Solving diameter-constrained minimum spanning tree problems by constraint programming
The diameter‐constrained minimum spanning tree problem consists in finding a minimum spanning tree of a given graph, subject to the constraint that the maximum number of edges between any two vertices in the tree is bounded from above by a given constant. This problem typically models network design...
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| Veröffentlicht in: | International transactions in operational research Jg. 17; H. 5; S. 653 - 665 |
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| Sprache: | Englisch |
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Oxford, UK
Blackwell Publishing Ltd
01.09.2010
Wiley |
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| ISSN: | 0969-6016, 1475-3995 |
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| Abstract | The diameter‐constrained minimum spanning tree problem consists in finding a minimum spanning tree of a given graph, subject to the constraint that the maximum number of edges between any two vertices in the tree is bounded from above by a given constant. This problem typically models network design applications where all vertices communicate with each other at a minimum cost, subject to a given quality requirement. We propose alternative formulations using constraint programming that circumvent weak lower bounds yielded by most mixed‐integer programming formulations. Computational results show that the proposed formulation, combined with an appropriate search procedure, solves larger instances and is faster than other approaches in the literature. |
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| AbstractList | The diameter-constrained minimum spanning tree problem consists in finding a minimum spanning tree of a given graph, subject to the constraint that the maximum number of edges between any two vertices in the tree is bounded from above by a given constant. This problem typically models network design applications where all vertices communicate with each other at a minimum cost, subject to a given quality requirement. We propose alternative formulations using constraint programming that circumvent weak lower bounds yielded by most mixed-integer programming formulations. Computational results show that the proposed formulation, combined with an appropriate search procedure, solves larger instances and is faster than other approaches in the literature. [PUBLICATION ABSTRACT] The diameter‐constrained minimum spanning tree problem consists in finding a minimum spanning tree of a given graph, subject to the constraint that the maximum number of edges between any two vertices in the tree is bounded from above by a given constant. This problem typically models network design applications where all vertices communicate with each other at a minimum cost, subject to a given quality requirement. We propose alternative formulations using constraint programming that circumvent weak lower bounds yielded by most mixed‐integer programming formulations. Computational results show that the proposed formulation, combined with an appropriate search procedure, solves larger instances and is faster than other approaches in the literature. |
| Author | Noronha, Thiago F. Ribeiro, Celso C. Santos, Andréa C. |
| Author_xml | – sequence: 1 givenname: Thiago F. surname: Noronha fullname: Noronha, Thiago F. organization: Department of Computer Science, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-010, BrazilE-mail tfn@dcc.ufmg.br – sequence: 2 givenname: Celso C. surname: Ribeiro fullname: Ribeiro, Celso C. organization: Department of Computer Science, Universidade Federal Fluminense, Rua Passo da Pátria 156, Niterói, 24210-240, BrazilE-mail celso@ic.uff.br – sequence: 3 givenname: Andréa C. surname: Santos fullname: Santos, Andréa C. organization: Blaise Pascal University, LIMOS, Complexe Scientifique des Cézeaux, Aubière 63173, FranceE-mail andrea@isima.fr |
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| Keywords | diameter constrained spanning trees bounded-diameter Spanning trees constraint programming |
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| References_xml | – reference: Hooker, J.N., 2007. Integrated Methods for Optimization. Springer, New York. – reference: Gouveia, L., Magnanti, T.L., 2003. Network flow models for designing diameter-constrained minimum-spanning and Steiner trees. Networks 41, 159-173. – reference: Trick, M.A., 2003. Integer and constraint programming approaches for round-robin tournament scheduling. Lecture Notes in Computer Science 2740, 63-77. – reference: Miller, C.E., Tucker, A.W., Zemlin, R.A., 1960. Integer programming formulations and traveling salesman problems. Journal of the ACM 7, 326-329. – reference: Raymond, K., 1989. A tree-based algorithm for distributed mutual exclusion. ACM Transactions on Computers 7, 61-77. – reference: Desrochers, M., Laporte, G., 1991. Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints. Operations Research Letters 10, 27-36. – reference: Walsh, T., Rossi, F., Van Beek, P., 2006. Handbook of Constraint Programming. Elsevier, Amsterdam. – reference: Santos, A.C., Lucena, A.P., Ribeiro, C.C., 2004. Solving diameter constrained minimum spanning tree problem in dense graphs. Lecture Notes in Computer Science 3059, 458-467. – reference: Achuthan, N.R., Caccetta, L., Caccetta, P.A., Geelen, J.F., 1994. Computational methods for the diameter restricted minimum weight spanning tree problem. Australasian Journal of Combinatorics 10, 51-71. – reference: Bookstein, A., Klein, S.T., 2001. Compression of correlated bitvectors. Information Systems 16, 110-118. – reference: Van Hentenryck, P., 1999. The OPL Optimization Programming Language. MIT Press, Cambridge. – reference: Deo, N., Abdalla, A., 2000. Computing a diameter-constrained minimum spanning tree in parallel. Lecture Notes in Computer Science 1767, 17-31. – reference: Handler, G.Y., 1978. Minimax location of a facility in an undirected graph. Transportation Science 7, 287-293. – volume: 7 start-page: 326 year: 1960 end-page: 329 article-title: Integer programming formulations and traveling salesman problems publication-title: Journal of the ACM – volume: 10 start-page: 51 year: 1994 end-page: 71 article-title: Computational methods for the diameter restricted minimum weight spanning tree problem publication-title: Australasian Journal of Combinatorics – volume: 10 start-page: 27 year: 1991 end-page: 36 article-title: Improvements and extensions to the Miller–Tucker–Zemlin subtour elimination constraints publication-title: Operations Research Letters – start-page: 297 year: 1992 end-page: 304 – volume: 1767 start-page: 17 year: 2000 end-page: 31 article-title: Computing a diameter‐constrained minimum spanning tree in parallel publication-title: Lecture Notes in Computer Science – volume: 3059 start-page: 458 year: 2004 end-page: 467 article-title: Solving diameter constrained minimum spanning tree problem in dense graphs publication-title: Lecture Notes in Computer Science – year: 2007 – start-page: 592 year: 1994 end-page: 599 – year: 2006 – volume: 16 start-page: 110 year: 2001 end-page: 118 article-title: Compression of correlated bitvectors publication-title: Information Systems – year: 2000 – volume: 7 start-page: 61 year: 1989 end-page: 77 article-title: A tree‐based algorithm for distributed mutual exclusion publication-title: ACM Transactions on Computers – volume: 2740 start-page: 63 year: 2003 end-page: 77 article-title: Integer and constraint programming approaches for round‐robin tournament scheduling publication-title: Lecture Notes in Computer Science – volume: 7 start-page: 287 year: 1978 end-page: 293 article-title: Minimax location of a facility in an undirected graph publication-title: Transportation Science – start-page: 178 year: 2005 end-page: 185 – volume: 41 start-page: 159 year: 2003 end-page: 173 article-title: Network flow models for designing diameter‐constrained minimum‐spanning and Steiner trees publication-title: Networks – year: 1999 – volume: 10 start-page: 51 year: 1994 ident: e_1_2_6_3_1 article-title: Computational methods for the diameter restricted minimum weight spanning tree problem publication-title: Australasian Journal of Combinatorics – ident: e_1_2_6_14_1 doi: 10.1145/58564.59295 – start-page: 297 volume-title: Optimization Techniques and Applications year: 1992 ident: e_1_2_6_2_1 – ident: e_1_2_6_5_1 doi: 10.1007/3-540-46521-9_2 – ident: e_1_2_6_6_1 doi: 10.1016/0167-6377(91)90083-2 – start-page: 178 volume-title: Proceedings of the 2nd International Network Optimization Conference year: 2005 ident: e_1_2_6_10_1 – ident: e_1_2_6_9_1 – volume: 7 start-page: 326 year: 1960 ident: e_1_2_6_13_1 article-title: Integer programming formulations and traveling salesman problems publication-title: Journal of the ACM doi: 10.1145/321043.321046 – volume-title: Handbook of Constraint Programming year: 2006 ident: e_1_2_6_18_1 – start-page: 592 volume-title: International Conference on Parallel and Distributed Systems year: 1994 ident: e_1_2_6_19_1 – volume: 16 start-page: 110 year: 2001 ident: e_1_2_6_4_1 article-title: Compression of correlated bitvectors publication-title: Information Systems – ident: e_1_2_6_7_1 – volume-title: The OPL Optimization Programming Language year: 1999 ident: e_1_2_6_17_1 – ident: e_1_2_6_11_1 doi: 10.1287/trsc.7.3.287 – ident: e_1_2_6_8_1 doi: 10.1002/net.10069 – volume-title: Integrated Methods for Optimization year: 2007 ident: e_1_2_6_12_1 – ident: e_1_2_6_16_1 doi: 10.1007/978-3-540-45157-0_4 – ident: e_1_2_6_15_1 doi: 10.1007/978-3-540-24838-5_34 |
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| Snippet | The diameter‐constrained minimum spanning tree problem consists in finding a minimum spanning tree of a given graph, subject to the constraint that the maximum... The diameter-constrained minimum spanning tree problem consists in finding a minimum spanning tree of a given graph, subject to the constraint that the maximum... |
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| SubjectTerms | bounded-diameter Computer Science constraint programming diameter constrained spanning trees Integer programming Mathematical programming Operations Research Spanning trees Studies |
| Title | Solving diameter-constrained minimum spanning tree problems by constraint programming |
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