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Ph.D. DIss ., Dep. of Electrical Engmeenng and Computer Science , Princeton Univ. , Princeton, N.J. , 1978 . HUNTER, G M Efficient computation and data structures for graphics. Ph.D. DIss., Dep. of Electrical Engmeenng and Computer Science, Princeton Univ., Princeton, N.J., 1978.",{},{"id":24,"text":441,"url":24,"identifiers":442},"HUNTER , G M , AND STEIGLITZ , K Operations on images using quadtrees . IEEE Trans. Pattern Anal Machme Intell PAMI-I , 2 ( April 1979 ), 145 - 153 . HUNTER, G M, AND STEIGLITZ, K Operations on images using quadtrees. IEEE Trans. Pattern Anal Machme Intell PAMI-I, 2 (April 1979), 145-153.",{"doi":443},"10.1109\u002FTPAMI.1979.4766900",{"id":24,"text":445,"url":24,"identifiers":446},"HUNTER , G M , AND STEIGLITZ , K Linear transformation of pictures represented by quadtrees . Comput Graph Image Proc 10 ( 1979 ), 289 - 296 HUNTER, G M, AND STEIGLITZ, K Linear transformation of pictures represented by quadtrees. 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The Design and Analysis of Computer Agorithms . Addison-Wesley , Reading, Mass ., 1974 , Ch 9, pp. 317 - 361 . AHO, A V., HoPcaoPr, J.E., AND ULLMAN, J.D. The Design and Analysis of Computer Agorithms. Addison-Wesley, Reading, Mass., 1974, Ch 9, pp. 317-361.",{},{"id":24,"text":598,"url":24,"identifiers":599},"KIMBALL , R B . A rapid substring searching algorithm in speech recognition Abstracted in Conf Record, IEEE Syrup on Speech Recognition, Pittsburgh , Pa. , April 1974 . KIMBALL, R B. A rapid substring searching algorithm in speech recognition Abstracted in Conf Record, IEEE Syrup on Speech Recognition, Pittsburgh, Pa., April 1974.",{},{"id":24,"text":601,"url":24,"identifiers":602},"KNUTH , D.E. The Art of Computer Programmzng, Vol. 3: Sorting and Searching. Addison-Wesley, Reading, Mass , 1973 , Ch. 6 . 3 , pp. 490 - 493 . KNUTH, D.E. The Art of Computer Programmzng, Vol. 3: Sorting and Searching. Addison-Wesley, Reading, Mass, 1973, Ch. 6.3, pp. 490-493.",{},{"id":24,"text":604,"url":24,"identifiers":605},"KSUTH , D.E Pattern matching in strings. Unpub. lecture notes , Trondheim , Norway , May 1973 . KSUTH, D.E Pattern matching in strings. Unpub. lecture notes, Trondheim, Norway, May 1973.",{},{"id":24,"text":607,"url":24,"identifiers":608},"KNUTH , D.E. , MORRIS , J.H. JR ., AND PRATT , V.R. Fast pattern matching in strings. Comput. Sei. Rep. STAN-CS-74-440, Stanford U., Stanford , Calif. , Aug. 1974 . KNUTH, D.E., MORRIS, J.H. JR., AND PRATT, V.R. Fast pattern matching in strings. Comput. Sei. Rep. STAN-CS-74-440, Stanford U., Stanford, Calif., Aug. 1974.",{},{"id":24,"text":610,"url":24,"identifiers":611},"PRATT , V R . Applications of the Weiner repetition finder. Unpub. paper , Cambridge , Mass ., May 1973 ; rev Oct. 1973 PRATT, V R. Applications of the Weiner repetition finder. 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Introduction to Interval Computations . Academic Press , Orlando, Fla .]] ALEFELD, G., AND HERZBERGER, J. 1983. Introduction to Interval Computations. Academic Press, Orlando, Fla.]]",{},{"id":24,"text":769,"url":24,"identifiers":770},"BENHAMOU , F. , AND OLDER , W. J. 1997 . Applying interval arithmetic to real, integer, and Boolean constraints . J. Logic Prog. 32 , 1 - 24 .]] BENHAMOU,F.,AND OLDER, W. J. 1997. Applying interval arithmetic to real, integer, and Boolean constraints. J. Logic Prog. 32, 1-24.]]",{"doi":771},"10.1016\u002FS0743-1066(96)00142-2",{"id":24,"text":773,"url":24,"identifiers":774},"FORSYTHE , G. E. 1970 . Pitfalls of computation, or why a math book isn't enough . Amer. Math. Monthly 77 , 931 - 956 .]] FORSYTHE, G. E. 1970. Pitfalls of computation, or why a math book isn't enough. Amer. Math. Monthly 77, 931-956.]]",{"doi":775},"10.1080\u002F00029890.1970.11992636",{"id":24,"text":777,"url":24,"identifiers":778},"HAMMER , R. , HOCKS , M. , KULISCH , U. , AND RATZ , D. 1993. Numerical Toolbox for Verified Computing I . Springer-Verlag , New York .]] HAMMER, R., HOCKS, M., KULISCH, U., AND RATZ, D. 1993. Numerical Toolbox for Verified Computing I. Springer-Verlag, New York.]]",{},{"id":24,"text":780,"url":24,"identifiers":781},"HANSEN , E. 1992. Global Optimization Using Interval Analysis . Marcel Dekker .]] HANSEN, E. 1992. Global Optimization Using Interval Analysis. Marcel Dekker.]]",{},{"id":24,"text":783,"url":24,"identifiers":784},"HICKEY , T. J. 2000 a. CLIP: A CLP(Intervals) Dialect for Metalevel Constraint Solving. In Proceedings of PADL'00 . Lecture Notes in Computer Science , vol. 1753 . Springer-Verlag , New York .]] HICKEY, T. J. 2000a. CLIP: A CLP(Intervals) Dialect for Metalevel Constraint Solving. In Proceedings of PADL'00. Lecture Notes in Computer Science, vol. 1753. Springer-Verlag, New York.]]",{},{"id":24,"text":786,"url":24,"identifiers":787},"HICKEY , T. J. 2000 b. Analytic constraint solving and interval arithmetic . In Proceedings of the 27th Annual ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages (Jan.). ACM , New York.]] 10.1145\u002F325694.325738 HICKEY, T. J. 2000b. Analytic constraint solving and interval arithmetic. In Proceedings of the 27th Annual ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages (Jan.). ACM, New York.]] 10.1145\u002F325694.325738",{},{"id":24,"text":789,"url":24,"identifiers":790},"HICKEY , T. J. , QIU , Z. , AND VAN EMDEN , M. H. 2000 . Interval constraint plotting for interactive visual exploration of implicitly defined relations. Special issue on Reliable Geometric Computations . Rel. Comput. 6 , 1 .]] HICKEY, T. J., QIU, Z., AND VAN EMDEN, M. H. 2000. Interval constraint plotting for interactive visual exploration of implicitly defined relations. Special issue on Reliable Geometric Computations. Rel. Comput. 6,1.]]",{"doi":791},"10.1023\u002FA:1009984921053",{"id":24,"text":793,"url":24,"identifiers":794},"KAHAN , W. M. 1968. A more complete interval arithmetic. Tech. rep. Univ . Toronto, Toronto , Ont., Canada .]] KAHAN, W. M. 1968. A more complete interval arithmetic. Tech. rep. Univ. Toronto, Toronto, Ont., Canada.]]",{},{"id":24,"text":796,"url":24,"identifiers":797},"LIPSCHUTZ S. 1965. General Topology. Schaum's Outline Series.]]  LIPSCHUTZ S. 1965. General Topology. Schaum's Outline Series.]]",{},{"id":24,"text":799,"url":24,"identifiers":800},"MOORE , R. E. 1966. Interval Analysis . Prentice-Hall , Englewood Cliffs , N.J.]] MOORE, R. E. 1966. Interval Analysis. Prentice-Hall, Englewood Cliffs, N.J.]]",{},{"id":24,"text":802,"url":24,"identifiers":803},"NOVOA M. 1993. Theory of preconditioners for the interval Gauss-Seidel method and exis-tence\u002F uniqueness theory with interval Newton methods. Dept. Mathematics , Univ. Southwestern Louisiana .]] NOVOA M. 1993. Theory of preconditioners for the interval Gauss-Seidel method and exis-tence\u002F uniqueness theory with interval Newton methods. Dept. Mathematics, Univ. Southwestern Louisiana.]]",{},{"id":24,"text":805,"url":24,"identifiers":806},"OLDER W. J. 1989. Interval arithmetic specification. Tech. rep. Bell-Northern Research Computing Research Laboratory.]]  OLDER W. J. 1989. Interval arithmetic specification. Tech. rep. Bell-Northern Research Computing Research Laboratory.]]",{},{"id":24,"text":808,"url":24,"identifiers":809},"RALL , L. B. 1969. Computational solution of nonlinear operator equations . Wiley , New York .]] RALL, L. B. 1969. Computational solution of nonlinear operator equations. Wiley, New York.]]",{},{"id":24,"text":811,"url":24,"identifiers":812},"RATZ , D. 1996. On extended interval arithmetic and inclusion isotonicity . Institut fur Angewandte Mathematik, Universit~t Karlsruhe .]] RATZ, D. 1996. On extended interval arithmetic and inclusion isotonicity. Institut fur Angewandte Mathematik, Universit~t Karlsruhe.]]",{},{"id":24,"text":814,"url":24,"identifiers":815},"STOLFI J. AND DE FIGUEIREDO L. 1997. Self-Validated Numerical Methods and Applications. IMPA Rio de Janiero Brazil.]]  STOLFI J. AND DE FIGUEIREDO L. 1997. Self-Validated Numerical Methods and Applications. IMPA Rio de Janiero Brazil.]]",{},{"id":24,"text":817,"url":24,"identifiers":818},"VAN HENTENRYCK , P. , MICHEL , L. , AND DEVILLE , Y. 1997 . Numerica: A Modeling Language for Global Optimization . MIT Press , Cambridge, Mass .]] VAN HENTENRYCK, P., MICHEL, L., AND DEVILLE, Y. 1997. Numerica: A Modeling Language for Global Optimization. MIT Press, Cambridge, Mass.]]",{"doi":819},"10.7551\u002Fmitpress\u002F5073.001.0001",{"id":24,"text":821,"url":24,"identifiers":822},"WALSTER G. W. 1996. The extended real interval system. Available on the internet http:\u002F\u002Fwww.mscs.mu.edu \u002F globsol \u002F readings.html.]]  WALSTER G. W. 1996. The extended real interval system. Available on the internet http:\u002F\u002Fwww.mscs.mu.edu \u002F globsol \u002F readings.html.]]",{},{"id":24,"text":824,"url":24,"identifiers":825},"WALSTER G.W. AND HANSEN E. R. 1998. Interval Algebra Composite Functions and Dependence in Compilers. Available on the internet http:\u002F\u002Fwww.mscs.mu.edu \u002Fglobsol \u002Freadings.html.]]  WALSTER G.W. AND HANSEN E. R. 1998. Interval Algebra Composite Functions and Dependence in Compilers. Available on the internet http:\u002F\u002Fwww.mscs.mu.edu \u002Fglobsol \u002Freadings.html.]]",{},{"id":827,"createTime":828,"updateTime":828,"relativeEntities":829,"slug":830,"properties":831,"entityType":132,"verifyStatus":133,"verifyTime":842,"verifyNote":134,"languages":843,"translateLanguages":24,"viewCount":25,"primaryUrl":844,"fullTextUrl":24,"authors":845,"publicationType":196,"publisherRelationship":865,"citationCount":926,"citationInfo":927,"publishDate":930,"publishYear":928,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":931,"openAccess":24,"references":932,"isForceReanalyzing":317},"3e0261ac-e452-4139-bd0c-371dbf90b2c3","2025-01-02T03:26:04.901+00:00",[],"Lower-bounds-for-orthogonal-range-searching-I-The-reporting-case",{"openalex":832,"mag":834,"abstract":836,"title":838,"doi":840},{"VOID":833},"W2093120238",{"VOID":835},"2093120238",{"EN":837},"\u003Cjats:p>\n            We establish lower bounds on the complexity of orthogonal range reporting in the static case. Given a collection of\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            points in\n            \u003Cjats:italic>d\u003C\u002Fjats:italic>\n            -space and a box [\n            \u003Cjats:italic>a\u003C\u002Fjats:italic>\n            \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            ,\n            \u003Cjats:italic>b\u003C\u002Fjats:italic>\n            \u003Cjats:sub>1\u003C\u002Fjats:sub>\n            ] X … X [\n            \u003Cjats:italic>\n              a\n              \u003Cjats:sub>d\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            ,\n            \u003Cjats:italic>\n              b\n              \u003Cjats:sub>d\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            ], report every point whose\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            th coordinate lies in [\n            \u003Cjats:italic>\n              a\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n              , b\n              \u003Cjats:sub>i\u003C\u002Fjats:sub>\n            \u003C\u002Fjats:italic>\n            ], for each\n            \u003Cjats:italic>i\u003C\u002Fjats:italic>\n            = l, … ,\n            \u003Cjats:italic>d\u003C\u002Fjats:italic>\n            . The collection of points is fixed once and for all and can be preprocessed. The box, on the other hand, constitutes a query that must be answered online. It is shown that on a pointer machine a query time of\n            \u003Cjats:italic>O\u003C\u002Fjats:italic>\n            (\n            \u003Cjats:italic>k\u003C\u002Fjats:italic>\n            + polylog(\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            )), where\n            \u003Cjats:italic>k\u003C\u002Fjats:italic>\n            is the number of points to be reported, can only be achieved at the expense of Ω(\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            (log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            \u002Flog log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            )\n            \u003Cjats:sup>\n              \u003Cjats:italic>d\u003C\u002Fjats:italic>\n              -1\n            \u003C\u002Fjats:sup>\n            ) storage. Interestingly, these bounds are optimal in the pointer machine model, but they can be improved (ever so slightly) on a random access machine. In a companion paper, we address the related problem of adding up weights assigned to the points in the query box.\n          \u003C\u002Fjats:p>",{"EN":839},"Lower bounds for orthogonal range searching: I. The reporting case",{"VOID":841},"10.1145\u002F77600.77614","2025-01-02T03:26:04.900+00:00",[136],"https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F77600.77614",[846],{"id":847,"sortIndex":25,"researcher":24,"roles":848,"affiliations":849,"properties":858,"displayName":862,"givenName":24,"familyName":24},"16600669-4913-46f8-b29c-02e1b357bfc3",[],[850],{"id":851,"sortIndex":25,"affiliation":852,"properties":24},"a8240dd0-f45b-4e75-9583-42c8be71e264",{"id":851,"createTime":24,"updateTime":24,"relativeEntities":853,"slug":24,"properties":854,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":857,"statistic":24},[],{"title":855},{"EN":856},"Princeton Univ., Princeton, NJ",[],{"orcid":859,"title":861,"openalex":863},{"VOID":860},"https:\u002F\u002Forcid.org\u002F0000-0001-8542-0247",{"EN":862},"Bernard Chazelle",{"VOID":864},"A5044565966",{"url":24,"publisher":866,"properties":920},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":867,"slug":10,"properties":868,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":873,"manageAffiliations":894,"indexDatabases":905,"url":111,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":869,"eissn":870,"issn":871,"title":872},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[874,878,882,886,890],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":875,"label":876,"description":877,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},{"id":34,"createTime":24,"updateTime":24,"relativeEntities":879,"label":880,"description":881,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":37},{},{"id":40,"createTime":24,"updateTime":24,"relativeEntities":883,"label":884,"description":885,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":43},{},{"id":46,"createTime":24,"updateTime":24,"relativeEntities":887,"label":888,"description":889,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":49},{},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":891,"label":892,"description":893,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":55},{},[895,900],{"id":59,"createTime":24,"updateTime":24,"relativeEntities":896,"slug":24,"properties":897,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":899,"statistic":24},[],{"title":898},{"EN":63},[],{"id":66,"createTime":24,"updateTime":24,"relativeEntities":901,"slug":24,"properties":902,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":904,"statistic":24},[],{"title":903},{"EN":70},[],[906,913],{"id":74,"indexDatabase":907,"url":87,"indexYears":24,"academicFieldIds":912,"indexDatabaseRanking":24},{"id":76,"createTime":24,"updateTime":24,"relativeEntities":908,"label":909,"description":910,"key":83,"publicationTags":911,"standard":24},[],{"EN":79,"VI":79},{"EN":81,"VI":82},[85,86],[89],{"id":91,"indexDatabase":914,"url":102,"indexYears":103,"academicFieldIds":919,"indexDatabaseRanking":110},{"id":93,"createTime":24,"updateTime":24,"relativeEntities":915,"label":916,"description":917,"key":99,"publicationTags":918,"standard":24},[],{"EN":96,"VI":96},{"EN":96,"VI":98},[101],[105,106,107,108,109],{"issue":921,"pages":922,"volume":924},{"VOID":572},{"VOID":923},"200-212",{"VOID":925},"37",157,{"total":926,"publishYear":928,"statisticByYear":929},1990,{"2012":755,"2013":263,"2014":180,"2015":265,"2016":265,"2017":267,"2018":268,"2019":755,"2020":266,"2021":265,"2022":264,"2023":268,"2024":160},"1990-04-01",[85,110],[933,937,940,943,946,950,954,957,960,964,968,972,975],{"id":24,"text":934,"url":24,"identifiers":935},"BENTLEY , J.L. Decomposable searching problems. Inf. Proc. Lett. 8 ( 1979 ), 244 - 251 . BENTLEY, J.L. Decomposable searching problems. Inf. Proc. Lett. 8 (1979), 244-251.",{"doi":936},"10.1016\u002F0020-0190(79)90117-0",{"id":24,"text":938,"url":24,"identifiers":939},"10.1145\u002F358841.358850",{"doi":938},{"id":24,"text":941,"url":24,"identifiers":942},"10.1137\u002F0215051",{"doi":941},{"id":24,"text":944,"url":24,"identifiers":945},"10.1137\u002F0217026",{"doi":944},{"id":24,"text":947,"url":24,"identifiers":948},"CHAZELLE , B. , AND EDELSBRUNNER , H. Linear space data structures for two types of range search. Discrete Comput. Geom. 2 ( 1987 ), 113 - 126 . CHAZELLE, B., AND EDELSBRUNNER, H. Linear space data structures for two types of range search. Discrete Comput. Geom. 2 (1987), 113-126.",{"doi":949},"10.1007\u002FBF02187875",{"id":24,"text":951,"url":24,"identifiers":952},"CHAZELLE , B. , AND GUIBAS , L.J. Fractional cascading : If. Applications. Algorithmica I ( 1986 ), 163 - 191 . CHAZELLE, B., AND GUIBAS, L.J. Fractional cascading: If. Applications. Algorithmica I (1986), 163-191.",{"doi":953},"10.1007\u002FBF01840441",{"id":24,"text":955,"url":24,"identifiers":956},"FELLER , W. All Introduction to Probability Theory and Its Applications, vol. l, 3rd ed . Wiley , New York , 1968 . FELLER, W. All Introduction to Probability Theory and Its Applications, vol. l, 3rd ed. Wiley, New York, 1968.",{},{"id":24,"text":958,"url":24,"identifiers":959},"LUEKER , G.S. A data structure for orthogonal range queries . In Proceedings of the 19th Annual IEEE Symposium on Foundations of Computer Science. IEEE , New York , 1978 , pp. 28 - 34 . LUEKER, G.S. A data structure for orthogonal range queries. In Proceedings of the 19th Annual IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1978, pp. 28-34.",{},{"id":24,"text":961,"url":24,"identifiers":962},"MCCREIGHT , E.M. Priority search trees. SIAMJ. Comput. 14 , 2 ( 1985 ), 257-276. MCCREIGHT, E.M. Priority search trees. SIAMJ. Comput. 14, 2 (1985), 257-276.",{"doi":963},"10.1137\u002F0214021",{"id":24,"text":965,"url":24,"identifiers":966},"MEHLHORN , K. Data Structures and Algorithms. 3: Multidimensional Searching and Computational Geometry . Springer-Verlag , Berlin , 1984 . MEHLHORN, K. Data Structures and Algorithms. 3: Multidimensional Searching and Computational Geometry. Springer-Verlag, Berlin, 1984.",{"doi":967},"10.1007\u002F978-3-642-69900-9",{"id":24,"text":969,"url":24,"identifiers":970},"TARJAN , R. E. A class of algorithms which require nonlinear time to maintain disjoint sets. J. Comput. System Sci. 18 ( 1979 ), 110 - 127 . TARJAN, R. E. A class of algorithms which require nonlinear time to maintain disjoint sets. J. Comput. System Sci. 18 (1979), 110-127.",{"doi":971},"10.1016\u002F0022-0000(79)90042-4",{"id":24,"text":973,"url":24,"identifiers":974},"10.1137\u002F0214019",{"doi":973},{"id":24,"text":976,"url":24,"identifiers":977},"10.1145\u002F3828.3839",{"doi":976},{"id":979,"createTime":980,"updateTime":980,"relativeEntities":981,"slug":982,"properties":983,"entityType":132,"verifyStatus":133,"verifyTime":980,"verifyNote":134,"languages":994,"translateLanguages":24,"viewCount":25,"primaryUrl":995,"fullTextUrl":24,"authors":996,"publicationType":196,"publisherRelationship":1073,"citationCount":1134,"citationInfo":1135,"publishDate":1141,"publishYear":1136,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":1142,"openAccess":24,"references":1143,"isForceReanalyzing":317},"fd419465-8d46-4a22-8e96-07be597a64e9","2024-12-27T09:53:02.131+00:00",[],"The-Locality-of-Distributed-Symmetry-Breaking",{"openalex":984,"mag":986,"abstract":988,"title":990,"doi":992},{"VOID":985},"W2467514673",{"VOID":987},"2467514673",{"EN":989},"\u003Cjats:p>\n            Symmetry-breaking problems are among the most well studied in the field of distributed computing and yet the most fundamental questions about their complexity remain open. In this article we work in the LOCAL model (where the input graph and underlying distributed network are identical) and study the\n            \u003Cjats:italic>randomized\u003C\u002Fjats:italic>\n            complexity of four fundamental symmetry-breaking problems on graphs: computing MISs (maximal independent sets), maximal matchings, vertex colorings, and ruling sets. A small sample of our results includes the following:\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            —An MIS algorithm running in\n            \u003Cjats:italic>O\u003C\u002Fjats:italic>\n            (log\n            \u003Cjats:sup>2\u003C\u002Fjats:sup>\n            Δ + 2\n            \u003Cjats:sup>\n              \u003Cjats:italic>o\u003C\u002Fjats:italic>\n              (√log log\n              \u003Cjats:italic>n\u003C\u002Fjats:italic>\n              )\n            \u003C\u002Fjats:sup>\n            ) time, where Δ is the maximum degree. This is the first MIS algorithm to improve on the 1986 algorithms of Luby and Alon, Babai, and Itai, when log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            ≪ Δ ≪ 2√log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            , and comes close to the Ω(log Δ \u002F log log Δ lower bound of Kuhn, Moscibroda, and Wattenhofer.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            —A maximal matching algorithm running in\n            \u003Cjats:italic>O\u003C\u002Fjats:italic>\n            (log Δ + log \n            \u003Cjats:sup>4\u003C\u002Fjats:sup>\n            log \n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            ) time. This is the first significant improvement to the 1986 algorithm of Israeli and Itai. Moreover, its dependence on Δ is\n            \u003Cjats:italic>nearly optimal\u003C\u002Fjats:italic>\n            .\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            —A (Δ + 1)-coloring algorithm requiring\n            \u003Cjats:italic>O\u003C\u002Fjats:italic>\n            (log Δ + 2\n            \u003Cjats:sup>\n              \u003Cjats:italic>o\u003C\u002Fjats:italic>\n              (√log log\n              \u003Cjats:italic>n\u003C\u002Fjats:italic>\n              )\n            \u003C\u002Fjats:sup>\n            time, improving on an\n            \u003Cjats:italic>O\u003C\u002Fjats:italic>\n            (log Δ + √log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            )-time algorithm of Schneider and Wattenhofer.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            —A method for reducing symmetry-breaking problems in low arboricity\u002Fdegeneracy graphs to low-degree graphs. (Roughly speaking, the arboricity or degeneracy of a graph bounds the density of any subgraph.) Corollaries of this reduction include an\n            \u003Cjats:italic>O\u003C\u002Fjats:italic>\n            (√log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            )-time maximal matching algorithm for graphs with arboricity up to 2√log\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            and an\n            \u003Cjats:italic>O\u003C\u002Fjats:italic>\n            (log \n            \u003Cjats:sup>2\u002F3\u003C\u002Fjats:sup>\n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            )-time MIS algorithm for graphs with arboricity up to 2\n            \u003Cjats:sup>\n              (log\n              \u003Cjats:italic>n\u003C\u002Fjats:italic>\n              )1\u002F3\n            \u003C\u002Fjats:sup>\n            .\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            Each of our algorithms is based on a simple but powerful technique for reducing a\n            \u003Cjats:italic>randomized\u003C\u002Fjats:italic>\n            symmetry-breaking task to a corresponding\n            \u003Cjats:italic>deterministic\u003C\u002Fjats:italic>\n            one on a poly(log \n            \u003Cjats:italic>n\u003C\u002Fjats:italic>\n            )-size graph.\n          \u003C\u002Fjats:p>",{"EN":991},"The Locality of Distributed Symmetry Breaking",{"VOID":993},"10.1145\u002F2903137",[136],"https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F2903137",[997,1016,1035,1054],{"id":998,"sortIndex":25,"researcher":24,"roles":999,"affiliations":1000,"properties":1009,"displayName":1013,"givenName":24,"familyName":24},"538fb035-4f9b-4878-bdea-b95b2513a704",[],[1001],{"id":1002,"sortIndex":25,"affiliation":1003,"properties":24},"647d468a-b533-43a3-aa5b-1af2c2c43f49",{"id":1002,"createTime":24,"updateTime":24,"relativeEntities":1004,"slug":24,"properties":1005,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1008,"statistic":24},[],{"title":1006},{"EN":1007},"Ben-Gurion University",[],{"orcid":1010,"title":1012,"openalex":1014},{"VOID":1011},"https:\u002F\u002Forcid.org\u002F0000-0002-9021-3549",{"EN":1013},"Leonid Barenboim",{"VOID":1015},"A5057471294",{"id":1017,"sortIndex":160,"researcher":24,"roles":1018,"affiliations":1019,"properties":1028,"displayName":1032,"givenName":24,"familyName":24},"5ffb4d25-f70f-43cd-8421-c54bec0aba93",[],[1020],{"id":1021,"sortIndex":25,"affiliation":1022,"properties":24},"1fefbb7b-8b43-4787-b54b-69fb381364b5",{"id":1021,"createTime":24,"updateTime":24,"relativeEntities":1023,"slug":24,"properties":1024,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1027,"statistic":24},[],{"title":1025},{"VI":1026},"Ben-Gurion University, Beer-Sheva, Israel",[],{"orcid":1029,"title":1031,"openalex":1033},{"VOID":1030},"https:\u002F\u002Forcid.org\u002F0000-0003-4257-2122",{"EN":1032},"Michael Elkin",{"VOID":1034},"A5075683085",{"id":1036,"sortIndex":180,"researcher":24,"roles":1037,"affiliations":1038,"properties":1047,"displayName":1051,"givenName":24,"familyName":24},"d6427a1f-30d4-4f5e-a861-b45192b03efc",[],[1039],{"id":1040,"sortIndex":25,"affiliation":1041,"properties":24},"90ca7495-379d-4fd1-91b7-024962ebd785",{"id":1040,"createTime":24,"updateTime":24,"relativeEntities":1042,"slug":24,"properties":1043,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1046,"statistic":24},[],{"title":1044},{"VI":1045},"University of Michigan, MI, USA",[],{"orcid":1048,"title":1050,"openalex":1052},{"VOID":1049},"https:\u002F\u002Forcid.org\u002F0000-0002-0495-3904",{"EN":1051},"Seth Pettie",{"VOID":1053},"A5076564426",{"id":1055,"sortIndex":267,"researcher":24,"roles":1056,"affiliations":1057,"properties":1066,"displayName":1070,"givenName":24,"familyName":24},"b0d6d3d2-8776-45e2-8eb0-0439332a05e6",[],[1058],{"id":1059,"sortIndex":25,"affiliation":1060,"properties":24},"8ac0b3e0-ba37-456d-b611-cc2bfbc6842a",{"id":1059,"createTime":24,"updateTime":24,"relativeEntities":1061,"slug":24,"properties":1062,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1065,"statistic":24},[],{"title":1063},{"VI":1064},"ETH, Zürich",[],{"orcid":1067,"title":1069,"openalex":1071},{"VOID":1068},"https:\u002F\u002Forcid.org\u002F0000-0002-3225-5564",{"EN":1070},"Johannes Schneider",{"VOID":1072},"A5101711824",{"url":24,"publisher":1074,"properties":1128},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1075,"slug":10,"properties":1076,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":1081,"manageAffiliations":1102,"indexDatabases":1113,"url":111,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":1077,"eissn":1078,"issn":1079,"title":1080},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[1082,1086,1090,1094,1098],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":1083,"label":1084,"description":1085,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},{"id":34,"createTime":24,"updateTime":24,"relativeEntities":1087,"label":1088,"description":1089,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":37},{},{"id":40,"createTime":24,"updateTime":24,"relativeEntities":1091,"label":1092,"description":1093,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":43},{},{"id":46,"createTime":24,"updateTime":24,"relativeEntities":1095,"label":1096,"description":1097,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":49},{},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":1099,"label":1100,"description":1101,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":55},{},[1103,1108],{"id":59,"createTime":24,"updateTime":24,"relativeEntities":1104,"slug":24,"properties":1105,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1107,"statistic":24},[],{"title":1106},{"EN":63},[],{"id":66,"createTime":24,"updateTime":24,"relativeEntities":1109,"slug":24,"properties":1110,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1112,"statistic":24},[],{"title":1111},{"EN":70},[],[1114,1121],{"id":74,"indexDatabase":1115,"url":87,"indexYears":24,"academicFieldIds":1120,"indexDatabaseRanking":24},{"id":76,"createTime":24,"updateTime":24,"relativeEntities":1116,"label":1117,"description":1118,"key":83,"publicationTags":1119,"standard":24},[],{"EN":79,"VI":79},{"EN":81,"VI":82},[85,86],[89],{"id":91,"indexDatabase":1122,"url":102,"indexYears":103,"academicFieldIds":1127,"indexDatabaseRanking":110},{"id":93,"createTime":24,"updateTime":24,"relativeEntities":1123,"label":1124,"description":1125,"key":99,"publicationTags":1126,"standard":24},[],{"EN":96,"VI":96},{"EN":96,"VI":98},[101],[105,106,107,108,109],{"issue":1129,"pages":1130,"volume":1132},{"VOID":411},{"VOID":1131},"1-45",{"VOID":1133},"63",172,{"total":1134,"publishYear":1136,"statisticByYear":1137},2016,{"2013":180,"2014":160,"2015":160,"2016":264,"2017":587,"2018":1138,"2019":1139,"2020":1140,"2021":1139,"2022":758,"2023":587,"2024":264},27,28,20,"2016-09-01",[85,110],[1144,1147,1150,1153,1156,1160,1163,1166,1169,1173,1176,1179,1182,1185,1188,1192,1195,1198,1201,1204,1207,1210,1213,1216,1219,1222,1225,1228,1231,1234,1237,1240,1243,1246,1249,1252,1255,1258,1261,1264,1267,1270,1273,1276,1279],{"id":24,"text":1145,"url":24,"identifiers":1146},"10.1002\u002Frsa.3240020403",{"doi":1145},{"id":24,"text":1148,"url":24,"identifiers":1149},"10.1016\u002F0196-6774(86)90019-2",{"doi":1148},{"id":24,"text":1151,"url":24,"identifiers":1152},"A. Amir O. Kapah T. Kopelowitz M. Naor and E. Porat. 2014. The family holiday gathering problem or fair and periodic scheduling of independent sets. CoRR abs\u002F1408.2279 (2014).  A. Amir O. Kapah T. Kopelowitz M. Naor and E. Porat. 2014. The family holiday gathering problem or fair and periodic scheduling of independent sets. CoRR abs\u002F1408.2279 (2014).",{},{"id":24,"text":1154,"url":24,"identifiers":1155},"10.1109\u002FSFCS.1989.63504",{"doi":1154},{"id":24,"text":1157,"url":24,"identifiers":1158},"R. Bar-Yehuda K. Censor-Hillel and G. Schwartzman. 2016. A distributed (2 + ε)-approximation for vertex cover in O(log Δ/εlog log Δ) rounds. CoRR abs\u002F1602.03713 (2016).  R. Bar-Yehuda K. Censor-Hillel and G. Schwartzman. 2016. A distributed (2 + ε)-approximation for vertex cover in O(log Δ/εlog log Δ) rounds. CoRR abs\u002F1602.03713 (2016).",{"doi":1159},"10.1145\u002F2933057.2933086",{"id":24,"text":1161,"url":24,"identifiers":1162},"10.1145\u002F2767386.2767410",{"doi":1161},{"id":24,"text":1164,"url":24,"identifiers":1165},"10.1007\u002Fs00446-009-0088-2",{"doi":1164},{"id":24,"text":1167,"url":24,"identifiers":1168},"10.1145\u002F2027216.2027221",{"doi":1167},{"id":24,"text":1170,"url":24,"identifiers":1171},"L. Barenboim and M. Elkin. 2013. Distributed Graph Coloring: Fundamentals and Recent Developments. Morgan & Claypool Publishers San Francisco CA.   L. Barenboim and M. Elkin. 2013. Distributed Graph Coloring: Fundamentals and Recent Developments. Morgan & Claypool Publishers San Francisco CA.",{"doi":1172},"10.1007\u002F978-3-031-02009-4",{"id":24,"text":1174,"url":24,"identifiers":1175},"10.1137\u002F12088848X",{"doi":1174},{"id":24,"text":1177,"url":24,"identifiers":1178},"10.1002\u002Frsa.3240020402",{"doi":1177},{"id":24,"text":1180,"url":24,"identifiers":1181},"10.1145\u002F2611462.2611512",{"doi":1180},{"id":24,"text":1183,"url":24,"identifiers":1184},"10.1145\u002F2611462.2611465",{"doi":1183},{"id":24,"text":1186,"url":24,"identifiers":1187},"10.1016\u002FS0019-9958(86)80023-7",{"doi":1186},{"id":24,"text":1189,"url":24,"identifiers":1190},"D. P. Dubhashi and A. Panconesi. 2009. Concentration of Measure for the Analysis of Randomized Algorithms. Cambridge University Press Cambridge.   D. P. Dubhashi and A. Panconesi. 2009. Concentration of Measure for the Analysis of Randomized Algorithms. Cambridge University Press Cambridge.",{"doi":1191},"10.1017\u002FCBO9780511581274",{"id":24,"text":1193,"url":24,"identifiers":1194},"10.1002\u002F(SICI)1098-2418(199809)13:2%3C99::AID-RSA1%3E3.0.CO;2-M",{"doi":1193},{"id":24,"text":1196,"url":24,"identifiers":1197},"M. Elkin , S. Pettie , and H. H. Su . 2015. (2Δ − 1)-edge coloring is much easier than maximal matching in the distributed setting . In Proceedings 26th ACM-SIAM Symposium on Discrete Algorithms (SODA). 355--370 . M. Elkin, S. Pettie, and H. H. Su. 2015. (2Δ − 1)-edge coloring is much easier than maximal matching in the distributed setting. In Proceedings 26th ACM-SIAM Symposium on Discrete Algorithms (SODA). 355--370.",{},{"id":24,"text":1199,"url":24,"identifiers":1200},"10.1145\u002F1281100.1281111",{"doi":1199},{"id":24,"text":1202,"url":24,"identifiers":1203},"10.5555\u002F2884435.2884455",{"doi":1202},{"id":24,"text":1205,"url":24,"identifiers":1206},"10.1137\u002FS0895480100373121",{"doi":1205},{"id":24,"text":1208,"url":24,"identifiers":1209},"10.1145\u002F2897518.2897533",{"doi":1208},{"id":24,"text":1211,"url":24,"identifiers":1212},"10.1016\u002F0020-0190(86)90144-4",{"doi":1211},{"id":24,"text":1214,"url":24,"identifiers":1215},"10.1016\u002FS0020-0190(99)00064-2",{"doi":1214},{"id":24,"text":1217,"url":24,"identifiers":1218},"10.1007\u002Fs00446-012-0174-8",{"doi":1217},{"id":24,"text":1220,"url":24,"identifiers":1221},"10.1145\u002F1993806.1993812",{"doi":1220},{"id":24,"text":1223,"url":24,"identifiers":1224},"K. Kothapalli and S. V. Pemmaraju . 2012. Super-fast 3-ruling sets . In Proceedings IARCS Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS). LIPIcs , Vol. 18 . Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 136--147. K. Kothapalli and S. V. Pemmaraju. 2012. Super-fast 3-ruling sets. In Proceedings IARCS Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS). LIPIcs, Vol. 18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 136--147.",{},{"id":24,"text":1226,"url":24,"identifiers":1227},"K. Kothapalli , C. Scheideler , M. Onus , and C. Schindelhauer . 2006. Distributed coloring in O˜(√log n) bit rounds . In Proceedings 20th International Parallel and Distributed Processing Symposium (IPDPS). K. Kothapalli, C. Scheideler, M. Onus, and C. Schindelhauer. 2006. Distributed coloring in O˜(√log n) bit rounds. In Proceedings 20th International Parallel and Distributed Processing Symposium (IPDPS).",{},{"id":24,"text":1229,"url":24,"identifiers":1230},"10.1145\u002F1011767.1011811",{"doi":1229},{"id":24,"text":1232,"url":24,"identifiers":1233},"F. Kuhn T. Moscibroda and R. Wattenhofer. 2010. Local computation: Lower and upper bounds. CoRR abs\u002F1011.5470 (2010).  F. Kuhn T. Moscibroda and R. Wattenhofer. 2010. Local computation: Lower and upper bounds. CoRR abs\u002F1011.5470 (2010).",{},{"id":24,"text":1235,"url":24,"identifiers":1236},"10.1145\u002F1146381.1146387",{"doi":1235},{"id":24,"text":1238,"url":24,"identifiers":1239},"10.1145\u002F1993806.1993813",{"doi":1238},{"id":24,"text":1241,"url":24,"identifiers":1242},"10.1137\u002F0221015",{"doi":1241},{"id":24,"text":1244,"url":24,"identifiers":1245},"10.1007\u002FBF01303516",{"doi":1244},{"id":24,"text":1247,"url":24,"identifiers":1248},"10.1137\u002F0215074",{"doi":1247},{"id":24,"text":1250,"url":24,"identifiers":1251},"10.1145\u002F1667053.1667060",{"doi":1250},{"id":24,"text":1253,"url":24,"identifiers":1254},"C. St . J. A. Nash-Williams . 1964 . Decomposition of finite graphs into forests . J. London Math. Soc. 39 (1964), 12 . C. St. J. A. Nash-Williams. 1964. Decomposition of finite graphs into forests. J. London Math. Soc. 39 (1964), 12.",{},{"id":24,"text":1256,"url":24,"identifiers":1257},"10.1007\u002FPL00008932",{"doi":1256},{"id":24,"text":1259,"url":24,"identifiers":1260},"10.1006\u002Fjagm.1996.0017",{"doi":1259},{"id":24,"text":1262,"url":24,"identifiers":1263},"D. Peleg . 2000. Distributed Computing: A Locality-Sensitive Approach . SIAM , Philadelphia, PA . D. Peleg. 2000. Distributed Computing: A Locality-Sensitive Approach. SIAM, Philadelphia, PA.",{},{"id":24,"text":1265,"url":24,"identifiers":1266},"10.1016\u002Fj.ic.2014.12.018",{"doi":1265},{"id":24,"text":1268,"url":24,"identifiers":1269},"R. Rubinfeld , G. Tamir , S. Vardi , and N. Xie . 2011. Fast local computation algorithms . In Proceedings of the 1st Symposium on Innovations in Computer Science (ICS). 223--238 . See also CoRR abs\u002F1104.1377. R. Rubinfeld, G. Tamir, S. Vardi, and N. Xie. 2011. Fast local computation algorithms. In Proceedings of the 1st Symposium on Innovations in Computer Science (ICS). 223--238. See also CoRR abs\u002F1104.1377.",{},{"id":24,"text":1271,"url":24,"identifiers":1272},"10.1016\u002Fj.tcs.2012.09.004",{"doi":1271},{"id":24,"text":1274,"url":24,"identifiers":1275},"10.1145\u002F1835698.1835760",{"doi":1274},{"id":24,"text":1277,"url":24,"identifiers":1278},"10.1007\u002Fs00446-010-0097-1",{"doi":1277},{"id":24,"text":1280,"url":24,"identifiers":1281},"10.1145\u002F167088.167156",{"doi":1280},{"id":1283,"createTime":1284,"updateTime":1284,"relativeEntities":1285,"slug":1286,"properties":1287,"entityType":132,"verifyStatus":133,"verifyTime":1284,"verifyNote":134,"languages":1298,"translateLanguages":24,"viewCount":25,"primaryUrl":1299,"fullTextUrl":24,"authors":1300,"publicationType":196,"publisherRelationship":1354,"citationCount":1416,"citationInfo":1417,"publishDate":1421,"publishYear":1418,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":1422,"openAccess":24,"references":1423,"isForceReanalyzing":317},"a734a282-44d8-4c11-81cb-b669f99ce88d","2024-12-27T09:53:02.009+00:00",[],"Communication-Steps-for-Parallel-Query-Processing",{"openalex":1288,"mag":1290,"abstract":1292,"title":1294,"doi":1296},{"VOID":1289},"W2765269579",{"VOID":1291},"2765269579",{"EN":1293},"\u003Cjats:p>\n            We study the problem of computing conjunctive queries over large databases on parallel architectures without shared storage. Using the structure of such a query\n            \u003Cjats:italic>q\u003C\u002Fjats:italic>\n            and the skew in the data, we study tradeoffs between the number of processors, the number of rounds of communication, and the per-processor\n            \u003Cjats:italic>load\u003C\u002Fjats:italic>\n            —the number of bits each processor can send or can receive in a single round—that are required to compute\n            \u003Cjats:italic>q\u003C\u002Fjats:italic>\n            . Since each processor must store its received bits, the load is at most the number of bits of storage per processor.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>When the data are free of skew, we obtain essentially tight upper and lower bounds for one round algorithms, and we show how the bounds degrade when there is skew in the data. In the case of skewed data, we show how to improve the algorithms when approximate degrees of the (necessarily small number of) heavy-hitter elements are available, obtaining essentially optimal algorithms for queries such as skewed simple joins and skewed triangle join queries.\u003C\u002Fjats:p>\n          \u003Cjats:p>\n            For queries that we identify as\n            \u003Cjats:italic>treelike\u003C\u002Fjats:italic>\n            , we also prove nearly matching upper and lower bounds for multi-round algorithms for a natural class of skew-free databases. One consequence of these latter lower bounds is that for any ε > 0, using\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            processors to compute the connected components of a graph, or to output the path, if any, between a specified pair of vertices of a graph with\n            \u003Cjats:italic>m\u003C\u002Fjats:italic>\n            edges and per-processor load that is\n            \u003Cjats:italic>O\u003C\u002Fjats:italic>\n            (\n            \u003Cjats:italic>m\u003C\u002Fjats:italic>\n            \u002F\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            \u003Cjats:sup>1−ε\u003C\u002Fjats:sup>\n            ) requires Ω(log\n            \u003Cjats:italic>p\u003C\u002Fjats:italic>\n            ) rounds of communication.\n          \u003C\u002Fjats:p>\n          \u003Cjats:p>\n            Our upper bounds are given by simple structured algorithms using MapReduce. Our one-round lower bounds are proved in a very general model, which we call the\n            \u003Cjats:italic>Massively Parallel Communication (MPC)\u003C\u002Fjats:italic>\n            model, that allows processors to communicate arbitrary bits. Our multi-round lower bounds apply in a restricted version of the MPC model in which processors in subsequent rounds after the first communication round are only allowed to send tuples.\n          \u003C\u002Fjats:p>",{"EN":1295},"Communication Steps for Parallel Query Processing",{"VOID":1297},"10.1145\u002F3125644",[136],"https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F3125644",[1301,1320,1337],{"id":1302,"sortIndex":25,"researcher":24,"roles":1303,"affiliations":1304,"properties":1313,"displayName":1317,"givenName":24,"familyName":24},"bb894eed-841c-4478-9a10-d2d9b17a51a0",[],[1305],{"id":1306,"sortIndex":25,"affiliation":1307,"properties":24},"19da5a30-e106-43d3-a9ef-0909b798516e",{"id":1306,"createTime":24,"updateTime":24,"relativeEntities":1308,"slug":24,"properties":1309,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1312,"statistic":24},[],{"title":1310},{"VI":1311},"University of Washington",[],{"orcid":1314,"title":1316,"openalex":1318},{"VOID":1315},"https:\u002F\u002Forcid.org\u002F0000-0002-2666-3545",{"EN":1317},"Paul Beame",{"VOID":1319},"A5042076941",{"id":1321,"sortIndex":160,"researcher":24,"roles":1322,"affiliations":1323,"properties":1330,"displayName":1334,"givenName":24,"familyName":24},"5aae483d-aee8-40d8-81cf-2db29a61df5f",[],[1324],{"id":1306,"sortIndex":25,"affiliation":1325,"properties":24},{"id":1306,"createTime":24,"updateTime":24,"relativeEntities":1326,"slug":24,"properties":1327,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1329,"statistic":24},[],{"title":1328},{"VI":1311},[],{"orcid":1331,"title":1333,"openalex":1335},{"VOID":1332},"https:\u002F\u002Forcid.org\u002F0000-0001-6309-1702",{"EN":1334},"Paraschos Koutris",{"VOID":1336},"A5040506752",{"id":1338,"sortIndex":180,"researcher":24,"roles":1339,"affiliations":1340,"properties":1347,"displayName":1351,"givenName":24,"familyName":24},"e9d8528c-47e7-4bd0-b6d9-dd4e019cd10a",[],[1341],{"id":1306,"sortIndex":25,"affiliation":1342,"properties":24},{"id":1306,"createTime":24,"updateTime":24,"relativeEntities":1343,"slug":24,"properties":1344,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1346,"statistic":24},[],{"title":1345},{"VI":1311},[],{"orcid":1348,"title":1350,"openalex":1352},{"VOID":1349},"https:\u002F\u002Forcid.org\u002F0000-0002-4144-0868",{"EN":1351},"Dan Suciu",{"VOID":1353},"A5048204602",{"url":24,"publisher":1355,"properties":1409},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1356,"slug":10,"properties":1357,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":1362,"manageAffiliations":1383,"indexDatabases":1394,"url":111,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":1358,"eissn":1359,"issn":1360,"title":1361},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[1363,1367,1371,1375,1379],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":1364,"label":1365,"description":1366,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},{"id":34,"createTime":24,"updateTime":24,"relativeEntities":1368,"label":1369,"description":1370,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":37},{},{"id":40,"createTime":24,"updateTime":24,"relativeEntities":1372,"label":1373,"description":1374,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":43},{},{"id":46,"createTime":24,"updateTime":24,"relativeEntities":1376,"label":1377,"description":1378,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":49},{},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":1380,"label":1381,"description":1382,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":55},{},[1384,1389],{"id":59,"createTime":24,"updateTime":24,"relativeEntities":1385,"slug":24,"properties":1386,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1388,"statistic":24},[],{"title":1387},{"EN":63},[],{"id":66,"createTime":24,"updateTime":24,"relativeEntities":1390,"slug":24,"properties":1391,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1393,"statistic":24},[],{"title":1392},{"EN":70},[],[1395,1402],{"id":74,"indexDatabase":1396,"url":87,"indexYears":24,"academicFieldIds":1401,"indexDatabaseRanking":24},{"id":76,"createTime":24,"updateTime":24,"relativeEntities":1397,"label":1398,"description":1399,"key":83,"publicationTags":1400,"standard":24},[],{"EN":79,"VI":79},{"EN":81,"VI":82},[85,86],[89],{"id":91,"indexDatabase":1403,"url":102,"indexYears":103,"academicFieldIds":1408,"indexDatabaseRanking":110},{"id":93,"createTime":24,"updateTime":24,"relativeEntities":1404,"label":1405,"description":1406,"key":99,"publicationTags":1407,"standard":24},[],{"EN":96,"VI":96},{"EN":96,"VI":98},[101],[105,106,107,108,109],{"issue":1410,"pages":1412,"volume":1414},{"VOID":1411},"6",{"VOID":1413},"1-58",{"VOID":1415},"64",97,{"total":1416,"publishYear":1418,"statisticByYear":1419},2017,{"2017":160,"2018":264,"2019":757,"2020":1140,"2021":761,"2022":1420,"2023":589,"2024":263},12,"2017-12-31",[85,110],[1424,1427,1430,1433,1436,1439,1442,1445,1448,1452,1455,1458,1461,1464,1467,1470,1474,1477,1480,1483,1486,1489,1492,1495,1498,1501,1504,1507,1510,1513,1516,1520,1523,1526,1529,1532,1535,1538,1541,1544,1547],{"id":24,"text":1425,"url":24,"identifiers":1426},"Foto N. Afrati , Manas R. Joglekar , Christopher Ré , Semih Salihoglu , and Jeffrey D. Ullman . 2017. GYM: A multiround distributed join algorithm . In Proceedings of the 20th International Conference on Database Theory (ICDT’17) . 4:1--4:18. DOI:http:\u002F\u002Fdx.doi.org\u002F10.4230\u002FLIPIcs.ICDT. 2017 .4 10.4230\u002FLIPIcs.ICDT.2017.4 Foto N. Afrati, Manas R. Joglekar, Christopher Ré, Semih Salihoglu, and Jeffrey D. Ullman. 2017. GYM: A multiround distributed join algorithm. In Proceedings of the 20th International Conference on Database Theory (ICDT’17). 4:1--4:18. DOI:http:\u002F\u002Fdx.doi.org\u002F10.4230\u002FLIPIcs.ICDT.2017.4",{},{"id":24,"text":1428,"url":24,"identifiers":1429},"F. N. Afrati A. D. Sarma S. Salihoglu and J. D. Ullman. 2012. Upper and lower bounds on the cost of a map-reduce computation. CoRR abs\u002F1206.4377 (2012).  F. N. Afrati A. D. Sarma S. Salihoglu and J. D. Ullman. 2012. Upper and lower bounds on the cost of a map-reduce computation. CoRR abs\u002F1206.4377 (2012).",{},{"id":24,"text":1431,"url":24,"identifiers":1432},"10.1145\u002F1739041.1739056",{"doi":1431},{"id":24,"text":1434,"url":24,"identifiers":1435},"10.1006\u002Fjcss.1997.1545",{"doi":1434},{"id":24,"text":1437,"url":24,"identifiers":1438},"10.1109\u002FFOCS.2008.43",{"doi":1437},{"id":24,"text":1440,"url":24,"identifiers":1441},"10.1145\u002F2463664.2465224",{"doi":1440},{"id":24,"text":1443,"url":24,"identifiers":1444},"10.1145\u002F2594538.2594558",{"doi":1443},{"id":24,"text":1446,"url":24,"identifiers":1447},"Johann Brault-Baron . 2016. Hypergraph acyclicity revisited. ACM Comput. Surv. 49, 3 ( 2016 ), 54:1--54:26. http:\u002F\u002Fdoi.acm.org\u002F10.1145\u002F2983573 Johann Brault-Baron. 2016. Hypergraph acyclicity revisited. ACM Comput. Surv. 49, 3 (2016), 54:1--54:26. http:\u002F\u002Fdoi.acm.org\u002F10.1145\u002F2983573",{},{"id":24,"text":1449,"url":24,"identifiers":1450},"S. Chaudhuri. 2012. What next?: A half-dozen data management research goals for big data and the cloud. In PODS. 1--4.  S. Chaudhuri. 2012. What next?: A half-dozen data management research goals for big data and the cloud. In PODS. 1--4.",{"doi":1451},"10.1145\u002F2213556.2213558",{"id":24,"text":1453,"url":24,"identifiers":1454},"10.1145\u002F2723372.2750545",{"doi":1453},{"id":24,"text":1456,"url":24,"identifiers":1457},"10.1145\u002F240455.240477",{"doi":1456},{"id":24,"text":1459,"url":24,"identifiers":1460},"J. Dean and S. Ghemawat. 2004. MapReduce: Simplified data processing on large clusters. In OSDI. 137--150.  J. Dean and S. Ghemawat. 2004. MapReduce: Simplified data processing on large clusters. In OSDI. 137--150.",{},{"id":24,"text":1462,"url":24,"identifiers":1463},"EMC Corporation. Data Science Revealed: A Data-Driven Glimpse into the Burgeoning New Field. Retrieved from http:\u002F\u002Fwww.emc.com\u002Fcollateral\u002Fabout\u002Fnews\u002Femc-data-science-study-wp.pdf.  EMC Corporation. Data Science Revealed: A Data-Driven Glimpse into the Burgeoning New Field. Retrieved from http:\u002F\u002Fwww.emc.com\u002Fcollateral\u002Fabout\u002Fnews\u002Femc-data-science-study-wp.pdf.",{},{"id":24,"text":1465,"url":24,"identifiers":1466},"10.1145\u002F1824777.1824786",{"doi":1465},{"id":24,"text":1468,"url":24,"identifiers":1469},"10.2307\u002F4145187",{"doi":1468},{"id":24,"text":1471,"url":24,"identifiers":1472},"A. Gál and P. Gopalan. 2007. Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence. In FOCS. 294--304.  A. Gál and P. Gopalan. 2007. Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence. In FOCS. 294--304.",{"doi":1473},"10.1109\u002FFOCS.2007.54",{"id":24,"text":1475,"url":24,"identifiers":1476},"10.1016\u002F0743-1066(92)90048-8",{"doi":1475},{"id":24,"text":1478,"url":24,"identifiers":1479},"10.1007\u002F978-3-642-25591-5_39",{"doi":1478},{"id":24,"text":1481,"url":24,"identifiers":1482},"10.1145\u002F1568318.1568320",{"doi":1481},{"id":24,"text":1484,"url":24,"identifiers":1485},"10.1145\u002F1109557.1109590",{"doi":1484},{"id":24,"text":1487,"url":24,"identifiers":1488},"Sudipto Guha and Zhiyi Huang . 2009. Revisiting the direct sum theorem and space lower bounds in random order streams . In ICALP (LNCS) , Vol. 5555 . Springer , 513--524. Sudipto Guha and Zhiyi Huang. 2009. Revisiting the direct sum theorem and space lower bounds in random order streams. In ICALP (LNCS), Vol. 5555. Springer, 513--524.",{},{"id":24,"text":1490,"url":24,"identifiers":1491},"10.1145\u002F2588555.2594530",{"doi":1490},{"id":24,"text":1493,"url":24,"identifiers":1494},"10.1007\u002F978-3-642-15369-3_46",{"doi":1493},{"id":24,"text":1496,"url":24,"identifiers":1497},"10.1137\u002F1.9781611973075.76",{"doi":1496},{"id":24,"text":1499,"url":24,"identifiers":1500},"10.1145\u002F3034786.3034788",{"doi":1499},{"id":24,"text":1502,"url":24,"identifiers":1503},"Paraschos Koutris , Paul Beame , and Dan Suciu . 2016 . Worst-case optimal algorithms for parallel query processing . In Proceedings of the 19th International Conference on Database Theory (ICDT’16) . 8:1--8:18. DOI:http:\u002F\u002Fdx.doi.org\u002F10.4230\u002FLIPIcs.ICDT.2016.8 10.4230\u002FLIPIcs.ICDT.2016.8 Paraschos Koutris, Paul Beame, and Dan Suciu. 2016. Worst-case optimal algorithms for parallel query processing. In Proceedings of the 19th International Conference on Database Theory (ICDT’16). 8:1--8:18. DOI:http:\u002F\u002Fdx.doi.org\u002F10.4230\u002FLIPIcs.ICDT.2016.8",{},{"id":24,"text":1505,"url":24,"identifiers":1506},"10.1145\u002F1989284.1989310",{"doi":1505},{"id":24,"text":1508,"url":24,"identifiers":1509},"10.1016\u002FS0065-2458(08)60342-3",{"doi":1508},{"id":24,"text":1511,"url":24,"identifiers":1512},"10.1145\u002F2213836.2213840",{"doi":1511},{"id":24,"text":1514,"url":24,"identifiers":1515},"10.14778\u002F1920841.1920886",{"doi":1514},{"id":24,"text":1517,"url":24,"identifiers":1518},"H. Q. Ngo E. Porat C. Ré and A. Rudra. 2012. Worst-case optimal join algorithms: (Extended abstract). In PODS. 37--48.  H. Q. Ngo E. Porat C. Ré and A. Rudra. 2012. Worst-case optimal join algorithms: (Extended abstract). In PODS. 37--48.",{"doi":1519},"10.1145\u002F2213556.2213565",{"id":24,"text":1521,"url":24,"identifiers":1522},"10.1145\u002F1376616.1376726",{"doi":1521},{"id":24,"text":1524,"url":24,"identifiers":1525},"10.1145\u002F2304576.2304607",{"doi":1524},{"id":24,"text":1527,"url":24,"identifiers":1528},"Spark. Apache Spark. http:\u002F\u002Fspark.apache.org\u002F.  Spark. Apache Spark. http:\u002F\u002Fspark.apache.org\u002F.",{},{"id":24,"text":1530,"url":24,"identifiers":1531},"Siddharth Suri and Sergei Vassilvitskii. 2011. Counting triangles and the curse of the last reducer. In WWW. 607--614.  Siddharth Suri and Sergei Vassilvitskii. 2011. Counting triangles and the curse of the last reducer. In WWW. 607--614.",{},{"id":24,"text":1533,"url":24,"identifiers":1534},"10.14778\u002F1687553.1687609",{"doi":1533},{"id":24,"text":1536,"url":24,"identifiers":1537},"10.1145\u002F31846.32978",{"doi":1536},{"id":24,"text":1539,"url":24,"identifiers":1540},"10.1145\u002F2331042.2331053",{"doi":1539},{"id":24,"text":1542,"url":24,"identifiers":1543},"10.1145\u002F79173.79181",{"doi":1542},{"id":24,"text":1545,"url":24,"identifiers":1546},"10.14778\u002F3007263.3007307",{"doi":1545},{"id":24,"text":1548,"url":24,"identifiers":1549},"A. C. Yao. 1977. Probabilistic computations: Toward a unified measure of complexity. In FOCS. 222--227.  A. C. Yao. 1977. Probabilistic computations: Toward a unified measure of complexity. In FOCS. 222--227.",{"doi":1550},"10.1109\u002FSFCS.1977.24",{"id":1552,"createTime":1553,"updateTime":1553,"relativeEntities":1554,"slug":1555,"properties":1556,"entityType":132,"verifyStatus":133,"verifyTime":1553,"verifyNote":134,"languages":1567,"translateLanguages":24,"viewCount":25,"primaryUrl":1568,"fullTextUrl":24,"authors":1569,"publicationType":196,"publisherRelationship":1589,"citationCount":1650,"citationInfo":1651,"publishDate":1664,"publishYear":579,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":1665,"openAccess":24,"references":1666,"isForceReanalyzing":317},"2d99b31b-fb83-4234-b391-8de05475e0e8","2024-12-18T09:15:12.887+00:00",[],"An-Algorithm-for-Subgraph-Isomorphism",{"openalex":1557,"mag":1559,"abstract":1561,"title":1563,"doi":1565},{"VOID":1558},"W2126359798",{"VOID":1560},"2126359798",{"EN":1562},"\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":1564},"An Algorithm for Subgraph Isomorphism",{"VOID":1566},"10.1145\u002F321921.321925",[136],"https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F321921.321925",[1570],{"id":1571,"sortIndex":25,"researcher":24,"roles":1572,"affiliations":1573,"properties":1582,"displayName":1586,"givenName":24,"familyName":24},"ce944546-be09-4d84-9e3b-bc33f7eca2c5",[],[1574],{"id":1575,"sortIndex":25,"affiliation":1576,"properties":24},"e9adb755-bfa0-484f-b8dc-b92f43505b4c",{"id":1575,"createTime":24,"updateTime":24,"relativeEntities":1577,"slug":24,"properties":1578,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1581,"statistic":24},[],{"title":1579},{"EN":1580},"Division of Computer Science, National Physical Laboratory, Teddington, Middlesex, TW11 OLW, England",[],{"orcid":1583,"title":1585,"openalex":1587},{"VOID":1584},"https:\u002F\u002Forcid.org\u002F0000-0002-9978-0726",{"EN":1586},"J. R. 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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":24,"text":1689,"url":24,"identifiers":1690},"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":24,"text":1692,"url":24,"identifiers":1693},"10.1145\u002F365628.365648",{"doi":1692},{"id":24,"text":1695,"url":24,"identifiers":1696},"10.1016\u002FS0146-664X(72)80003-0",{"doi":1695},{"id":24,"text":1698,"url":24,"identifiers":1699},"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":1701,"createTime":1702,"updateTime":1702,"relativeEntities":1703,"slug":1704,"properties":1705,"entityType":132,"verifyStatus":133,"verifyTime":1702,"verifyNote":134,"languages":1716,"translateLanguages":24,"viewCount":25,"primaryUrl":1717,"fullTextUrl":24,"authors":1718,"publicationType":196,"publisherRelationship":1751,"citationCount":1812,"citationInfo":1813,"publishDate":1816,"publishYear":1814,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":1817,"openAccess":24,"references":1818,"isForceReanalyzing":317},"9c0e9a20-720d-468b-a771-975454ee4cde","2024-12-10T18:59:20.225+00:00",[],"How-to-assign-votes-in-a-distributed-system",{"openalex":1706,"mag":1708,"abstract":1710,"title":1712,"doi":1714},{"VOID":1707},"W2052960791",{"VOID":1709},"2052960791",{"EN":1711},"\u003Cjats:p>\n            In a distributed system, one strategy for achieving mutual exclusion of groups of nodes without communication is to assign to each node a number of votes. Only a group with a majority of votes can execute the critical operations, and mutual exclusion is achieved because at any given time there is at most one such group. A second strategy, which\n            \u003Cjats:italic>appears\u003C\u002Fjats:italic>\n            to be similar to votes, is to define a priori a set of groups that intersect each other. Any group of nodes that finds itself in this set can perform the restricted operations. In this paper, both of these strategies are studied in detail and it is shown that they are\n            \u003Cjats:italic>not\u003C\u002Fjats:italic>\n            equivalent in general (although they are in some cases). In doing so, a number of other interesting properties are proved. These properties will be of use to a system designer who is selecting a vote assignment or a set of groups for a specific application.\n          \u003C\u002Fjats:p>",{"EN":1713},"How to assign votes in a distributed system",{"VOID":1715},"10.1145\u002F4221.4223",[136],"https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F4221.4223",[1719,1734],{"id":1720,"sortIndex":25,"researcher":24,"roles":1721,"affiliations":1722,"properties":1729,"displayName":1731,"givenName":24,"familyName":24},"92805af8-dcc4-4075-91a7-809b19849dd2",[],[1723],{"id":851,"sortIndex":25,"affiliation":1724,"properties":24},{"id":851,"createTime":24,"updateTime":24,"relativeEntities":1725,"slug":24,"properties":1726,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1728,"statistic":24},[],{"title":1727},{"EN":856},[],{"title":1730,"openalex":1732},{"EN":1731},"Héctor García-Molina",{"VOID":1733},"A5055883336",{"id":1735,"sortIndex":160,"researcher":24,"roles":1736,"affiliations":1737,"properties":1744,"displayName":1748,"givenName":24,"familyName":24},"c014f826-97e8-4655-8ab0-1d0b95fb22e1",[],[1738],{"id":851,"sortIndex":25,"affiliation":1739,"properties":24},{"id":851,"createTime":24,"updateTime":24,"relativeEntities":1740,"slug":24,"properties":1741,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1743,"statistic":24},[],{"title":1742},{"EN":856},[],{"orcid":1745,"title":1747,"openalex":1749},{"VOID":1746},"https:\u002F\u002Forcid.org\u002F0000-0002-2830-1038",{"EN":1748},"Daniel Barbará",{"VOID":1750},"A5089029917",{"url":24,"publisher":1752,"properties":1806},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1753,"slug":10,"properties":1754,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":1759,"manageAffiliations":1780,"indexDatabases":1791,"url":111,"thumbnailPath":24,"statistic":24,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":1755,"eissn":1756,"issn":1757,"title":1758},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[1760,1764,1768,1772,1776],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":1761,"label":1762,"description":1763,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},{"id":34,"createTime":24,"updateTime":24,"relativeEntities":1765,"label":1766,"description":1767,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":37},{},{"id":40,"createTime":24,"updateTime":24,"relativeEntities":1769,"label":1770,"description":1771,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":43},{},{"id":46,"createTime":24,"updateTime":24,"relativeEntities":1773,"label":1774,"description":1775,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":49},{},{"id":52,"createTime":24,"updateTime":24,"relativeEntities":1777,"label":1778,"description":1779,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":55},{},[1781,1786],{"id":59,"createTime":24,"updateTime":24,"relativeEntities":1782,"slug":24,"properties":1783,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1785,"statistic":24},[],{"title":1784},{"EN":63},[],{"id":66,"createTime":24,"updateTime":24,"relativeEntities":1787,"slug":24,"properties":1788,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":1790,"statistic":24},[],{"title":1789},{"EN":70},[],[1792,1799],{"id":74,"indexDatabase":1793,"url":87,"indexYears":24,"academicFieldIds":1798,"indexDatabaseRanking":24},{"id":76,"createTime":24,"updateTime":24,"relativeEntities":1794,"label":1795,"description":1796,"key":83,"publicationTags":1797,"standard":24},[],{"EN":79,"VI":79},{"EN":81,"VI":82},[85,86],[89],{"id":91,"indexDatabase":1800,"url":102,"indexYears":103,"academicFieldIds":1805,"indexDatabaseRanking":110},{"id":93,"createTime":24,"updateTime":24,"relativeEntities":1801,"label":1802,"description":1803,"key":99,"publicationTags":1804,"standard":24},[],{"EN":96,"VI":96},{"EN":96,"VI":98},[101],[105,106,107,108,109],{"issue":1807,"pages":1808,"volume":1810},{"VOID":254},{"VOID":1809},"841-860",{"VOID":1811},"32",574,{"total":1812,"publishYear":1814,"statisticByYear":1815},1985,{"2012":1140,"2013":754,"2014":263,"2015":754,"2016":263,"2017":266,"2018":590,"2019":265,"2020":265,"2021":266,"2022":265,"2023":265,"2024":160},"1985-10-01",[85,110],[1819,1823,1826,1829,1832,1835,1838,1841,1844,1848,1851,1854,1857,1860],{"id":24,"text":1820,"url":24,"identifiers":1821},"BENZAKEN , C. Critical hypergraphs for the weak chromatic number . J. Comb. Theory, Series B 29 , ( 1980 ), 328 - 338 . BENZAKEN, C.Critical hypergraphs for the weak chromatic number. J. Comb. Theory, Series B 29, (1980), 328-338.",{"doi":1822},"10.1016\u002F0095-8956(80)90090-8",{"id":24,"text":1824,"url":24,"identifiers":1825},"BERGE , C. Graphs and Hypergraphs . American Elsevier , New York , 1973 . BERGE, C. Graphs and Hypergraphs. American Elsevier, New York, 1973.",{},{"id":24,"text":1827,"url":24,"identifiers":1828},"DAVIDSON , S. Evaluation of an optimistic protocol for partitioned distributed database systems. Tech. Rep. 299, Dept. of Electrical Engineering and Comput. Sci ., Princeton Univ. , May 1982 . DAVIDSON, S.Evaluation of an optimistic protocol for partitioned distributed database systems. Tech. Rep. 299, Dept. of Electrical Engineering and Comput. Sci., Princeton Univ., May 1982.",{},{"id":24,"text":1830,"url":24,"identifiers":1831},"DOLEV , D. , AND STRONG , H. R. polynomial algorithms for multiple processor agreement . In Proceedings of the 14th ACM Symposium on Theory of Computing ( San Francisco, Calif., May 5-7). ACM, New York , 1982 , pp. 401 - 407 . 10.1145\u002F800070.802215 DOLEV, D., AND STRONG, H. R.polynomial algorithms for multiple processor agreement. In Proceedings of the 14th ACM Symposium on Theory of Computing (San Francisco, Calif., May 5-7). ACM, New York, 1982, pp. 401-407. 10.1145\u002F800070.802215",{},{"id":24,"text":1833,"url":24,"identifiers":1834},"GARCIA-MOLINA , H. Reliability issues for fully replicated distributed databases . IEEE Trans. Comput. 15 , 9 ( Sept. 1982 ) 34-42. GARCIA-MOLINA, H.Reliability issues for fully replicated distributed databases. IEEE Trans. Comput. 15, 9 (Sept. 1982) 34-42.",{},{"id":24,"text":1836,"url":24,"identifiers":1837},"FFORD , Do K~ Weighted voting for replicated data . In Proceedings of the 7th Symposium on Operating System Principles (Pacific Grove, Calif., Dec.). ACM , New York , 1979 , pp. 150 - 162 . 10.1145\u002F800215.806583 FFORD, Do K~ Weighted voting for replicated data. In Proceedings of the 7th Symposium on Operating System Principles (Pacific Grove, Calif., Dec.). ACM, New York, 1979, pp. 150-162. 10.1145\u002F800215.806583",{},{"id":24,"text":1839,"url":24,"identifiers":1840},"LAMPORT , L. The implementation of reliable distributed multiprocess systems . Comput. Networks 2 ( 1978 ), 95 - 114 . LAMPORT, L.The implementation of reliable distributed multiprocess systems. Comput. Networks 2 (1978), 95-114.",{},{"id":24,"text":1842,"url":24,"identifiers":1843},"10.1145\u002F357172.357176",{"doi":1842},{"id":24,"text":1845,"url":24,"identifiers":1846},"LOVASZ , L . On chromatic number of finite set systems . Acta Math. Acad. Sci. Hungary 19 (I968), 59 - 67 . LOVASZ, L. On chromatic number of finite set systems. Acta Math. Acad. Sci. Hungary 19 (I968), 59-67.",{"doi":1847},"10.1007\u002FBF01894680",{"id":24,"text":1849,"url":24,"identifiers":1850},"LOVASZ , L. Coverings and colorings of hypergraphs . In Proceedings of the 4th Southeastern Conference on Combinatorics, Graph Theory and Computing ( Florida Atlantic University). Utilitas Mathematica, Winnipeg, Canada , 1973 , pp. 3 - 12 . LOVASZ, L. Coverings and colorings of hypergraphs. In Proceedings of the 4th Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic University). Utilitas Mathematica, Winnipeg, Canada, 1973, pp. 3-12.",{},{"id":24,"text":1852,"url":24,"identifiers":1853},"LYNCH , N. FISCHER , M. , AND FOWLER , R. A simple and efficient byzantine generals algorithm . In Proceedings of the 2nd Symposium on Reliability in Distributed Software and Database Systems ( Univ. of Pittsburgh, July). iEEE, New York, i982 , pp. 46 - 52 . LYNCH, N. FISCHER, M., AND FOWLER, R. A simple and efficient byzantine generals algorithm. In Proceedings of the 2nd Symposium on Reliability in Distributed Software and Database Systems (Univ. of Pittsburgh, July). iEEE, New York, i982, pp. 46-52.",{},{"id":24,"text":1855,"url":24,"identifiers":1856},"ROTHNIE , J. B. , AND GOODMAN , N. A survey of research and development in distributed database management . In Proceedings of the 3rd International Conference on Very Large Database ( Tokyo, Japan, Oct. 6-8). ACM, New York , 1977 , pp. 48 - 62 . ROTHNIE, J. B., AND GOODMAN, N.A survey of research and development in distributed database management. In Proceedings of the 3rd International Conference on Very Large Database (Tokyo, Japan, Oct. 6-8). ACM, New York, 1977, pp. 48-62.",{},{"id":24,"text":1858,"url":24,"identifiers":1859},"SKEEN , D. A quorum-based commit protocol . In Proceedings of the 6th Berkeley Workshop on Distributed Data Management and Computer Networks (Asilomar, Calif., Feb.). Lawrence Berkeley Laboratories , Berkeley, Calif. , 1982 , pp. 69 - 80 . SKEEN, D.A quorum-based commit protocol. In Proceedings of the 6th Berkeley Workshop on Distributed Data Management and Computer Networks (Asilomar, Calif., Feb.). 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