139,"2022":459,"2023":451,"2024":357,"2025":49,"2026":48},{"2021":42,"2022":123,"2023":161,"2024":529,"2025":360,"2026":530},136,83,{"2021":105,"2022":513,"2023":532,"2024":127,"2025":533,"2026":534},0.62,25.43,13.83,{"id":536,"createTime":537,"updateTime":382,"relativeEntities":538,"slug":539,"properties":540,"entityType":25,"verifyStatus":26,"verifyTime":28,"verifyNote":28,"languages":552,"translateLanguages":28,"viewCount":133,"subjectFields":553,"manageAffiliations":554,"indexDatabases":555,"url":556,"thumbnailPath":557,"statistic":558,"gsStatistic":594,"type":55,"analyzePriority":28},"6984a56a-db70-403b-9cc4-4013e1ceaffa","2023-05-09T06:47:40.346+00:00",[],"T%E1%BA%A1p%20ch%C3%AD%20Nghi%C3%AAn%20c%E1%BB%A9u%20n%C6%B0%E1%BB%9Bc%20ngo%C3%A0i",{"country":541,"issn":542,"title":544,"introduce":547,"gsId":550},{"VOID":15},{"VOID":543},"25252445",{"EN":545,"VI":546},"VNU Journal of Foreign Studies","Tạp chí Nghiên cứu nước ngoài",{"EN":548,"VI":549},"{\"ops\":[{\"insert\":\"\\n\\nThe \\n\"},{\"attributes\":{\"italic\":true},\"insert\":\"VNU Journal of Science\"},{\"insert\":\"\\n was established in 1985 for the publication of national and international research papers in all fields of natural sciences and technology, social sciences and humanities. 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Introduction to Informetrics Elsevier North-Holland Am-sterdam The Netherlands.  EGGHE L. AND ROUSSEAU R. 1990. Introduction to Informetrics Elsevier North-Holland Am-sterdam The Netherlands.",{},{"id":28,"text":1162,"url":28,"identifiers":1163},"FIELDER M., 1973, Algebraic connectivity of graphs, Czech. Math. J., 23, 298, 10.21136\u002FCMJ.1973.101168",{"doi":1164},"10.21136\u002FCMJ.1973.101168",{"id":28,"text":1166,"url":28,"identifiers":1167},"FRIEZE A., 1998, Proceedings of the 39th IEEE Symposium on Foundations of Computer Science (Palo Alto, Calif., Nov. 8-11)",{},{"id":28,"text":1169,"url":28,"identifiers":1170},"10.1145\u002F48511.48518",{"doi":1169},{"id":28,"text":1172,"url":28,"identifiers":1173},"GARFIELD E., 1972, Citation analysis as a tool in journal evaluation, Science, 178, 471, 10.1126\u002Fscience.178.4060.471",{"doi":1174},"10.1126\u002Fscience.178.4060.471",{"id":28,"text":1176,"url":28,"identifiers":1177},"GELLER N., 1978, On the citation influence methodology of Pinski and, Narin. Inf. Proc. 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H., 1965, An input-output approach to clique identification, Sociometry, 28, 377, 10.2307\u002F2785990",{"doi":1195},"10.2307\u002F2785990",{"id":28,"text":1197,"url":28,"identifiers":1198},"HUBERMAN B. PIROLLI P. PITKOW J. AND LUKOSE R. 1998. Strong regularities in world wide web surfing. Science 280.  HUBERMAN B. PIROLLI P. PITKOW J. AND LUKOSE R. 1998. Strong regularities in world wide web surfing. Science 280.",{"doi":1199},"10.1126\u002Fscience.280.5360.95",{"id":28,"text":1201,"url":28,"identifiers":1202},"JOLLIFFE I. T. 1986. Principal Component Analysis. Springer-Verlag New York.  JOLLIFFE I. T. 1986. Principal Component Analysis. Springer-Verlag New York.",{"doi":1203},"10.1007\u002F978-1-4757-1904-8",{"id":28,"text":1205,"url":28,"identifiers":1206},"KATZ L., 1953, A new status index derived from sociometric analysis, Psychometrika, 18, 39, 10.1007\u002FBF02289026",{"doi":1207},"10.1007\u002FBF02289026",{"id":28,"text":1209,"url":28,"identifiers":1210},"KESSLER M. M., 1963, Bibliographic coupling between scientific papers, Amer. Document., 14, 10, 10.1002\u002Fasi.5090140103",{"doi":1211},"10.1002\u002Fasi.5090140103",{"id":28,"text":1213,"url":28,"identifiers":1214},"LARSON R., 1996, Proceedings of the Annual Meeting of the American Society of Information Science",{},{"id":28,"text":1216,"url":28,"identifiers":1217},"LEVINE J. 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Proc ACM-SIGOPS Third Symposmm on Operating System Principles, Stanford U., Stanford, Calif. , Oct. 1971 , pp. 109 - 113 . 10.1145\u002F800212.806508 BASKETT, F The dependence of computer system queues upon processing time distribution and central processor scheduling. Proc ACM-SIGOPS Third Symposmm on Operating System Principles, Stanford U., Stanford, Calif., Oct. 1971, pp. 109-113. 10.1145\u002F800212.806508",{},{"id":28,"text":2259,"url":28,"identifiers":2260},"BASKETT , F. , ~t ND PALACZOS , F G . Processor shanng in a central server queueing model of mtfltaprogrammmg with apphcations . Proc. Sixth Annual Princeton Conference on Information Sciences and Systems, Princeton U , Princeton, N j. March 1972 , pp. 598 - 603 . BASKETT, F., ~tND PALACZOS, F G. Processor shanng in a central server queueing model of mtfltaprogrammmg with apphcations. Proc. Sixth Annual Princeton Conference on Information Sciences and Systems, Princeton U, Princeton, N j. March 1972, pp. 598-603.",{},{"id":28,"text":2262,"url":28,"identifiers":2263},"BUZEN , J. Queueing network models of multiprogramming. Ph.D. Th., Div. of Eng. and Appl. Sci ., Harvard. U. , Cambridge, Mass , 1971 . BUZEN, J. Queueing network models of multiprogramming. Ph.D. Th., Div. of Eng. and Appl. Sci., Harvard. U., Cambridge, Mass, 1971.",{},{"id":28,"text":2265,"url":28,"identifiers":2266},"B~ rzw N, J . Analysis of system bottlenecks using a queuemgnetwork model . Proc. ACM-SIGOPS Workshop on System Performance Evaluation , April 1971 , pp. 82 - 103 . 10.1145\u002F800024.808355 B~rzwN, J. Analysis of system bottlenecks using a queuemgnetwork model. Proc. ACM-SIGOPS Workshop on System Performance Evaluation, April 1971, pp. 82-103. 10.1145\u002F800024.808355",{},{"id":28,"text":2268,"url":28,"identifiers":2269},"CHANDY , K. M The analysis and solutions for general queueing networks Proc . Sixth Annual Princeton Conference on Information Sciences and Systems, Princeton U ,, Princeton, N. J. , March 1972 , pp. 224 - 228 . CHANDY, K. M The analysis and solutions for general queueing networks Proc. Sixth Annual Princeton Conference on Information Sciences and Systems, Princeton U,, Princeton, N. J., March 1972, pp. 224-228.",{},{"id":28,"text":2271,"url":28,"identifiers":2272},"CHAND~C , K M ., KELLER , T. W. , AND BROWNE , J. C. Design automation and queueing networks: An interactive system for the evaluation of computer queueing models Proc . Ninth Annual Design Automation Workshop, Dallas, Tex. , June 1972 , pp 151 - 153 . 10.1145\u002F800153.804968 CHAND~C, K M., KELLER, T. W., AND BROWNE, J. C. Design automation and queueing networks: An interactive system for the evaluation of computer queueing models Proc. Ninth Annual Design Automation Workshop, Dallas, Tex., June 1972, pp 151-153. 10.1145\u002F800153.804968",{},{"id":28,"text":2274,"url":28,"identifiers":2275},"Cox, D.R . A use of complex probabilities m the theory of stochastic processes. Proc. Cambr~.dge Phd . Soc. 51 ( 1955 ), 313 - 319 Cox, D.R. A use of complex probabilities m the theory of stochastic processes. Proc. Cambr~.dge Phd. Soc. 51 (1955), 313-319",{},{"id":28,"text":2277,"url":28,"identifiers":2278},"F~ : LLER , W. An Introduction to Probab~hty Theory and Its Apphcat~ons , Vol. 1 , 3 rd ed Wiley , New York , 1968 . F~:LLER, W. An Introduction to Probab~hty Theory and Its Apphcat~ons, Vol. 1, 3rd ed Wiley, New York, 1968.",{},{"id":28,"text":2280,"url":28,"identifiers":2281},"F~ :RDI NAND , A. E. An analysis of the machine interference model IBM Syst. J. 10, 2 ( 1971 ), 129-142. F~:RDINAND, A.E. An analysis of the machine interference model IBM Syst. J. 10, 2 (1971), 129-142.",{},{"id":28,"text":2283,"url":28,"identifiers":2284},"GORDON , W J , AND NEWELL , G F . Closed queuemg systems with exponential servers Oper Res 15 ( 1967 ), 254-265 GORDON, W J, AND NEWELL, G F. Closed queuemg systems with exponential servers Oper Res 15 (1967), 254-265",{},{"id":28,"text":2286,"url":28,"identifiers":2287},"JACKSON , J R Jobshop-like queueing systems Manage . Sc~ 10 , 1 ( Oct 1963 ), 131-142 JACKSON, J R Jobshop-like queueing systems Manage. Sc~ 10, 1 (Oct 1963), 131-142",{},{"id":28,"text":2289,"url":28,"identifiers":2290},"L, ~VENBERO , S. S Queueing analysls of a multlprogrammed computer system having a multilevel storage hierarchy . SIAM J Comput 2 , 4 ( 1973 ), 232-252. L,~VENBERO, S. S Queueing analysls of a multlprogrammed computer system having a multilevel storage hierarchy. SIAM J Comput 2, 4 (1973), 232-252.",{},{"id":28,"text":2292,"url":28,"identifiers":2293},"P~LACIOS , F G An analytic model of a multiprogrammingsystem including a job mix Rep TR4 , De\u002F). of Computer Sciences, U. of Texas at Austin , Austin, Tex ., June 1972 . P~LACIOS, F G An analytic model of a multiprogrammingsystem including a job mix Rep TR4, De\u002F). of Computer Sciences, U. of Texas at Austin, Austin, Tex., June 1972.",{},{"id":28,"text":2295,"url":28,"identifiers":2296},"POSNER , M. , AND BERNHOLTZ , B Closed fimte queuemg networks with time lags and with several classes of units Oper Res. 16 ( 1968 ), 977-985. POSNER, M., AND BERNHOLTZ, B Closed fimte queuemg networks with time lags and with several classes of units Oper Res. 16 (1968), 977-985.",{},{"id":28,"text":2298,"url":28,"identifiers":2299},"S. ~KATA , M. , NOGUCHI , S. , AND OIZUMI , J Analysm of a processor-shared queueing model for time-sharing systems Proc Second Hawaii Internatmnal Conference on System Scmnces, U. of Hawaii, Hono}ulu , Hawaii , Jan 1969 , pp 625 - 628 . S.~KATA, M., NOGUCHI, S., AND OIZUMI, J Analysm of a processor-shared queueing model for time-sharing systems Proc Second Hawaii Internatmnal Conference on System Scmnces, U. of Hawaii, Hono}ulu, Hawaii, Jan 1969, pp 625-628.",{},{"id":28,"text":2301,"url":28,"identifiers":2302},"WHITTLE , P Nonhnear migration processes. Internat. Stalzst Inst Bull ~2 , Bk. 1 ( 1969 ), 642 - 647 . WHITTLE, P Nonhnear migration processes. Internat. Stalzst Inst Bull ~2, Bk. 1 (1969), 642- 647.",{},{"id":28,"text":2304,"url":28,"identifiers":2305},"rHITTLE P. Equilibrium dlstnbutmns for an open mlgratmn process. J A ppl. Probabd. 5  rHITTLE P. Equilibrium dlstnbutmns for an open mlgratmn process. J A ppl. 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Algorithm for solution of a problem of maximum flow in a network with power estimation. Soy. Math. Dokl. 11 ( 1970 ), 1277 - 1280 . DINIC, E.A. Algorithm for solution of a problem of maximum flow in a network with power estimation. Soy. Math. Dokl. 11 (1970), 1277-1280.",{},{"id":28,"text":2433,"url":28,"identifiers":2434},"EDMONDS , J. Paths, trees and flowers. Canadian J. Math. 17 ( 1965 ), 449 467 . EDMONDS, J. Paths, trees and flowers. Canadian J. Math. 17 (1965), 449 467.",{"doi":2435},"10.4153\u002FCJM-1965-045-4",{"id":28,"text":2437,"url":28,"identifiers":2438},"EDMONDS , J. , AND KARP , R.M. Theoretical improvements in algorithmic efficiency for network flow problems . Combinatorial Structures and Their Applications. Gordon and Breach , New York , 1970 , pp. 93 - 96 (abstract presented at Calgary International Conference on Combinatorial Structures and Their Applications, June 1969). EDMONDS, J., AND KARP, R.M. Theoretical improvements in algorithmic efficiency for network flow problems. Combinatorial Structures and Their Applications. Gordon and Breach, New York, 1970, pp. 93-96 (abstract presented at Calgary International Conference on Combinatorial Structures and Their Applications, June 1969).",{},{"id":28,"text":2440,"url":28,"identifiers":2441},"EDMONDS , J. , AND FULKERSON , D. R. Bottleneck extrema . RAND Corp. Memorandum RM- 5375-PR ( Jan. 1968 ). EDMONDS, J., AND FULKERSON, D. R. Bottleneck extrema. RAND Corp. Memorandum RM-5375-PR (Jan. 1968).",{},{"id":28,"text":2443,"url":28,"identifiers":2444},"FORD , L. I{., AND FULKERSON , I). R. Flows in Networks . Princeton U. Press , Princeton, N.J. , 1962 . FORD, L. I{., AND FULKERSON, I). R. Flows in Networks. Princeton U. Press, Princeton, N.J., 1962.",{},{"id":28,"text":2446,"url":28,"identifiers":2447},"FULKERSON , D. ll. On the equivalence of the capacity-constrained transshipment problem and the Hitchcock problems . RAND Corp. Memorandum RM- 2480 ( Jan. 1960 ). FULKERSON, D. ll. On the equivalence of the capacity-constrained transshipment problem and the Hitchcock problems. RAND Corp. Memorandum RM-2480 (Jan. 1960).",{},{"id":28,"text":2449,"url":28,"identifiers":2450},"WAGNER , H.M. On a class of capacitated transportation problems. Manag. Sci. 5 ( 1959 ), 304 318 . WAGNER, H.M. On a class of capacitated transportation problems. Manag. Sci. 5 (1959), 304 318.",{"doi":2451},"10.1287\u002Fmnsc.5.3.304",{"id":2453,"createTime":2454,"updateTime":2454,"relativeEntities":2455,"slug":2456,"properties":2457,"entityType":985,"verifyStatus":26,"verifyTime":2454,"verifyNote":986,"languages":2468,"translateLanguages":28,"viewCount":32,"primaryUrl":2469,"fullTextUrl":28,"authors":2470,"publicationType":1009,"publisherRelationship":2578,"citationCount":2639,"citationInfo":2640,"publishDate":2646,"publishYear":2641,"citationAnalyzeStatus":884,"lastCitationAnalyze":28,"indexDatabases":2647,"openAccess":28,"references":2648,"isForceReanalyzing":1288},"22791f6a-b610-40c2-9fa7-7fdc693eea77","2024-10-15T08:05:17.709+00:00",[],"An-optimal-algorithm-for-approximate-nearest-neighbor-searching-fixed-dimensions",{"openalex":2458,"mag":2460,"abstract":2462,"title":2464,"doi":2466},{"VOID":2459},"W2427881153",{"VOID":2461},"2427881153",{"EN":2463},"\u003Cjats:p>\n            Consider a set of\n            \u003Cjats:italic>S\u003C\u002Fjats:italic>\n            of\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            data points in real\n            \u003Cjats:italic>d\u003C\u002Fjats:italic>\n            -dimensional space, R\n            \u003Cjats:sup>d\u003C\u002Fjats:sup>\n            , where distances are measured using any Minkowski metric. In nearest neighbor searching, we preprocess\n            \u003Cjats:italic>S\u003C\u002Fjats:italic>\n            into a data structure, so that given any query point\n            \u003Cjats:italic>q\u003C\u002Fjats:italic>\n            ∈ R\n            \u003Cjats:sup>d\u003C\u002Fjats:sup>\n            , is the closest point of S to\n            \u003Cjats:italic>q\u003C\u002Fjats:italic>\n            can be reported quickly. Given any positive real ϵ, data point\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            is a (1 +ϵ)-\n            \u003Cjats:italic>approximate nearest neighbor\u003C\u002Fjats:italic>\n            of\n            \u003Cjats:italic>q\u003C\u002Fjats:italic>\n            if its distance from\n            \u003Cjats:italic>q\u003C\u002Fjats:italic>\n            is within a factor of (1 + ϵ) of the distance to the true nearest neighbor. We show that it is possible to preprocess a set of\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            points in  R\n            \u003Cjats:sup>d\u003C\u002Fjats:sup>\n            in\n            \u003Cjats:italic>O(dn\u003C\u002Fjats:italic>\n            log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            ) time and\n            \u003Cjats:italic>O(dn)\u003C\u002Fjats:italic>\n            space, so that given a query point\n            \u003Cjats:italic>q\u003C\u002Fjats:italic>\n            ∈ R\n            \u003Cjats:sup>d\u003C\u002Fjats:sup>\n            , and ϵ > 0, a (1 + ϵ)-approximate nearest neighbor of\n            \u003Cjats:italic>q\u003C\u002Fjats:italic>\n            can be computed in\n            \u003Cjats:italic>O\u003C\u002Fjats:italic>\n            (\n            \u003Cjats:italic>c\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>d\u003C\u002Fjats:italic>\n              , ϵ\n            \u003C\u002Fjats:sub>\n            log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            ) time, where\n            \u003Cjats:italic>\n              c\n              \u003Cjats:sub>d,ϵ\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            ≤\n            \u003Cjats:italic>d\u003C\u002Fjats:italic>\n            ⌈1 + 6d\u002Fϵ⌉\n            \u003Cjats:sup>d\u003C\u002Fjats:sup>\n            is a factor depending only on dimension and ϵ. In general, we show that given an integer\n            \u003Cjats:italic>k\u003C\u002Fjats:italic>\n            ≥ 1, (1 + ϵ)-approximations to the\n            \u003Cjats:italic>k\u003C\u002Fjats:italic>\n            nearest neighbors of\n            \u003Cjats:italic>q\u003C\u002Fjats:italic>\n            can be computed in additional\n            \u003Cjats:italic>O(kd\u003C\u002Fjats:italic>\n            log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            ) time.\n          \u003C\u002Fjats:p>",{"EN":2465},"An optimal algorithm for approximate nearest neighbor searching fixed dimensions",{"VOID":2467},"10.1145\u002F293347.293348",[31],"https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F293347.293348",[2471,2490,2509,2536,2559],{"id":2472,"sortIndex":32,"researcher":28,"roles":2473,"affiliations":2474,"properties":2483,"displayName":2487,"givenName":28,"familyName":28},"d7dbaa25-49c7-497a-a779-e48a117713b3",[],[2475],{"id":2476,"sortIndex":32,"affiliation":2477,"properties":28},"ea980adc-d7e3-4eec-8966-e9902340d8a8",{"id":2476,"createTime":28,"updateTime":28,"relativeEntities":2478,"slug":28,"properties":2479,"entityType":28,"verifyStatus":28,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":28,"url":28,"parentIds":2482,"statistic":28},[],{"title":2480},{"EN":2481},"Hong Kong Univ. of Science of Technology, Kowloon, Hong Kong",[],{"orcid":2484,"title":2486,"openalex":2488},{"VOID":2485},"https:\u002F\u002Forcid.org\u002F0000-0003-0939-4192",{"EN":2487},"Sunil Arya",{"VOID":2489},"A5022760571",{"id":2491,"sortIndex":40,"researcher":28,"roles":2492,"affiliations":2493,"properties":2502,"displayName":2506,"givenName":28,"familyName":28},"e1d19c01-d5b6-424a-b897-0c546972d320",[],[2494],{"id":2495,"sortIndex":32,"affiliation":2496,"properties":28},"d33c6885-4b28-41ab-9061-12168aaa4c8a",{"id":2495,"createTime":28,"updateTime":28,"relativeEntities":2497,"slug":28,"properties":2498,"entityType":28,"verifyStatus":28,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":28,"url":28,"parentIds":2501,"statistic":28},[],{"title":2499},{"VI":2500},"Univ. of Maryland, College Park",[],{"orcid":2503,"title":2505,"openalex":2507},{"VOID":2504},"https:\u002F\u002Forcid.org\u002F0000-0002-3290-8932",{"EN":2506},"David M. 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Approximate nearest neighbor queries in fixed dimensions . In Proceedings of the 4th A CM-SIAM Symposium on Discrete Algorithms. ACM , New York , pp. 271 - 280 . ARYA, S., AND MOUNT, D.M. 1993b. Approximate nearest neighbor queries in fixed dimensions. In Proceedings of the 4th A CM-SIAM Symposium on Discrete Algorithms. ACM, New York, pp. 271-280.",{},{"id":28,"text":2659,"url":28,"identifiers":2660},"10.1145\u002F220279.220298",{"doi":2659},{"id":28,"text":2662,"url":28,"identifiers":2663},"10.1145\u002F220279.220315",{"doi":2662},{"id":28,"text":2665,"url":28,"identifiers":2666},"ARYA , S. , MOUNT , D. M. , NETANYAHU , N. , SILVERMAN , R. , AND WU , A. Y. 1994 . An optimal algorithm for approximate nearest neighbor searching in fixed dimensions . In Proceedings of the 5th ACM-SIAM Symposium on Discrete Algorithms. ACM , New York , pp. 573 - 582 . ARYA, S., MOUNT, D. M., NETANYAHU, N., SILVERMAN, R., AND WU, A. Y. 1994. An optimal algorithm for approximate nearest neighbor searching in fixed dimensions. In Proceedings of the 5th ACM-SIAM Symposium on Discrete Algorithms. ACM, New York, pp. 573-582.",{},{"id":28,"text":2668,"url":28,"identifiers":2669},"10.1109\u002FTCOM.1985.1096214",{"doi":2668},{"id":28,"text":2671,"url":28,"identifiers":2672},"10.1145\u002F355921.355927",{"doi":2671},{"id":28,"text":2674,"url":28,"identifiers":2675},"10.1145\u002F263661.263671",{"doi":2674},{"id":28,"text":2677,"url":28,"identifiers":2678},"BERCHTOLD , S. , KEIM , D. A. , AND KRIEGEL , H.-P. 1996 . The X-tree: An index structure for high dimensional data . In Proceedings of the 22nd VLDB Conference. pp. 28 - 39 . BERCHTOLD, S., KEIM, D. A., AND KRIEGEL, H.-P. 1996. The X-tree: An index structure for high dimensional data. In Proceedings of the 22nd VLDB Conference. pp. 28-39.",{},{"id":28,"text":2680,"url":28,"identifiers":2681},"10.1016\u002F0020-0190(93)90222-U",{"doi":2680},{"id":28,"text":2683,"url":28,"identifiers":2684},"BERN , M. , EPPSTEIN , D. , AND TENS , S.-H. 1993. Parallel construction of quadtrees and quality triangulations . In Proceedings of the 3rd Workshop Algorithms Data Structures . Lecture Notes in Computer Science , vol. 709 . Springer-Verlag , New York , pp. 188 - 199 . BERN, M., EPPSTEIN, D., AND TENS, S.-H. 1993. Parallel construction of quadtrees and quality triangulations. In Proceedings of the 3rd Workshop Algorithms Data Structures. Lecture Notes in Computer Science, vol. 709. Springer-Verlag, New York, pp. 188-199.",{},{"id":28,"text":2686,"url":28,"identifiers":2687},"10.1145\u002F220279.220296",{"doi":2686},{"id":28,"text":2689,"url":28,"identifiers":2690},"10.1145\u002F129712.129766",{"doi":2689},{"id":28,"text":2692,"url":28,"identifiers":2693},"CALLAHAN , P. 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AAAI Press\u002FMIT Press, Cambridge, Mass.",{},{"id":28,"text":2742,"url":28,"identifiers":2743},"10.1145\u002F62212.62255",{"doi":2742},{"id":28,"text":2745,"url":28,"identifiers":2746},"10.1109\u002F2.410146",{"doi":2745},{"id":28,"text":2748,"url":28,"identifiers":2749},"10.1137\u002F0214055",{"doi":2748},{"id":28,"text":2751,"url":28,"identifiers":2752},"FREDERICKSON , G.N. 1993 . A data structure for dynamically maintaining rooted trees . In Proceedings of the 4th Annual A CM-SIAM Symposium on Discrete Algorithms. ACM , New York , pp. 175 - 194 . FREDERICKSON, G.N. 1993. A data structure for dynamically maintaining rooted trees. In Proceedings of the 4th Annual A CM-SIAM Symposium on Discrete Algorithms. ACM, New York, pp. 175-194.",{},{"id":28,"text":2754,"url":28,"identifiers":2755},"10.1145\u002F28869.28874",{"doi":2754},{"id":28,"text":2757,"url":28,"identifiers":2758},"10.1145\u002F355744.355745",{"doi":2757},{"id":28,"text":2760,"url":28,"identifiers":2761},"10.1109\u002FT-C.1975.224110",{"doi":2760},{"id":28,"text":2763,"url":28,"identifiers":2764},"GALPERIN , I. , AND RIVEST , R. L. 1993 . Scapegoat trees . In Proceedings of the 4th ACM-SIAM Symposium on Discrete Algorithms. ACM , New York , pp. 165 - 174 . GALPERIN, I., AND RIVEST, R. L. 1993. Scapegoat trees. In Proceedings of the 4th ACM-SIAM Symposium on Discrete Algorithms. ACM, New York, pp. 165-174.",{},{"id":28,"text":2766,"url":28,"identifiers":2767},"GERSHO , A. , AND GRAY , R. M. 1991. Vector Quantization and Signal Compression . Kluwer Academic , Boston, Mass . GERSHO, A., AND GRAY, R. M. 1991. Vector Quantization and Signal Compression. Kluwer Academic, Boston, Mass.",{},{"id":28,"text":2769,"url":28,"identifiers":2770},"10.1016\u002F0167-8655(92)90098-K",{"doi":2769},{"id":28,"text":2772,"url":28,"identifiers":2773},"10.1145\u002F276698.276876",{"doi":2772},{"id":28,"text":2775,"url":28,"identifiers":2776},"10.1145\u002F258533.258653",{"doi":2775},{"id":28,"text":2778,"url":28,"identifiers":2779},"10.1145\u002F276698.276877",{"doi":2778},{"id":28,"text":2781,"url":28,"identifiers":2782},"10.1049\u002Fip-vis:19941140",{"doi":2781},{"id":28,"text":2784,"url":28,"identifiers":2785},"10.5555\u002F615204.615210",{"doi":2784},{"id":28,"text":2787,"url":28,"identifiers":2788},"10.1006\u002Finco.1993.1057",{"doi":2787},{"id":28,"text":2790,"url":28,"identifiers":2791},"MOUNT , D. M. , NETANYAHU , N. , SILVERMAN , R. , AND WU , A. Y. 1995 . Chromatic nearest neighbor searching: A query sensitive approach . In Proceedings of the 7th Canadian Conference on Computer Geometry. (Quebec City, Que., Canada, Aug. 10-13) . pp. 261 - 266 . MOUNT, D. M., NETANYAHU, N., SILVERMAN, R., AND WU, A. Y. 1995. Chromatic nearest neighbor searching: A query sensitive approach. In Proceedings of the 7th Canadian Conference on Computer Geometry. (Quebec City, Que., Canada, Aug. 10-13). pp. 261-266.",{},{"id":28,"text":2793,"url":28,"identifiers":2794},"10.1007\u002F978-1-4612-1098-6",{"doi":2793},{"id":28,"text":2796,"url":28,"identifiers":2797},"RIVEST , R.L. 1974. On the optimality of Elais's algorithm for performing best-match searches . In Information Processing . North-Holland Publishing Company , Amsterdam, The Netherlands, pp. 678 - 681 . RIVEST, R.L. 1974. On the optimality of Elais's algorithm for performing best-match searches. In Information Processing. North-Holland Publishing Company, Amsterdam, The Netherlands, pp. 678-681.",{},{"id":28,"text":2799,"url":28,"identifiers":2800},"10.1145\u002F223784.223794",{"doi":2799},{"id":28,"text":2802,"url":28,"identifiers":2803},"SAMET , n . 1990 . The Design and Analysis of Spatial Data Structures. Addison-Wesley , Reading, Mass. SAMET, n. 1990. The Design and Analysis of Spatial Data Structures. Addison-Wesley, Reading, Mass.",{},{"id":28,"text":2805,"url":28,"identifiers":2806},"10.1007\u002FBF01377181",{"doi":2805},{"id":28,"text":2808,"url":28,"identifiers":2809},"10.1016\u002F0022-0000(83)90006-5",{"doi":2808},{"id":28,"text":2811,"url":28,"identifiers":2812},"10.1007\u002FBF01759061",{"doi":2811},{"id":28,"text":2814,"url":28,"identifiers":2815},"10.1007\u002FBF02187718",{"doi":2814},{"id":28,"text":2817,"url":28,"identifiers":2818},"10.5555\u002F645481.655573",{"doi":2817},{"id":28,"text":2820,"url":28,"identifiers":2821},"10.1145\u002F22145.22163",{"doi":2820},{"id":2823,"createTime":2824,"updateTime":2824,"relativeEntities":2825,"slug":2826,"properties":2827,"entityType":985,"verifyStatus":26,"verifyTime":2824,"verifyNote":986,"languages":2838,"translateLanguages":28,"viewCount":32,"primaryUrl":2839,"fullTextUrl":28,"authors":2840,"publicationType":1009,"publisherRelationship":2860,"citationCount":2922,"citationInfo":2923,"publishDate":2928,"publishYear":2924,"citationAnalyzeStatus":884,"lastCitationAnalyze":28,"indexDatabases":2929,"openAccess":28,"references":2930,"isForceReanalyzing":1288},"2d99b31b-fb83-4234-b391-8de05475e0e8","2024-12-18T09:15:12.887+00:00",[],"An-Algorithm-for-Subgraph-Isomorphism",{"openalex":2828,"mag":2830,"abstract":2832,"title":2834,"doi":2836},{"VOID":2829},"W2126359798",{"VOID":2831},"2126359798",{"EN":2833},"\u003Cjats:p>Subgraph isomorphism can be determined by means of a brute-force tree-search enumeration procedure. In this paper a new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search. To assess the time actually taken by the new algorithm, subgraph isomorphism, clique detection, graph isomorphism, and directed graph isomorphism experiments have been carried out with random and with various nonrandom graphs.\u003C\u002Fjats:p>\n          \u003Cjats:p>A parallel asynchronous logic-in-memory implementation of a vital part of the algorithm is also described, although this hardware has not actually been built. The hardware implementation would allow very rapid determination of isomorphism.\u003C\u002Fjats:p>",{"EN":2835},"An Algorithm for Subgraph Isomorphism",{"VOID":2837},"10.1145\u002F321921.321925",[31],"https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F321921.321925",[2841],{"id":2842,"sortIndex":32,"researcher":28,"roles":2843,"affiliations":2844,"properties":2853,"displayName":2857,"givenName":28,"familyName":28},"ce944546-be09-4d84-9e3b-bc33f7eca2c5",[],[2845],{"id":2846,"sortIndex":32,"affiliation":2847,"properties":28},"e9adb755-bfa0-484f-b8dc-b92f43505b4c",{"id":2846,"createTime":28,"updateTime":28,"relativeEntities":2848,"slug":28,"properties":2849,"entityType":28,"verifyStatus":28,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":28,"url":28,"parentIds":2852,"statistic":28},[],{"title":2850},{"EN":2851},"Division of Computer Science, National Physical Laboratory, Teddington, Middlesex, TW11 OLW, England",[],{"orcid":2854,"title":2856,"openalex":2858},{"VOID":2855},"https:\u002F\u002Forcid.org\u002F0000-0002-9978-0726",{"EN":2857},"J. 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J. Problem-Solvzng Methods zn Artzficzal intellzgence . McGraw-Hill , New York , 1971 NILSSON, N. J. Problem-Solvzng Methods zn Artzficzal intellzgence. McGraw-Hill, New York, 1971",{},{"id":28,"text":2953,"url":28,"identifiers":2954},"OSTEEN , R. E. , AND TOU , J.T. Achque-detectlon algorithm based on neighbourhoods in graphs. lnt J of Comput and Inform Sczs g, 4 (Dec . 1973 ), 257-268. OSTEEN, R. E., AND TOU, J.T. Achque-detectlon algorithm based on neighbourhoods in graphs. lnt J of Comput and Inform Sczs g, 4 (Dec. 1973), 257-268.",{},{"id":28,"text":2956,"url":28,"identifiers":2957},"10.1145\u002F365628.365648",{"doi":2956},{"id":28,"text":2959,"url":28,"identifiers":2960},"10.1016\u002FS0146-664X(72)80003-0",{"doi":2959},{"id":28,"text":2962,"url":28,"identifiers":2963},"ULL~ANN ;- J. R Pattern Recogn~tzon Teehnzques. Butterworths, London, and Crane Russak , New York , 1973 . ULL~ANN;-J. R Pattern Recogn~tzon Teehnzques. Butterworths, London, and Crane Russak, New York, 1973.",{},{"id":2965,"createTime":2966,"updateTime":2966,"relativeEntities":2967,"slug":2968,"properties":2969,"entityType":985,"verifyStatus":26,"verifyTime":2966,"verifyNote":986,"languages":2980,"translateLanguages":28,"viewCount":32,"primaryUrl":2981,"fullTextUrl":28,"authors":2982,"publicationType":1009,"publisherRelationship":3000,"citationCount":3062,"citationInfo":3063,"publishDate":3068,"publishYear":3064,"citationAnalyzeStatus":884,"lastCitationAnalyze":28,"indexDatabases":3069,"openAccess":28,"references":3070,"isForceReanalyzing":1288},"28f74252-1524-4083-825b-62c210f29e5a","2024-09-28T18:30:24.991+00:00",[],"A-New-Method-of-Interpolation-and-Smooth-Curve-Fitting-Based-on-Local-Procedures",{"openalex":2970,"mag":2972,"abstract":2974,"title":2976,"doi":2978},{"VOID":2971},"W2006650073",{"VOID":2973},"2006650073",{"EN":2975},"\u003Cjats:p>A new mathematical method is developed for interpolation from a given set of data points in a plane and for fitting a smooth curve to the points. This method is devised in such a way that the resultant curve will pass through the given points and will appear smooth and natural. It is based on a piecewise function composed of a set of polynomials, each of degree three, at most, and applicable to successive intervals of the given points. In this method, the slope of the curve is determined at each given point locally, and each polynomial representing a portion of the curve between a pair of given points is determined by the coordinates of and the slopes at the points. Comparison indicates that the curve obtained by this new method is closer to a manually drawn curve than those drawn by other mathematical methods.\u003C\u002Fjats:p>",{"EN":2977},"A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures",{"VOID":2979},"10.1145\u002F321607.321609",[31],"https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F321607.321609",[2983],{"id":2984,"sortIndex":32,"researcher":28,"roles":2985,"affiliations":2986,"properties":2995,"displayName":2997,"givenName":28,"familyName":28},"c64ae1ba-54b0-44cb-97f8-9511581d6ce2",[],[2987],{"id":2988,"sortIndex":32,"affiliation":2989,"properties":28},"ee9e85ea-c3f9-4b38-886d-d73083d3e2a7",{"id":2988,"createTime":28,"updateTime":28,"relativeEntities":2990,"slug":28,"properties":2991,"entityType":28,"verifyStatus":28,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":28,"url":28,"parentIds":2994,"statistic":28},[],{"title":2992},{"EN":2993},"ESSA Research Laboratories, Institute for Telecommunication Sciences, Boulder, Colorado",[],{"title":2996,"openalex":2998},{"EN":2997},"Hiroshi Akima",{"VOID":2999},"A5017361188",{"url":28,"publisher":3001,"properties":3055},{"id":868,"createTime":869,"updateTime":870,"relativeEntities":3002,"slug":872,"properties":3003,"entityType":25,"verifyStatus":884,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":32,"subjectFields":3008,"manageAffiliations":3029,"indexDatabases":3040,"url":964,"thumbnailPath":28,"statistic":28,"gsStatistic":28,"type":28,"analyzePriority":28},[],{"country":3004,"eissn":3005,"issn":3006,"title":3007},{"VOID":875},{"VOID":877},{"VOID":879},{"EN":881},[3009,3013,3017,3021,3025],{"id":887,"createTime":28,"updateTime":28,"relativeEntities":3010,"label":3011,"description":3012,"parentId":28,"standard":28,"scholarHubFieldId":28},[],{"EN":890},{},{"id":893,"createTime":28,"updateTime":28,"relativeEntities":3014,"label":3015,"description":3016,"parentId":28,"standard":28,"scholarHubFieldId":28},[],{"EN":896},{},{"id":899,"createTime":28,"updateTime":28,"relativeEntities":3018,"label":3019,"description":3020,"parentId":28,"standard":28,"scholarHubFieldId":28},[],{"EN":902},{},{"id":905,"createTime":28,"updateTime":28,"relativeEntities":3022,"label":3023,"description":3024,"parentId":28,"standard":28,"scholarHubFieldId":28},[],{"EN":908},{},{"id":911,"createTime":28,"updateTime":28,"relativeEntities":3026,"label":3027,"description":3028,"parentId":28,"standard":28,"scholarHubFieldId":28},[],{"EN":914},{},[3030,3035],{"id":918,"createTime":28,"updateTime":28,"relativeEntities":3031,"slug":28,"properties":3032,"entityType":28,"verifyStatus":28,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":28,"url":28,"parentIds":3034,"statistic":28},[],{"title":3033},{"EN":922},[],{"id":925,"createTime":28,"updateTime":28,"relativeEntities":3036,"slug":28,"properties":3037,"entityType":28,"verifyStatus":28,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":28,"url":28,"parentIds":3039,"statistic":28},[],{"title":3038},{"EN":929},[],[3041,3048],{"id":933,"indexDatabase":3042,"url":945,"indexYears":28,"academicFieldIds":3047,"indexDatabaseRanking":28},{"id":935,"createTime":28,"updateTime":28,"relativeEntities":3043,"label":3044,"description":3045,"key":942,"publicationTags":3046,"standard":28},[],{"EN":938,"VI":938},{"EN":940,"VI":941},[944,813],[947],{"id":949,"indexDatabase":3049,"url":955,"indexYears":956,"academicFieldIds":3054,"indexDatabaseRanking":963},{"id":775,"createTime":28,"updateTime":28,"relativeEntities":3050,"label":3051,"description":3052,"key":781,"publicationTags":3053,"standard":28},[],{"EN":778,"VI":778},{"EN":778,"VI":780},[783],[958,959,960,961,962],{"issue":3056,"pages":3058,"volume":3060},{"VOID":3057},"4",{"VOID":3059},"589-602",{"VOID":3061},"17",1804,{"total":3062,"publishYear":3064,"statisticByYear":3065},1970,{"2012":328,"2013":328,"2014":325,"2015":157,"2016":151,"2017":567,"2018":206,"2019":829,"2020":3066,"2021":608,"2022":3067,"2023":2425,"2024":566},104,133,"1970-10-01",[944,963],[3071,3074,3077,3080,3083],{"id":28,"text":3072,"url":28,"identifiers":3073},"ACKLAND , T . G . On osculatory interpolation, where the given values of the function are at unequal intervals . J. Inst. Actuar. 9 ( 1915 ), 369 - 375 . ACKLAND, T .G . On osculatory interpolation, where the given values of the function are at unequal intervals. J. Inst. Actuar. 9 (1915), 369-375.",{},{"id":28,"text":3075,"url":28,"identifiers":3076},"GREVILLE , T. N . E . Spline functions, interpolation, and numerical quadrature . In Mathematical Methods for Digital Computers , Vol. 2 , A. Ralston and H. S. Wilf (Eds.), Wiley , New York, 1967 , Ch. 8. GREVILLE, T. N .E . Spline functions, interpolation, and numerical quadrature. In Mathematical Methods for Digital Computers, Vol. 2, A. Ralston and H. S. Wilf (Eds.), Wiley, New York, 1967, Ch. 8.",{},{"id":28,"text":3078,"url":28,"identifiers":3079},"HILDEBRAND , F . B . Introduction to Numerical Analysis . McGraw-Hill , New York , 1956 , Ch. 2, 3, 4, and 9. HILDEBRAND, F .B . Introduction to Numerical Analysis. McGraw-Hill, New York, 1956, Ch. 2, 3, 4, and 9.",{},{"id":28,"text":3081,"url":28,"identifiers":3082},"KARUP , J. On a new mechanical method of graduation . In Transactions of the Second International Actuarial Congress. C. and E. Layton , London , 1899 , pp. 78 - 109 . KARUP, J. On a new mechanical method of graduation. In Transactions of the Second International Actuarial Congress. C. and E. Layton, London, 1899, pp. 78-109.",{},{"id":28,"text":3084,"url":28,"identifiers":3085},"MILNE , W. E. Numerical Calculus . Princeton U. Press , Princeton, N. J. , 1949 , Ch. III. MILNE, W. E. Numerical Calculus. Princeton U. Press, Princeton, N. J., 1949, Ch. III.",{"doi":3086},"10.1515\u002F9781400875900",{"id":3088,"createTime":3089,"updateTime":3089,"relativeEntities":3090,"slug":3091,"properties":3092,"entityType":985,"verifyStatus":26,"verifyTime":3103,"verifyNote":986,"languages":3104,"translateLanguages":28,"viewCount":32,"primaryUrl":3105,"fullTextUrl":28,"authors":3106,"publicationType":1009,"publisherRelationship":3156,"citationCount":3217,"citationInfo":3218,"publishDate":3225,"publishYear":3219,"citationAnalyzeStatus":884,"lastCitationAnalyze":28,"indexDatabases":3226,"openAccess":28,"references":3227,"isForceReanalyzing":1288},"8c942cec-6235-48fe-9b3d-3edd5a6d8692","2024-09-18T18:11:38.464+00:00",[],"Integer-Programming-Formulation-of-Traveling-Salesman-Problems",{"openalex":3093,"mag":3095,"abstract":3097,"title":3099,"doi":3101},{"VOID":3094},"W2049287714",{"VOID":3096},"2049287714",{"EN":3098},"\u003Cjats:p>\n            It has been observed by many people that a striking number of quite diverse mathematical problems can be formulated as problems in integer programming, that is, linear programming problems in which some or all of the variables are required to assume integral values. This fact is rendered quite interesting by recent research on such problems, notably by R. E. Gomory [2, 3], which gives promise of yielding efficient computational techniques for their solution. The present paper provides yet another example of the versatility of integer programming as a mathematical modeling device by representing a generalization of the well-known “Travelling Salesman Problem” in integer programming terms. The authors have developed several such models, of which the one presented here is the most efficient in terms of generality, number of variables, and number of constraints. This model is due to the second author [4] and was presented briefly at the Symposium on Combinatorial Problems held at Princeton University, April 1960, sponsored by SIAM and IBM. The problem treated is: (1) A salesman is required to visit each of\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            cities, indexed by 1, … ,\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            . He leaves from a “base city” indexed by 0, visits each of the\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            other cities exactly once, and returns to city 0. During his travels he must return to 0 exactly\n            \u003Cjats:italic>t\u003C\u002Fjats:italic>\n            times, including his final return (here\n            \u003Cjats:italic>t\u003C\u002Fjats:italic>\n            may be allowed to vary), and he must visit no more than\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            cities in one tour. (By a tour we mean a succession of visits to cities without stopping at city 0.) It is required to find such an itinerary which minimizes the total distance traveled by the salesman.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            Note that if\n            \u003Cjats:italic>t\u003C\u002Fjats:italic>\n            is fixed, then for the problem to have a solution we must have\n            \u003Cjats:italic>tp\u003C\u002Fjats:italic>\n            ≧\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            . For\n            \u003Cjats:italic>t\u003C\u002Fjats:italic>\n            = 1,\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            ≧\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            , we have the standard traveling salesman problem.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            Let\n            \u003Cjats:italic>\n              d\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            (\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            ≠\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            = 0, 1, … ,\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            ) be the distance covered in traveling from city\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            to city\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            . The following integer programming problem will be shown to be equivalent to (1): (2) Minimize the linear form ∑\n            \u003Cjats:sub>\n              0≦\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n              ≠\n              \u003Cjats:italic>j\u003C\u002Fjats:italic>\n              ≦\n              \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sub>\n            ∑\n            \u003Cjats:italic>\n              d\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            over the set determined by the relations ∑\n            \u003Cjats:sup>\n              \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sup>\n            \u003Cjats:sub>\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n              =0\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n              ≠\n              \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sub>\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            = 1 (\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            = 1, … ,\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            ) ∑\n            \u003Cjats:sup>\n              \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sup>\n            \u003Cjats:sub>\n              \u003Cjats:italic>j\u003C\u002Fjats:italic>\n              =0\n              \u003Cjats:italic>j\u003C\u002Fjats:italic>\n              ≠\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sub>\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            = 1 (\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            = 1, … ,\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            )\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            -\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>j\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            +\n            \u003Cjats:italic>\n              px\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            ≦\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            - 1 (1 ≦\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            ≠\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            ≦\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            ) where the\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            are non-negative integers and the\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            (\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            = 1, …,\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            ) are arbitrary real numbers. (We shall see that it is permissible to restrict the\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            to be non-negative integers as well.)\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            If\n            \u003Cjats:italic>t\u003C\u002Fjats:italic>\n            is fixed it is necessary to add the additional relation: ∑\n            \u003Cjats:sup>\n              \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sup>\n            \u003Cjats:sub>\n              \u003Cjats:italic>u\u003C\u002Fjats:italic>\n              =1\n            \u003C\u002Fjats:sub>\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n              0\n            \u003C\u002Fjats:sub>\n            =\n            \u003Cjats:italic>t\u003C\u002Fjats:italic>\n            Note that the constraints require that\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            = 0 or 1, so that a natural correspondence between these two problems exists if the\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            are interpreted as follows: The salesman proceeds from city\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            to city\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            if and only if\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            = 1. Under this correspondence the form to be minimized in (2) is the total distance to be traveled by the salesman in (1), so the burden of proof is to show that the two feasible sets correspond; i.e., a feasible solution to (2) has\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            which do define a legitimate itinerary in (1), and, conversely a legitimate itinerary in (1) defines\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            , which, together with appropriate\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            , satisfy the constraints of (2).\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>Consider a feasible solution to (2).\u003C\u002Fjats:p>\n          \u003Cjats:p>\n            The number of returns to city 0 is given by ∑\n            \u003Cjats:sup>\n              \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sup>\n            \u003Cjats:sub>\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n              =1\n            \u003C\u002Fjats:sub>\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n              0\n            \u003C\u002Fjats:sub>\n            . The constraints of the form ∑\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            = 1, all\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            non-negative integers, represent the conditions that each city (other than zero) is visited exactly once. The\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            play a role similar to node potentials in a network and the inequalities involving them serve to eliminate tours that do not begin and end at city 0 and tours that visit more than\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            cities. Consider any\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>0\u003C\u002Fjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            = 1 (\n            \u003Cjats:italic>r\u003C\u002Fjats:italic>\n            \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            ≠ 0). There exists a unique\n            \u003Cjats:italic>r\u003C\u002Fjats:italic>\n            \u003Cjats:sub>2\u003C\u002Fjats:sub>\n            such that\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>1\u003C\u002Fjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>2\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            = 1. Unless\n            \u003Cjats:italic>r\u003C\u002Fjats:italic>\n            \u003Cjats:sub>2\u003C\u002Fjats:sub>\n            = 0, there is a unique\n            \u003Cjats:italic>r\u003C\u002Fjats:italic>\n            \u003Cjats:sub>3\u003C\u002Fjats:sub>\n            with\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>2\u003C\u002Fjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>3\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            = 1. We proceed in this fashion until some\n            \u003Cjats:italic>\n              r\n              \u003Cjats:sub>j\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            = 0. This must happen since the alternative is that at some point we reach an\n            \u003Cjats:italic>\n              r\n              \u003Cjats:sub>k\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            =\n            \u003Cjats:italic>\n              r\n              \u003Cjats:sub>j\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            ,\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            + 1 <\n            \u003Cjats:italic>k\u003C\u002Fjats:italic>\n            .\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            Since none of the\n            \u003Cjats:italic>r\u003C\u002Fjats:italic>\n            's are zero we have\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>\n                r\n                \u003Cjats:sub>i\u003C\u002Fjats:sub>\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            -\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>i\u003C\u002Fjats:italic>\n                + 1\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            +\n            \u003Cjats:italic>px\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>\n                r\n                \u003Cjats:sub>i\u003C\u002Fjats:sub>\n              \u003C\u002Fjats:italic>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>i\u003C\u002Fjats:italic>\n                + 1\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            ≦\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            - 1 or\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>\n                r\n                \u003Cjats:sub>i\u003C\u002Fjats:sub>\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            -\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>i\u003C\u002Fjats:italic>\n                + 1\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            ≦ - 1. Summing from\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            =\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            to\n            \u003Cjats:italic>k\u003C\u002Fjats:italic>\n            - 1, we have\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>\n                r\n                \u003Cjats:sub>j\u003C\u002Fjats:sub>\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            -\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>\n                r\n                \u003Cjats:sub>k\u003C\u002Fjats:sub>\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            = 0 ≦\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            + 1 -\n            \u003Cjats:italic>k\u003C\u002Fjats:italic>\n            , which is a contradiction. Thus all tours include city 0. It remains to observe that no tours is of length greater than\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            . Suppose such a tour exists,\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              0\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            ,\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>1\u003C\u002Fjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>2\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            , … ,\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>\n                r\n                \u003Cjats:sub>p\u003C\u002Fjats:sub>\n                r\n              \u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>p\u003C\u002Fjats:italic>\n                +1\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            = 1 with all\n            \u003Cjats:italic>\n              r\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            ≠ 0. Then, as before,\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              1\n            \u003C\u002Fjats:sub>\n            -\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>p\u003C\u002Fjats:italic>\n                +1\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            ≦ -\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            or\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>p\u003C\u002Fjats:italic>\n                +1\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            -\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            ≧\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            .\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            But we have\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>p\u003C\u002Fjats:italic>\n                +1\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            -\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            +\n            \u003Cjats:italic>px\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>p\u003C\u002Fjats:italic>\n                +1\n              \u003C\u002Fjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            ≦\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            - 1 or\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>p\u003C\u002Fjats:italic>\n                +1\n              \u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            -\n            \u003Cjats:italic>u\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            ≦\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            (1 -\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>\n                \u003Cjats:italic>p\u003C\u002Fjats:italic>\n                +1\n              \u003C\u002Fjats:sub>\n              \u003Cjats:italic>r\u003C\u002Fjats:italic>\n              \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:sub>\n            ) - 1 ≦\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            - 1, which is a contradiction.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            Conversely, if the\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            correspond to a legitimate itinerary, it is clear that the\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            can be adjusted so that\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            =\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            if city\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            is the\n            \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            th city visited in the tour which includes city\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            , for we then have\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            -\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>j\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            = - 1 if\n            \u003Cjats:italic>\n              x\n              \u003Cjats:sub>ij\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            = 1, and always\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            -\n            \u003Cjats:italic>\n              u\n              \u003Cjats:sub>j\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            ≦\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            - 1.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            The above integer program involves\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u003Cjats:sup>2\u003C\u002Fjats:sup>\n            +\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            constraints (if\n            \u003Cjats:italic>t\u003C\u002Fjats:italic>\n            is not fixed) in\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u003Cjats:sup>2\u003C\u002Fjats:sup>\n            + 2\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            variables. Since the inequality form of constraint is fundamental for integer programming calculations, one may eliminate 2\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            variables, say the\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n              0\n            \u003C\u002Fjats:sub>\n            and\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              0\n              \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sub>\n            , by means of the equation constraints and produce an equivalent problem with\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u003Cjats:sup>2\u003C\u002Fjats:sup>\n            +\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            inequalities and\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u003Cjats:sup>2\u003C\u002Fjats:sup>\n            variables.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>The currently known integer programming procedures are sufficiently regular in their behavior to cast doubt on the heuristic value of machine experiments with our model. However, it seems appropriate to report the results of the five machine experiments we have conducted so far. The solution procedure used was the all-integer algorithm of R. E. Gomory [3] without the ranking procedure he describes.\u003C\u002Fjats:p>\n          \u003Cjats:p>The first three experiments were simple model verification tests on a four-city standard traveling salesman problem with distance matrix [ 20 23 4 30 7 27 25 5 25 3 21 26 ]\u003C\u002Fjats:p>\n          \u003Cjats:p>The first experiment was with a model, now obsolete, using roughly twice as many constraints and variables as the current model (for this problem, 28 constraints in 21 variables). The machine was halted after 4000 pivot steps had failed to produce a solution.\u003C\u002Fjats:p>\n          \u003Cjats:p>\n            The second experiment used the earlier model with the\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n              0\n            \u003C\u002Fjats:sub>\n            and\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              0\n              \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sub>\n            eliminated, resulting in a 28-constraint, 15-variable problem. Here the machine produced the optimal solution in 41 pivot steps.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            The third experiment used the current formulation with the\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              \u003Cjats:italic>i\u003C\u002Fjats:italic>\n              0\n            \u003C\u002Fjats:sub>\n            and\n            \u003Cjats:italic>x\u003C\u002Fjats:italic>\n            \u003Cjats:sub>\n              0\n              \u003Cjats:italic>j\u003C\u002Fjats:italic>\n            \u003C\u002Fjats:sub>\n            eliminated, yielding 13 constraints and 9 variables. The optimal solution was reached in 7 pivot steps.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>The fourth and fifth experiments were used on a standard ten-city problem, due to Barachet, solved by Dantzig, Johnson and Fulkerson [1]. The current formulation was used, yielding 91 constraints in 81 variables. The fifth problem differed from the fourth only in that the ordering of the rows was altered to attempt to introduce more favorable pivot choices. In each case the machine was stopped after over 250 pivot steps had failed to produce the solution. In each case the last 100 pivot steps had failed to change the value of the objective function.\u003C\u002Fjats:p>\n          \u003Cjats:p>It seems hopeful that more efficient integer programming procedures now under development will yield a satisfactory algorithmic solution to the traveling salesman problem, when applied to this model. In any case, the model serves to illustrate how problems of this sort may be succinctly formulated in integer programming terms.\u003C\u002Fjats:p>",{"EN":3100},"Integer Programming Formulation of Traveling Salesman Problems",{"VOID":3102},"10.1145\u002F321043.321046","2024-09-18T18:11:38.463+00:00",[31],"https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F321043.321046",[3107,3124,3141],{"id":3108,"sortIndex":32,"researcher":28,"roles":3109,"affiliations":3110,"properties":3119,"displayName":3121,"givenName":28,"familyName":28},"bab4a680-b360-4571-a896-25ebdf756ef1",[],[3111],{"id":3112,"sortIndex":32,"affiliation":3113,"properties":28},"e1eb7a33-d1a2-4c91-a19f-bc814acf3d5e",{"id":3112,"createTime":28,"updateTime":28,"relativeEntities":3114,"slug":28,"properties":3115,"entityType":28,"verifyStatus":28,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":28,"url":28,"parentIds":3118,"statistic":28},[],{"title":3116},{"EN":3117},"Standard Oil Company of California, San Francisco, California",[],{"title":3120,"openalex":3122},{"EN":3121},"Casey Miller",{"VOID":3123},"A5007984296",{"id":3125,"sortIndex":40,"researcher":28,"roles":3126,"affiliations":3127,"properties":3136,"displayName":3138,"givenName":28,"familyName":28},"62a9ebd4-7ac5-4664-9384-efa20e3b7970",[],[3128],{"id":3129,"sortIndex":32,"affiliation":3130,"properties":28},"418398c8-f466-42d4-ae85-c9074a03285d",{"id":3129,"createTime":28,"updateTime":28,"relativeEntities":3131,"slug":28,"properties":3132,"entityType":28,"verifyStatus":28,"verifyTime":28,"verifyNote":28,"languages":28,"translateLanguages":28,"viewCount":28,"url":28,"parentIds":3135,"statistic":28},[],{"title":3133},{"VI":3134},"Princeton University, Princeton, New Jersey",[],{"title":3137,"openalex":3139},{"EN":3138},"A. 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E. An algorithm for integer solutions to linear programs. Princetonq IBM Math. Research Project Techn. Report No. 1 1958.  GOMORY R. E. An algorithm for integer solutions to linear programs. Princetonq IBM Math. Research Project Techn. Report No. 1 1958.",{},{"id":28,"text":3235,"url":28,"identifiers":3236},"TUCKER A. W, 1960, Research Project Techn. Report",{}]