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The method subdivides a large problem in two smaller ones (or recursive iterations of the same procedure), in order to lower down the global computational complexity of the original problem, at the expense of a moderate loss of quality in the solution. Theoretical mathematical results are presented to assure a successful algorithmic application of the method and to suggest the potential strategies for its implementation. In contrast, due to the lack of theoretical results, the solution’s quality deterioration is measured empirically by means of Monte Carlo simulations for several types and values of the chosen strategies. Finally, introducing parameters of efficiency we suggest the best strategies depending on the data input.",{"EN":134},"Analysis of Divide-and-Conquer strategies for the 0–1 minimization knapsack problem",{"VOID":136},"[]",{"VOID":138},"Baños R, Gil C, Ortega J, Montoya FG (2003) Multilevel heuristic algorithm for graph partitioning. In Workshops on applications of evolutionary computation, p 143–153. Springer\nBlum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35(3):268–308\nBlum C, Puchinger J, Raidl GR, Roli A (2011) Hybrid metaheuristics in combinatorial optimization: a survey. Appl Soft Comput 11(6):4135–4151\nChris W (2008) Multilevel refinement for combinatorial optimisation: boosting metaheuristic performance. Hybrid metaheuristics. Springer, Berlin, pp 261–289\nGlover F, Hanafi S (2002) Tabu search and finite convergence. Discret Appl Math 119(1):3–36 Special Issue devoted to Foundation of Heuristics in Combinatorial Optimization\nGross Jonathan L, Jay Y (2006) Graph theory and its applications. Discrete mathematics and its applications. Chapman and Hall, Boca Raton\nGutjahr WJ (2003) A converging ACO algorithm for stochastic combinatorial optimization. In: Albrecht A, Steinhöfel K (eds) Stochastic algorithms: foundations and applications. Springer, Berlin, pp 10–25\nGutjahr WJ (2010) Convergence analysis of metaheuristics. Springer, Boston, pp 159–187\nHanafi S (2001) On the convergence of tabu search. J Heuristics 7(1):47–58\nJuan AA, Faulin J, Grasman SE, Rabe M, Figueira G (2015) A review of simheuristics: extending metaheuristics to deal with stochastic combinatorial optimization problems. Oper Res Perspect 2:62–72\nKellerer H, Pferschy U, Pisinger D (2004) Knapsack problems. Discrete mathematics and its applications. Springer, Berlin\nLin EY-H (1998) A bibliographical survey on some well-known non-standard knapsack problems. Inf Syst Oper Res 36(4):274–317\nMartello S, Pisinger D, Toth P (1999) Dynamic programming and strong bounds for the 0–1 knapsack problem. Manag Sci 45(3):414–424\nPatrick B (1995) Probability and measure. Wiley series in probability and mathematical statistics. Wiley, New York\nPisinger D (2005) Where are the hard knapsack problems? Comput Oper Res 32(9):2271–2284\nSilvano M, Paolo T (1990) Knapsack problems: algorithms and computer implementations. Wiley-Interscience series in discrete mathematics and optimization. Wiley, West Sussex\nVoss S, Maniezzo V, Stützle T (2009) Matheuristics: Hybridizing metaheuristics and mathematical programming (annals of information systems)\nWilbaut C, Hanafi S, Salhi S (2008) A survey of effective heuristics and their application to a variety of knapsack problems. IMA J Manag Math 19(3):227–244",{"VOID":140},"10.1007\u002Fs10878-020-00584-2","PUBLICATION","VERIFIED","2024-09-04T15:56:13.030+00:00","Auto Verify","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs10878-020-00584-2",[147,163],{"id":148,"sortIndex":19,"researcher":18,"roles":149,"affiliations":151,"properties":160},"f5bc1097-0f06-417a-84e9-89492ff101e4",[150],"AUTHOR",[152],{"id":153,"sortIndex":19,"affiliation":154,"properties":18},"32c06421-b021-4872-b2e0-59833e6085cd",{"id":153,"createTime":18,"updateTime":18,"relativeEntities":155,"slug":18,"properties":156,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":159,"statistic":18},[],{"title":157},{"VI":158},"Escuela de Matemáticas, Universidad Nacional de Colombia Sede Medellín, Medellín, Colombia",[],{"title":161},{"VI":162},"Fernando A. Morales",{"id":164,"sortIndex":112,"researcher":18,"roles":165,"affiliations":166,"properties":175},"f4e6c3e0-3a0b-490d-8f18-a0ff2d1e9131",[150],[167],{"id":168,"sortIndex":19,"affiliation":169,"properties":18},"050745ea-4fff-4291-9adb-98b92de66ecd",{"id":168,"createTime":18,"updateTime":18,"relativeEntities":170,"slug":18,"properties":171,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":174,"statistic":18},[],{"title":172},{"VI":173},"Departamento de Ciencias Matemáticas, Universidad EAFIT, Medellín, Colombia",[],{"title":176},{"VI":177},"Jairo A. Martínez","ARTICLE",{"url":145,"publisher":180,"properties":237},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":181,"slug":10,"properties":182,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":185,"manageAffiliations":206,"indexDatabases":217,"url":18,"thumbnailPath":18,"statistic":232,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"issn":183,"title":184},{"VOID":13},{"EN":15},[186,190,194,198,202],{"id":22,"createTime":18,"updateTime":18,"relativeEntities":187,"label":188,"description":189,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":25},{},{"id":28,"createTime":18,"updateTime":18,"relativeEntities":191,"label":192,"description":193,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":31},{},{"id":34,"createTime":18,"updateTime":18,"relativeEntities":195,"label":196,"description":197,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":37},{},{"id":40,"createTime":18,"updateTime":18,"relativeEntities":199,"label":200,"description":201,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":43},{},{"id":46,"createTime":18,"updateTime":18,"relativeEntities":203,"label":204,"description":205,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":49},{},[207,212],{"id":53,"createTime":18,"updateTime":18,"relativeEntities":208,"slug":18,"properties":209,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":211,"statistic":18},[],{"title":210},{"EN":57},[],{"id":60,"createTime":18,"updateTime":18,"relativeEntities":213,"slug":18,"properties":214,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":216,"statistic":18},[],{"title":215},{"EN":64},[66],[218,225],{"id":69,"indexDatabase":219,"url":80,"indexYears":81,"academicFieldIds":224,"indexDatabaseRanking":88},{"id":71,"createTime":18,"updateTime":18,"relativeEntities":220,"label":221,"description":222,"key":77,"publicationTags":223,"standard":18},[],{"EN":74,"VI":74},{"EN":74,"VI":76},[79],[83,84,85,86,87],{"id":90,"indexDatabase":226,"url":103,"indexYears":18,"academicFieldIds":231,"indexDatabaseRanking":18},{"id":92,"createTime":18,"updateTime":18,"relativeEntities":227,"label":228,"description":229,"key":99,"publicationTags":230,"standard":18},[],{"EN":95,"VI":95},{"EN":97,"VI":98},[101,102],[105,106],{"impactFactor":19,"impactFactorByYear":233,"i10Index":109,"i10IndexLast5Year":19,"totalPublication":110,"totalPublicationByYear":234,"totalCitation":113,"totalCitationByYear":235,"totalCitationPerPublication":117,"totalCitationPerPublicationByYear":236,"hindexLast5Year":110,"hindex":110},{},{"2003":112,"2004":109},{"2003":115,"2004":116},{"2003":115,"2004":119},{"pages":238,"volume":240},{"VOID":239},"234-278",{"VOID":241},"40","2020-05-28",2020,"ERROR_IN_GET_PLATFORM_ID","2026-08-20T01:51:34.809+00:00",[88,101],false,{"id":249,"createTime":250,"updateTime":251,"relativeEntities":252,"slug":253,"properties":254,"entityType":141,"verifyStatus":142,"verifyTime":265,"verifyNote":144,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":266,"fullTextUrl":18,"authors":267,"publicationType":178,"publisherRelationship":325,"citationCount":19,"citationInfo":388,"publishDate":391,"publishYear":389,"citationAnalyzeStatus":392,"lastCitationAnalyze":393,"indexDatabases":394,"openAccess":18,"references":18,"isForceReanalyzing":247},"d5e68570-a9f3-48d1-8107-07e224ae8834","2023-12-13T07:06:59.793+00:00","2026-07-27T19:59:46.110+00:00",[],"Reconfiguration-of-dominating-sets",{"abstract":255,"title":257,"gsPaper":259,"references":261,"doi":263},{"EN":256},"We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph G is a set S of vertices such that each vertex is either in S or has a neighbour in S. In a reconfiguration problem, the goal is to determine whether there exists a sequence of feasible solutions connecting given feasible solutions s and t such that each pair of consecutive solutions is adjacent according to a specified adjacency relation. Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex. For various values of k, we consider properties of \n                  \n                    \n                  \n                  $$D_k(G)$$\n                  \n                    \n                  \n                , the graph consisting of a node for each dominating set of size at most k and edges specified by the adjacency relation. Addressing an open question posed by Haas and Seyffarth, we demonstrate that \n                  \n                    \n                  \n                  $$D_{\\varGamma (G)+1}(G)$$\n                  \n                    \n                  \n                 is not necessarily connected, for \n                  \n                    \n                  \n                  $$\\varGamma (G)$$\n                  \n                    \n                  \n                 the maximum cardinality of a minimal dominating set in G. The result holds even when graphs are constrained to be planar, of bounded tree-width, or b-partite for \n                  \n                    \n                  \n                  $$b \\ge 3$$\n                  \n                    \n                  \n                . Moreover, we construct an infinite family of graphs such that \n                  \n                    \n                  \n                  $$D_{\\gamma (G)+1}(G)$$\n                  \n                    \n                  \n                 has exponential diameter, for \n                  \n                    \n                  \n                  $$\\gamma (G)$$\n                  \n                    \n                  \n                 the minimum size of a dominating set. On the positive side, we show that \n                  \n                    \n                  \n                  $$D_{n-\\mu }(G)$$\n                  \n                    \n                  \n                 is connected and of linear diameter for any graph G on n vertices with a matching of size at least \n                  \n                    \n                  \n                  $$\\mu +1$$\n                  \n                    \n                  \n                .",{"EN":258},"Reconfiguration of dominating sets",{"VOID":260},"[\"17563669425000947633\"]",{"VOID":262},"Bonamy M, Bousquet N (2013) Recoloring bounded treewidth graphs. Electron Notes Discret Math 44:257–262\nBonsma P (2012) The complexity of rerouting shortest paths. In: Proceedings of the mathematical foundations of computer science, pp 222–233\nBonsma P (2014) Independent set reconfiguration in cographs. In: Proceedings of the 40th international workshop on graph-theoretic concepts in computer science. Lecture notes in computer science, vol. 8747. Springer, Berlin, pp 105–116\nBonsma P, Cereceda L (2009) Finding paths between graph colourings: PSPACE-completeness and superpolynomial distances. Theor Comput Sci 410(50):5215–5226\nCereceda L, van den Heuvel J, Johnson M (2008) Connectedness of the graph of vertex-colourings. Discret Math 308(56):913–919\nCereceda L, van den Heuvel J, Johnson M (2009) Mixing 3-colourings in bipartite graphs. Eur J Comb 30(7):1593–1606\nCereceda L, van den Heuvel J, Johnson M (2011) Finding paths between 3-colorings. J Graph Theory 67(1):69–82\nDemaine ED, Demaine ML, Fox-Epstein E, Hoang DA, Ito T, Ono H, Otachi Y, Uehara R, Yamada T (2014) Polynomial-time algorithm for sliding tokens on trees. In: Proceedings of the 25th international symposium on algorithms and computation. Lecture notes in computer science, vol 8889. Springer, Berlin, pp 389–400\nFricke G, Hedetniemi SM, Hedetniemi ST, Hutson KR (2011) \\(\\gamma \\)-Graphs of graphs. Discuss Math Graph Theory 31(3):517–531\nGopalan P, Kolaitis PG, Maneva EN, Papadimitriou C (2009) The connectivity of boolean satisfiability: computational and structural dichotomies. SIAM J Comput 38(6):2330–2355\nHaas R, Seyffarth K (2014) The \\(k\\)-dominating graph. Graphs Comb 30(3):609–617\nHaddadan A, Ito T, Mouawad AE, Nishimura N, Ono H, Suzuki A, Tebbal Y (2015) The complexity of dominating set reconfiguration. In: Proceedings of the 14th algorithms and data structures symposium\nHearn RA, Demaine ED (2005) PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation. Theor Comput Sci 343(1–2):72–96\nIto T, Demaine ED (2011) Approximability of the subset sum reconfiguration problem. In: Proceedings of the 8th annual conference on theory and applications of models of computation, pp 58–69\nIto T, Demaine ED, Harvey NJA, Papadimitriou CH, Sideri M, Uehara R, Uno Y (2011) On the complexity of reconfiguration problems. Theor Comput Sci 412(12–14):1054–1065\nIto T, Kamiński M, Demaine ED (2012a) Reconfiguration of list edge-colorings in a graph. Discret Appl Math 160(15):2199–2207\nIto T, Kawamura K, Ono H, Zhou X (2012b) Reconfiguration of list L(2,1)-labelings in a graph. In: Proceedings of the 23rd international symposium on algorithms and computation, pp 34–43\nIto T, Kaminski M, Ono H (2014a) Fixed-parameter tractability of token jumping on planar graphs. In: Proceedings of the 25th international symposium on algorithms and computation. Lecture notes in computer science, vol 8889. Springer, Berlin, pp 208–219\nIto T, Kaminski M, Ono H, Suzuki A, Uehara R, Yamanaka K (2014b) On the parameterized complexity for token jumping on graphs. In: Theory and applications of models of computation. Lecture notes in computer science, vol 8402. Springer, Berlin, pp 341–351\nIto T, Nooka H, Zhou X (2015) Reconfiguration of vertex covers in a graph. In: Proceedings of the 25th international workshop on combinatorial algorithms. Lecture notes in computer science, vol 8986. Springer, Berlin, pp 164–175\nJohnson M, Kratsch D, Kratsch S, Patel V, Paulusma D (2014) Finding shortest paths between graph colourings. In: Proceedings of the 9th international symposium on parameterized and exact computation. Lecture notes in computer science, vol 8894. Springer, Berlin, pp 221–233\nKamiński M, Medvedev P, Milanič M (2011) Shortest paths between shortest paths. Theor Comput Sci 412(39):5205–5210\nKamiński M, Medvedev P, Milanič M (2012) Complexity of independent set reconfigurability problems. Theor Comput Sci 439:9–15\nLokshtanov D, Mouawad AE, Panolan F, Ramanujan M, Saurabh S (2015) Reconfiguration on sparse graphs. In: Proceedings of the 14th algorithms and data structures symposium\nMayr EW, Plaxton CG (1992) On the spanning trees of weighted graphs. Combinatorica 12(4):433–447\nMouawad AE, Nishimura N, Raman V, Simjour N, Suzuki A (2013) On the parameterized complexity of reconfiguration problems. In: Proceedings of the 8th international symposium on parameterized and exact computation, pp 281–294\nMouawad AE, Nishimura N, Raman V (2014) Vertex cover reconfiguration and beyond. In: Proceedings of the 25th international symposium on algorithms and computation. Lecture notes in computer science, vol 8889. Springer, Berlin, pp 452–463\nvan den Heuvel J (2013) The complexity of change. 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A dataset is k-anonymous if each record is identical to at least (k−1) other records in the dataset. The basic k-anonymization problem, which minimizes the number of dataset entries that must be suppressed to achieve k-anonymity, is NP-hard and hence not solvable both quickly and optimally in general. We apply parameterized complexity analysis to explore algorithmic options for restricted versions of this problem that occur in practice. We present the first fixed-parameter algorithms for this problem and identify key techniques that can be applied to this and other k-anonymization problems.",{"EN":405},"Fixed-parameter tractability of anonymizing data by suppressing entries",{"VOID":407},"[\"10948124758875378181\"]",{"VOID":409},"Aggarwal G, Feder T, Kenthapadi K, Motwani R, Panigrahy R, Thomas D, Zhu A (2005) Approximation algorithms for k-anonymity. J Priv Technol, paper 20051120001\nBrankovic L, Estivill-Castro V (1999) Privacy issues in knowledge discovery and data mining. In: Proceedings of Australian institute of computer ethics conference (AICEC99), pp 89–99\nBrankovic L, Miller M, Horak P, Wrightson G (1997) Usability of compromise-free statistical databases. In: Proceedings of the ninth international conference on scientific and statistical database management (SSDBM 1997). IEEE Press, New York, pp 144–154\nBonizzoni P, Della Vedova G, Dondi R (2007) Anonymizing binary tables is APX-hard. The Computing Research Repository (CoRR) 0707.0421. http:\u002F\u002Farxiv.org\u002Fabs\u002F0707.0421\nChaytor R (2006) Utility preserving k-anonymity. Technical report MUN-CS 2006-01, Dept Computer Science, Memorial University of Newfoundland\nChaytor R (2007) Allowing privacy protection algorithms to jump out of local optimums: an ordered greed framework. In: Bonchi F et al. (eds) Proceedings of the 1st SIGKDD international workshop on privacy, security, and trust in KDD (PinKDD’07). LNCS, vol 4890. Springer, Berlin, pp 33–55\nDowney R, Fellows M (1999) Parameterized complexity. Springer, Berlin\nEr MC (1988) A fast algorithm for generating set partitions. Comput J 31:283–284\nFernau H (2004) Complexity of a {0,1}-matrix problem. Australasian J Comb 29:273–300\nHorak P, Brankovic L, Miller M (1999) A combinatorial problem in database security. Discrete Appl Math 91:119–126\nIslam MZ, Brankovic L (2004) A framework for privacy preserving classification in data mining. In: Proceedings of the second workshop on Australasian information security, data mining and web intelligence, and software internationalisation (ACSW Frontiers 2004), pp 163–168\nMacDonald (2005) personal communication\nMeyerson A, Williams R (2004) On the complexity of optimal k-anonymity. In: Proceedings of 23rd ACM symposium on principles of database systems (PODS’04), pp 223–228\nNiedermeier R (2006) Invitation to fixed-parameter algorithms. Oxford University Press, Oxford\nSamarati P, Sweeney L (1998) Protecting privacy when disclosing information: k-anonymity and its enforcement through generalization and suppression. Technical report SRI-CSL-98-04, SRI International, Computer Science Laboratory\nSweeney L (2002) Achieving k-anonymity privacy protection using generalization and suppression. Int J Uncertain Fuzziness Knowl-Based Syst 10(5):571–588\nWang K, Yu P, Chakraborty S (2004) Bottom-up generalization: a data mining solution to privacy protection. In: Proceedings of 4th IEEE international conference on data mining (ICDM’04), pp 249–256\nWareham T (1999) Systematic parameterized complexity analysis in computational phonology. PhD thesis, Dept Computer Science, University of Victoria",{"VOID":411},"10.1007\u002Fs10878-009-9253-6","2024-06-24T23:00:22.413+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs10878-009-9253-6",[415,430,447],{"id":416,"sortIndex":19,"researcher":18,"roles":417,"affiliations":418,"properties":427},"05d5235a-b6de-458b-b896-a6a896251536",[150],[419],{"id":420,"sortIndex":19,"affiliation":421,"properties":18},"4462afe5-92d5-4835-bcc6-05a307d4a377",{"id":420,"createTime":18,"updateTime":18,"relativeEntities":422,"slug":18,"properties":423,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":426,"statistic":18},[],{"title":424},{"VI":425},"Faculty of Computer Science, University of New Brunswick, Fredericton, Canada",[],{"title":428},{"VI":429},"Patricia A. 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graph G is outer-1-planar with near-independent crossings if it can be drawn in the plane so that all vertices are on the outer face and \n                  \n                    \n                  \n                  $$|M_G(c_1)\\cap M_G(c_2)|\\le 1$$\n                  \n                    \n                  \n                 for any two distinct crossings \n                  \n                    \n                  \n                  $$c_1$$\n                  \n                    \n                  \n                 and \n                  \n                    \n                  \n                  $$c_2$$\n                  \n                    \n                  \n                 in G, where \n                  \n                    \n                  \n                  $$M_G(c)$$\n                  \n                    \n                  \n                 consists of the end-vertices of the two crossed edges that generate c. In Zhang and Liu (Total coloring of pseudo-outerplanar graphs, \n                  arXiv:1108.5009\n                  \n                ), it is showed that the total chromatic number of every outer-1-planar graph with near-independent crossings and with maximum degree at least 5 is \n                  \n                    \n                  \n                  $$\\Delta +1$$\n                  \n                    \n                  \n                . In this paper we extend the result to maximum degree 4 by proving that the total chromatic number of every outer-1-planar graph with near-independent crossings and with maximum degree 4 is exactly 5.",{"EN":542},"Total coloring of outer-1-planar graphs with near-independent crossings",{"VOID":136},{"VOID":545},"Auer C, Bachmaier C, Brandenburg FJ et al (2016) Outer 1-planar graphs. Algorithmica 74(4):1293–1320\nBehzad M (1965) Graphs and their chromatic numbers. Doctoral thesis, Michigan State University\nEggleton RB (1986) Rectilinear drawings of graphs. Utilitas Math 29:149–172\nVizing V (1968) Some unsolved problems in graph theory. Uspekhi Mat Nauk 23:117–134\nWang W, Zhang K (1999) \\(\\Delta \\)-Matchings and edge-face chromatic numbers. Acta Math Appl Sin 22:236–242\nWu JL, Hu D (2004) Total coloring of series-parallel graphs. ARS Comb 73:209–211\nYap HP (1996) Total colourings of graphs. Lecture notes in mathematics 1623. Springer, Berlin\nZhang X (2013) List total coloring of pseodo-outerplanar graphs. Discret Math 313:2297–2306\nZhang X (2014) Drawing complete multipartite graphs on the plane with restrictions on crossings. Acta Math Sin (Engl Ser) 30(12):2045–2053\nZhang X, Liu G Total coloring of pseudo-outerplanar graphs. arXiv:1108.5009\nZhang X, Liu G, Wu JL (2012) Edge covering pseudo-outerplanar graphs with forests. Discret Math 312:2788–2799\nZhang Z, Zhang J, Wang J (1988) The total chromatic number of some graphs. 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recent and very promising approach for combinatorial optimization is to embed local search into the framework of evolutionary algorithms. In this paper, we present such hybrid algorithms for the graph coloring problem. These algorithms combine a new class of highly specialized crossover operators and a well-known tabu search algorithm. Experiments of such a hybrid algorithm are carried out on large DIMACS Challenge benchmark graphs. Results prove very competitive with and even better than those of state-of-the-art algorithms. Analysis of the behavior of the algorithm sheds light on ways to further improvement.",{"EN":975},"Hybrid Evolutionary Algorithms for Graph Coloring",{"VOID":977},"[\"14770478819680990737\"]",{"VOID":979},"D. Br´elaz, \"New methods to color vertices of a graph,\" Communications of ACM, vol. 22, pp. 251–256, 1979.\nG.J. Chaitin, \"Register Allocation and Spilling via Graph Coloring,\" in Proc. of ACM SIGPLAN 82 Symposium on Compiler Construction, New York, 1982, pp. 98–105.\nM. Chams, A. Hertz, and D. de Werra, \"Some experiments with simulated annealing for coloring graphs,\" European Journal of Operational Research, vol. 32, pp. 260–266, 1987.\nD. Costa, A. Hertz, and O. Dubuis, \"Embedding of a sequential procedure within an evolutionary algorithm for coloring problems in graphs,\" Journal of Heuristics, vol. 1, no. 1, pp. 105–128, 1995.\nL. Davis, Handbook of Genetic Algorithms, Van Nostrand Reinhold: New York, 1991.\nR. Dorne and J.K. Hao, \"Tabu search for graph coloring, T-coloring and set T-colorings,\" in Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, S. Voss, S. Martello, I.H. Osman and C. Roucairol (Eds.), Kluwer Academic Publishers, 1999, Chapter 6, pp. 77–92.\nR. Dorne and J.K. Hao, \"A new genetic local search algorithm for graph coloring,\" Lecture Notes in Computer Science 1498, Springer-Verlag, 1998, pp. 745–754.\nE. Falkenauer, \"A hybrid grouping genetic algorithm for bin packing,\" Journal of Heuristics, vol. 2, no. 1, pp. 5–30, 1996.\nC. Fleurent and J.A. Ferland, \"Object-Oriented Implementation of Heuristic Search Methods for Graph Coloring, Maximum Clique, and Satisfiability,\" in Proceedings of the 2nd DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, D.S. Johnson and M.A. Trick (Eds.), American Mathematical Society, vol. 26, 1996, pp. 619–652.\nB. Freisleben and P. Merz, \"New genetic local search operators for the travelling salesman problem,\" Lecture Notes in Computer Science 1141, Springer-Verlag, 1996, pp. 890–899.\nA. Gamst, \"Some lower bounds for a class of frequency assignment problems,\" IEEE Transactions on Vehicular Technology, vol. 35, no. 1, pp. 8–14, 1986.\nM.R. Garey and D.S. Johnson, Computer and Intractability, Freeman: San Francisco, 1979.\nF. Glover and M. Laguna, Tabu Search, Kluwer Academic Publishers, 1997.\nD.E. Goldberg, Genetic Algorithms in Search; Optimization and Machine Learning, Addison-Wesley, 1989.\nJ.J. Greffenstette, \"Incorporating problem specific knowledge into a genetic algorithm,\" in Genetic Algorithms and Simulated Annealing, L. Davis (Ed.), Morgan Kauffmann Publishers, 1987, pp. 42–60.\nA. Hertz and D. de Werra, \"Using tabu search techniques for graph coloring,\" Computing, vol. 39, pp. 345–351, 1987.\nJ.H. Holland, Adaptation and Artificial Systems, University of Michigan Press: Ann Arbor, 1975.\nD.S. Johnson, C.R. Aragon, L.A. McGeoch, and C. Schevon, \"Optimization by simulated annealing: an experimental evaluation; part II, graph coloring and number partitioning,\" Operations Research, vol. 39, no. 3, pp. 378–406, 1991.\nD.S. Johnson and M.A. Trick (Eds.), in Proceedings of the 2nd DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26, American Mathematical Society, 1996.\nF.T. Leighton, \"A graph coloring algorithm for large scheduling problems,\" Journal of Research of the National Bureau Standard, vol. 84, pp. 489–505, 1979.\nP. Merz and B. Freisleben, \"A Genetic Local Search Approach to the Quadratic Assignment Problem,\" in Proc. of the 7th International Conference of Genetic Algorithms, Morgan Kauffman Publishers, 1997, pp. 465–472.\nC. Morgenstern, \"Distributed Coloration Neighborhood Search,\" in Proceedings of the 2nd DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, D.S. Johnson and M.A. Trick (Eds.), American Mathematical Society, vol. 26, 1996, pp. 335–358.\nH. M¨uehlenbein, M. Gorges-Schleuter, and O. Kr¨amer, \"Evolution algorithms in combinatorial optimization,\" Parallel Computing, vol. 7, pp. 65–88, 1988.\nP.M. Pardalos, T. Mavridou, and J. Xue, \"The graph coloring problem: A bibliographic survey,\" in Handbook of Combinatorial Optimization, D.-Z. Du and P. Pardalos (Eds.), Kluwer Academic Publishers, vol. 2, 1998, pp. 331–395.",{"VOID":981},"10.1023\u002FA:1009823419804","2024-05-06T21:59:17.928+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1023\u002FA:1009823419804",[985,1000],{"id":986,"sortIndex":19,"researcher":18,"roles":987,"affiliations":988,"properties":997},"620b9379-d884-4eae-8d6b-b604417095f0",[150],[989],{"id":990,"sortIndex":19,"affiliation":991,"properties":18},"4ab29059-2a6a-4459-b2e9-8e09b399ee0f",{"id":990,"createTime":18,"updateTime":18,"relativeEntities":992,"slug":18,"properties":993,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":996,"statistic":18},[],{"title":994},{"VI":995},"LGI2P, EMA-EERIE, Parc Scientifique Georges Besse, Nîmes, France",[],{"title":998},{"VI":999},"Philippe Galinier",{"id":1001,"sortIndex":112,"researcher":18,"roles":1002,"affiliations":1003,"properties":1012},"aaa96c30-93ed-40b5-909a-60fb53aae1f2",[150],[1004],{"id":1005,"sortIndex":19,"affiliation":1006,"properties":18},"604d7ac4-75ec-4698-8d3c-d2735bf9cab3",{"id":1005,"createTime":18,"updateTime":18,"relativeEntities":1007,"slug":18,"properties":1008,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1011,"statistic":18},[],{"title":1009},{"VI":1010},"LERIA, Université d’Angers, Angers, France",[],{"title":1013,"gsAuthor":1015},{"VI":1014},"Jin-Kao Hao",{"VOID":1016},"[\"6k2WBGIAAAAJ\"]",{"url":983,"publisher":1018,"properties":1075},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1019,"slug":10,"properties":1020,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":1023,"manageAffiliations":1044,"indexDatabases":1055,"url":18,"thumbnailPath":18,"statistic":1070,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"issn":1021,"title":1022},{"VOID":13},{"EN":15},[1024,1028,1032,1036,1040],{"id":22,"createTime":18,"updateTime":18,"relativeEntities":1025,"label":1026,"description":1027,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":25},{},{"id":28,"createTime":18,"updateTime":18,"relativeEntities":1029,"label":1030,"description":1031,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":31},{},{"id":34,"createTime":18,"updateTime":18,"relativeEntities":1033,"label":1034,"description":1035,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":37},{},{"id":40,"createTime":18,"updateTime":18,"relativeEntities":1037,"label":1038,"description":1039,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":43},{},{"id":46,"createTime":18,"updateTime":18,"relativeEntities":1041,"label":1042,"description":1043,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":49},{},[1045,1050],{"id":53,"createTime":18,"updateTime":18,"relativeEntities":1046,"slug":18,"properties":1047,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1049,"statistic":18},[],{"title":1048},{"EN":57},[],{"id":60,"createTime":18,"updateTime":18,"relativeEntities":1051,"slug":18,"properties":1052,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1054,"statistic":18},[],{"title":1053},{"EN":64},[66],[1056,1063],{"id":69,"indexDatabase":1057,"url":80,"indexYears":81,"academicFieldIds":1062,"indexDatabaseRanking":88},{"id":71,"createTime":18,"updateTime":18,"relativeEntities":1058,"label":1059,"description":1060,"key":77,"publicationTags":1061,"standard":18},[],{"EN":74,"VI":74},{"EN":74,"VI":76},[79],[83,84,85,86,87],{"id":90,"indexDatabase":1064,"url":103,"indexYears":18,"academicFieldIds":1069,"indexDatabaseRanking":18},{"id":92,"createTime":18,"updateTime":18,"relativeEntities":1065,"label":1066,"description":1067,"key":99,"publicationTags":1068,"standard":18},[],{"EN":95,"VI":95},{"EN":97,"VI":98},[101,102],[105,106],{"impactFactor":19,"impactFactorByYear":1071,"i10Index":109,"i10IndexLast5Year":19,"totalPublication":110,"totalPublicationByYear":1072,"totalCitation":113,"totalCitationByYear":1073,"totalCitationPerPublication":117,"totalCitationPerPublicationByYear":1074,"hindexLast5Year":110,"hindex":110},{},{"2003":112,"2004":109},{"2003":115,"2004":116},{"2003":115,"2004":119},{"pages":1076,"volume":1078},{"VOID":1077},"379-397",{"VOID":1079},"3",{"total":19,"publishYear":1081,"statisticByYear":1082},1999,{},"1999-12-01","2026-07-18T17:11:12.335+00:00",[88,101],{"id":1087,"createTime":1088,"updateTime":1089,"relativeEntities":1090,"slug":1091,"properties":1092,"entityType":141,"verifyStatus":142,"verifyTime":1103,"verifyNote":144,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1104,"fullTextUrl":18,"authors":1105,"publicationType":178,"publisherRelationship":1136,"citationCount":311,"citationInfo":1199,"publishDate":1201,"publishYear":243,"citationAnalyzeStatus":392,"lastCitationAnalyze":1202,"indexDatabases":1203,"openAccess":18,"references":18,"isForceReanalyzing":247},"9fb73179-cfdf-487c-8124-2676ba99bea5","2024-01-16T05:08:00.017+00:00","2026-07-18T13:13:35.291+00:00",[],"Marginal-contributions-and-derivatives-for-set-functions-in-cooperative-games",{"abstract":1093,"title":1095,"gsPaper":1097,"references":1099,"doi":1101},{"EN":1094},"A cooperative game (N, v) is said to be monotone if $$v(S)\\ge v(T)$$ for all $$T\\subseteq S\\subseteq N$$, and k-monotone for $$k\\ge 2$$ if $$v(\\cup _{i=1}^k S_i)\\ge \\sum _{I:\\,\\emptyset \\ne I\\subseteq \\{1,\\ldots , k\\}} (-1)^{|I|-1} v(\\cap _{i\\in I} S_i)$$ for all k subsets $$S_1,\\ldots ,S_k$$ of N. Call a set function v totally monotone if it is monotone and k-monotone for all $$k\\ge 2$$. To generalize both of marginal contribution and Harsanyi dividend, we define derivatives of v as $$v^{(0)}=v$$ and for pairwise disjoint subsets $$R_1,\\dots ,R_k$$ of N, $$v'_{R_1}(S)=v(S\\cup R_1)-v(S)$$ for $$S\\subseteq N\\setminus R_1$$, and $$v^{(k)}_{R1,\\dots ,R_k}(S)=(v^{(k-1)}_{R_1,\\dots ,R_{k-1}})'_{R_k}(S)$$ for $$S\\subseteq N\\setminus \\cup _{i=1}^k R_i$$. We generalize the equivalence between convexity and monotonicity of marginal contribution of v to total monotonicity and higher derivatives of v from several aspects. We also give the Taylor expansion of any game (set function) v.",{"EN":1096},"Marginal contributions and derivatives for set functions in cooperative games",{"VOID":1098},"[\"2266456615555646448\"]",{"VOID":1100},"Asano T, Kojima H (2014) Modularity and monotonicity of games. Math Meth Oper Res 80:29–46\nBranzei R, Dimitrov D, Tijs S (2008) Models in cooperative game theory. Springer, Berlin\nChateauneuf A, Jaffray J-Y (1989) Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Math Soc Sci 17:263–283\nGrabisch M (2016) Set functions, games and capacities in decision making. Springer, Berlin\nHarsanyi JC (1959) A bargaining model for cooperative \\(n\\)-person games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games IV, Princeton University Press, Princeton, pp 325–355\nHarsanyi JC (1963) A simplified bargaining model for cooperative \\(n\\)-person game. Internat Econ Rev 4:194–220\nIchiishi T (1981) Super modularity: application to convex games and to the greedy algorithm for LP. J Econ Theory 25:283–286\nKajii A, Kojima H, Ui T (2007) Cominimum additive operators. J Math Econ 43:18–230\nPeleg B, Sudhölter P (2003) Introduction to the theory of cooperative games. Kluver, Dorderecht\nShafer G (1976) A mathematical theory of evidence. Priceton University Press, Priceton\nShapley LS (1953) A value for \\(n\\)-person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games, vol II. Princeton University Press, Princeton, pp 307–317\nShapley LS (1971) Cores of convex games. Internat J Game Theory 1(1):11–26",{"VOID":1102},"10.1007\u002Fs10878-020-00526-y","2024-05-27T22:57:56.870+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs10878-020-00526-y",[1106,1121],{"id":1107,"sortIndex":19,"researcher":18,"roles":1108,"affiliations":1109,"properties":1118},"636ca61d-cc13-4871-be46-ce27387447c9",[150],[1110],{"id":1111,"sortIndex":19,"affiliation":1112,"properties":18},"c6a766e5-3a58-4f8a-8c42-40612da3dc7c",{"id":1111,"createTime":18,"updateTime":18,"relativeEntities":1113,"slug":18,"properties":1114,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1117,"statistic":18},[],{"title":1115},{"VI":1116},"Shanghai Business School, Shanghai, People’s Republic of China",[],{"title":1119},{"VI":1120},"Daniel Li Li",{"id":1122,"sortIndex":112,"researcher":18,"roles":1123,"affiliations":1124,"properties":1133},"d8206f64-6b30-4216-b4d2-f68950fbb93d",[150],[1125],{"id":1126,"sortIndex":19,"affiliation":1127,"properties":18},"b6ca762d-c819-4242-8ce1-3b395dc6b00a",{"id":1126,"createTime":18,"updateTime":18,"relativeEntities":1128,"slug":18,"properties":1129,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1132,"statistic":18},[],{"title":1130},{"VI":1131},"School of Management, Shanghai University, Shanghai, People’s Republic of China",[],{"title":1134},{"VI":1135},"Erfang Shan",{"url":1104,"publisher":1137,"properties":1194},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1138,"slug":10,"properties":1139,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":1142,"manageAffiliations":1163,"indexDatabases":1174,"url":18,"thumbnailPath":18,"statistic":1189,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"issn":1140,"title":1141},{"VOID":13},{"EN":15},[1143,1147,1151,1155,1159],{"id":22,"createTime":18,"updateTime":18,"relativeEntities":1144,"label":1145,"description":1146,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":25},{},{"id":28,"createTime":18,"updateTime":18,"relativeEntities":1148,"label":1149,"description":1150,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":31},{},{"id":34,"createTime":18,"updateTime":18,"relativeEntities":1152,"label":1153,"description":1154,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":37},{},{"id":40,"createTime":18,"updateTime":18,"relativeEntities":1156,"label":1157,"description":1158,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":43},{},{"id":46,"createTime":18,"updateTime":18,"relativeEntities":1160,"label":1161,"description":1162,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":49},{},[1164,1169],{"id":53,"createTime":18,"updateTime":18,"relativeEntities":1165,"slug":18,"properties":1166,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1168,"statistic":18},[],{"title":1167},{"EN":57},[],{"id":60,"createTime":18,"updateTime":18,"relativeEntities":1170,"slug":18,"properties":1171,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1173,"statistic":18},[],{"title":1172},{"EN":64},[66],[1175,1182],{"id":69,"indexDatabase":1176,"url":80,"indexYears":81,"academicFieldIds":1181,"indexDatabaseRanking":88},{"id":71,"createTime":18,"updateTime":18,"relativeEntities":1177,"label":1178,"description":1179,"key":77,"publicationTags":1180,"standard":18},[],{"EN":74,"VI":74},{"EN":74,"VI":76},[79],[83,84,85,86,87],{"id":90,"indexDatabase":1183,"url":103,"indexYears":18,"academicFieldIds":1188,"indexDatabaseRanking":18},{"id":92,"createTime":18,"updateTime":18,"relativeEntities":1184,"label":1185,"description":1186,"key":99,"publicationTags":1187,"standard":18},[],{"EN":95,"VI":95},{"EN":97,"VI":98},[101,102],[105,106],{"impactFactor":19,"impactFactorByYear":1190,"i10Index":109,"i10IndexLast5Year":19,"totalPublication":110,"totalPublicationByYear":1191,"totalCitation":113,"totalCitationByYear":1192,"totalCitationPerPublication":117,"totalCitationPerPublicationByYear":1193,"hindexLast5Year":110,"hindex":110},{},{"2003":112,"2004":109},{"2003":115,"2004":116},{"2003":115,"2004":119},{"pages":1195,"volume":1197},{"VOID":1196},"849-858",{"VOID":1198},"39",{"total":311,"publishYear":243,"statisticByYear":1200},{"2023":112,"2024":112},"2020-01-13","2026-07-18T13:13:35.290+00:00",[88,101],{"id":1205,"createTime":1206,"updateTime":1207,"relativeEntities":1208,"slug":1209,"properties":1210,"entityType":141,"verifyStatus":142,"verifyTime":1221,"verifyNote":144,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1222,"fullTextUrl":18,"authors":1223,"publicationType":178,"publisherRelationship":1252,"citationCount":19,"citationInfo":1315,"publishDate":1318,"publishYear":1316,"citationAnalyzeStatus":392,"lastCitationAnalyze":1319,"indexDatabases":1320,"openAccess":18,"references":18,"isForceReanalyzing":247},"022da19b-ed43-48c1-80f4-cb6571a61088","2024-02-12T02:03:53.251+00:00","2026-07-15T19:07:01.669+00:00",[],"On-broadcasting-in-unicyclic-graphs",{"abstract":1211,"title":1213,"gsPaper":1215,"references":1217,"doi":1219},{"EN":1212},"\n                        Broadcasting is an information dissemination problem in a connected network, in which one node, called the originator, disseminates a message to all other nodes by placing a series of calls along the communication lines of the network. Finding the broadcast time of a vertex in an arbitrary graph is NP-complete. The polynomial time solvability is shown only for trees. In this paper we present a linear algorithm that determines the broadcast time of any originator in an arbitrary unicyclic graph. As a byproduct, we find a broadcast center of the unicyclic graph. We also present an O(|V|+k\n                        2) algorithm to find the broadcast time of an arbitrary unicyclic graph, where k is the length of the cycle. In the last section we give tight lower and upper bounds on broadcast time of a spanning tree based on the broadcast time of the unicyclic graph.",{"EN":1214},"On broadcasting in unicyclic graphs",{"VOID":1216},"[\"16093352552379800143\"]",{"VOID":1218},"Aiello W, Chung F, Lu L (2001) Random evolution in massive graphs. In: Proceedings of the 42nd annual IEEE symposium on foundations of computer science, FOCS’01, pp 510–519\nBar-Noy A, Guha S, Naor J, Schieber B (1998) Multicasting in heterogeneous networks. In: Proceedings of ACM symposium on theory of computing, STOC’98, pp 18–36\nBeier R, Sibeyn JF (2000) A powerful heuristic for telephone gossiping. In: Proceedings of the 7th international colloquium on structural information & communication complexity, SIROCCO’00, L’Aquila, Italy, pp 17–36\nDoar MB (1996) A better model for generating test networks (1996) In: IEEE GLOBECOM’96, London, UK, pp 152–158\nElkin M, Kortsarz G (2002) A combinatorial logarithmic approximation algorithm for the directed telephone broadcast problem. In: Proceedings of ACM Symposium on Theory of Computing, STOC’02, pp 438–447\nElkin M, Kortsarz G (2003) Sublogarithmic approximation for telephone multicast: path out of jungle. In: Proceedings of symposium on discrete algorithms, SODA’03, Baltimore, MD, pp 76–85\nFeige U, Peleg D, Raghavan P, Upfal E (1990) Randomized broadcast in networks. In: Proceedings of international symposium on algorithms, SIGAL’90, pp 128–137\nFraigniaud P, Lazard E (1994) Methods and problems of communication in usual networks. Discrete Appl Math 53:79–133\nFraigniaud P, Vial S (1997a) Approximation algorithms for broadcasting and gossiping. J Parallel Distributed Comput 43(1):47–55\nFraigniaud P, Vial S (1997b) Heuristic algorithms for personalized communication problems in point-to-point networks. In: Proceedings of the 4th colloquium on structural information and communication complexity, SIROCCO’97, pp 240–252\nFraigniaud P, Vial S (1999) Comparison of heuristics for one-to-all and all-to-all communication in partial meshes. Parallel Process Lett 9(1):9–20\nHarutyunyan HA, Maraachlian E (2007) Linear algorithm for broadcasting in unicyclic graphs. In: Proceedings of 13th annual COCOON, Banff, Canada, pp 372–383\nHarutyunyan HA, Shao B (2006) An efficient heuristic for broadcasting in networks. J Parallel Distributed Comput 66(1):68–76\nHedetniemi SM, Hedetniemi ST, Liestman AL (1988) A survey of gossiping and broadcasting in communication networks. Networks 18:319–349\nHromkovic J, Klasing R, Monien B, Peine R (1996) Dissemination of information in interconnection networks. In: Du D-Z, Hsu DF (eds) Combinatorial network theory. Kluwer Academic, Dordrecht, pp 125–212\nJohnson D, Garey M (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco\nKortsarz G, Peleg D (1995) Approximation algorithms for minimum time broadcast. SIAM J Discrete Math 8:401–427\nRavi R (1994) Rapid rumor ramification: Approximating the minimum broadcast time. In: Proceedings of 35th symposium on foundation of computer science, FOCS’94, pp 202–213\nSlater PJ, Cockayne EJ, Hedetniemi ST (1981) Information dissemination in trees. SIAM J Comput 10(4):692–701\nScheuerman P, Wu G (1984) Heuristic algorithms for broadcasting in point-to-point computer network. IEEE Trans Comput C 33(9):804–811\nZegura EW, Calvert K, Bhattacharjee S (1996) How to model an internetwork. In: Proceedings of the IEEE conference on computer communications, INFOCOM’96, San Francisco, CA, pp 804–814",{"VOID":1220},"10.1007\u002Fs10878-008-9160-2","2024-05-15T14:05:13.073+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs10878-008-9160-2",[1224,1239],{"id":1225,"sortIndex":19,"researcher":18,"roles":1226,"affiliations":1227,"properties":1236},"2bb83aac-6aab-4862-8a3e-6f3f49923ace",[150],[1228],{"id":1229,"sortIndex":19,"affiliation":1230,"properties":18},"400d35da-a9a0-4566-a074-5a9fc059c296",{"id":1229,"createTime":18,"updateTime":18,"relativeEntities":1231,"slug":18,"properties":1232,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1235,"statistic":18},[],{"title":1233},{"VI":1234},"Department of Computer Science, Concordia University, Montreal, Canada",[],{"title":1237},{"VI":1238},"Hovhannes A. 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Our objective is to minimize the makespan for agent A, subject to an upper bound on the makespan for agent B. When the number of machines, denoted by \n                  \n                    \n                  \n                  $$m$$\n                  \n                    \n                  \n                , is chosen arbitrarily, we provide an \n                  \n                    \n                  \n                  $$O(n)$$\n                  \n                    \n                  \n                 algorithm with performance ratio \n                  \n                    \n                  \n                  $$2-\\frac{1}{m}$$\n                  \n                    \n                  \n                , i.e., the makespan for agent A given by the algorithm is no more than \n                  \n                    \n                  \n                  $$2-\\frac{1}{m}$$\n                  \n                    \n                  \n                 times the optimal value, while the makespan for agent B is no more than \n                  \n                    \n                  \n                  $$2-\\frac{1}{m}$$\n                  \n                    \n                  \n                 times the threshold value. This ratio is proved to be tight. Moreover, when \n                  \n                    \n                  \n                  $$m=2$$\n                  \n                    \n                  \n                , we present an \n                  \n                    \n                  \n                  $$O(nlogn)$$\n                  \n                    \n                  \n                 algorithm with performance ratio \n                  \n                    \n                  \n                  $$\\frac{1+\\sqrt{17}}{4}\\approx 1.28$$\n                  \n                    \n                  \n                 which is smaller than \n                  \n                    \n                  \n                  $$\\frac{3}{2}$$\n                  \n                    \n                  \n                . The ratio is weakly tight.",{"EN":1331},"Two approximation algorithms for two-agent scheduling on parallel machines to minimize makespan",{"VOID":1333},"[\"16314908153693058438\"]",{"VOID":1335},"Agnetis A, Mirchandani PB, Pacciarelli D, Pacifici A (2004) Scheduling problem with two competing agents. Oper Res 52:229–242\nAgnetis A, Pacciarelli D, Pacifici A (2007) Multi-agent single machine scheduling. Ann Oper Res 150:3–15\nAgnetis A, Pascale G, Pacciarelli D (2009) A Lagrangian approach to single-machine scheduling problems with two competing agents. J Sched 12:401–415\nBrewer PJ, Plott CR (1996) A binary conflict ascending price (BICAP) mechanism for the decentralized allocation of the right to use railroad tracks. Int J Ind Organ 14:857–886\nBaker KR, Smith JC (2003) A multiple-criterion model for machine scheduling. J Sched 6:7–16\nBalasubramanian H, Fowler J, Keha A, Pfund M (2009) Scheduling interfering job sets on parallel machines. Eur J Oper Res 199:55–67\nCheng TCE, Ng CT, Yuan JJ (2006) Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theor Comput Sci 362:273–281\nCheng TCE, Ng CT, Yuan JJ (2008) Multi-agent scheduling on a single machine with max-form criteria. Eur J Oper Res 188:603–609\nElvikis D, Hamacher HW, T’kindt V (2010) Scheduling two agents on uniform parallel machines with makespan and cost functions. J Sched 14:471–481\nElvikis D, T’kindt V (2012) Two-agent scheduling on uniform parallel machines with min-max criteria. Ann Oper Res. doi:10.1007\u002Fs10479-012-1099-0\nFan BQ, Cheng TCE, Li SS, Feng Q (2013) Bounded parallel-batching scheduling with two competing agents. J Sched 16:261–271\nGraham RL (1966) Bounds for certain multiprocessing anomalies. Bell Syst Tech J 45:1563–1581\nGraham RL (1969) Bounds on multiprocessing timing anomalies. SIAM J Appl Math 17:416–429\nGraham RL, Lawler EL, Lenstra JK (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discret Math 5:287–326\nLee K, Choi B-C, Leung JY-T, Pinedo ML (2009) Approximation algorithms for multi-agent scheduling to minimize total weighted completion time. Inf Process Lett 109:913–917\nLeung JY-T, Pinedo M, Wan G (2010) Competitive two-agent scheduling and its applications. Oper Res 58:458–469\nLuo W, Chen L, Zhang G (2012) Approximation schemes for two-machine flow shop scheduling with two agents. J Comb Optim 24:229–239\nLi S, Yuan JJ (2012) Unbounded parallel-batching scheduling with two competitive agents. J Sched 15:629–640\nNg CT, Cheng TCE, Yuan JJ (2006) A note on the complexity of the problem of two-agent scheduling on a single machine. J Comb Optim 12:387–394\nSchultz DC, Oh S-H, Grecas CF, Albani M, Sanchez J, Arbib C, Arvia V, Servilio M, Del Sorbo F, Giralda A, Lombardi G (2002) A QoS concept for packet oriented S-UMTS services. In: Proceedings of the 1st Mobile Summit, Thessaloniki, Greece\nSaule E, Trystram D (2009) Multi-users scheduling in parallel systems. In: Proc. of IEEE international parallel and distributed processing symposium 2009, Washington, DC, USA, May 2009, pp 1–9\nZhao K, Lu X (2013) Approximation schemes for two-agent scheduling on parallel machines. 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