Separation of partition inequalities with terminals

Discrete Optimization

Volumn 1, Issue 2, 2004, Pages 129-140

  Barahona, Francisco ^a   Kerivin, Hervé ^b  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Partition inequalities; Separation problem; Submodular flows

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; GRAPH THEORY; HEURISTIC METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING;

NETWORK TOPOLOGY; PARTITION INEQUALITIES; SEPARATION PROBLEMS; SUBMODULAR FLOWS;

TELECOMMUNICATION NETWORKS;

EID: 13944250352     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2004.05.001     Document Type: Article

References (26)

1. M. Baïou, F. Barahona, and A.R. Mahjoub Separation of partition inequalities Math. Oper. Res. 25 2000 243 254
2. F. Barahona Separating from the dominant of the spanning tree polytope Oper. Res. Lett. 12 1992 201 203
3. W.H. Cunningham Optimal attack and reinforcement of a network J. Assoc. Comput. Mach. 32 1985 549 561
4. W.H. Cunningham Minimum cuts, modular functions, and matroid polyhedra Networks 15 1985 205 215
5. E. Dahlhaus, D.S. Johnson, C.H. Papadimitriou, P.D. Seymour, and M. Yannakakis The complexity of multiterminal cuts SIAM J. Comput. 23 1994 864 894
6. M. Didi Diha, H. Kerivin, A.R. Mahjoub, On the polytope of the (1,2)-survivable network design problem, 2003, in preparation.
7. J. Edmonds, and R. Giles A min-max relation for submodular functions on graphs Ann. Discrete Math. 1 1977 185 204
8. S. Fujishige, and X. Zhang New algorithm for the intersection problem of submodular system Jpn. J. Ind. Appl. Math. 9 1992 369 382
9. A.V. Goldberg, and R.E. Tarjan A new approach to the maximum flow problem J. Assoc. Comput. Mach. 35 1988 921 940
10. M. Grötschel, and C.L. Monma Integer polyhedra arising from certain network design problems with connectivity constraints SIAM J. Discrete Math. 3 1990 502 523
11. M. Grötschel, C.L. Monma, and M. Stoer Facets for polyhedra arising in the design of communication networks with low-connectivity constraints SIAM J. Optim. 2 3 1992 474 504
12. M. Grötschel, C.L. Monma, and M. Stoer Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints Oper. Res. 40 1992 309 330
13. M. Grötschel, C.L. Monma, and M. Stoer Design of survivable networks M.O. Ball Handbook in Operations Research and Management Science Vol. 7 1995 North-Holland Amsterdam 617 671
14. S. Iwata, L. Fleischer, and S. Fujishige A combinatorial strongly polynomial algorithm for minimizing submodular functions J. Assoc. Comput. Mach. 48 2001 761 777
15. H. Kerivin, and A.R. Mahjoub Separation of partition inequalities for the (1,2)-survivable network design problem Oper. Res. Lett. 30 2002 265 268
16. H. Kerivin, C. Nocq, A.R. Mahjoub. (1,2)-survivable networks: facets and branch-and-cut, in: M. Grötschel (Ed.), Book: The Sharpest Cut, MPS/SIAM on Optimization, 2004, pp. 139-173.
17. J.B. Kruskal On the shortest spanning subtree of a graph and the traveling salesman problem Proc. Amer. Math. Soc. 7 1956 48 50
18. L. Lovász Submodular functions and convexity A. Bachem M. Grötschel B. Korte Mathematical Programming - The State of the Art 1983 Springer Berlin 234 257
19. A.R. Mahjoub Two edge connected spanning subgraphs and polyhedra Math. Programming 64 1994 199 208
20. C.L. Monma, and D.F. Shallcross Methods for designing communication networks with certain two-connected survivability constraints Oper. Res. 37 1989 531 541
21. C.S.J.A. Nash-Williams Edge-disjoint spanning tree of finite graphs J. London Math. Soc. 36 1961 445 450
22. M.W. Padberg, and A. Wolsey Trees and cuts Ann. Discrete Math. 17 1983 511 517
23. J.C. Picard, and M. Queyranne Selected applications of minimum cuts in networks INFOR-Canada J. Oper. Res. Inform. Process. 20 1982 394 422
24. A. Schrijver A combinatorial algorithm minimizing submodular functions in strongly polynomial time J. Combin. Theory Ser. B 80 2000 346 355
25. M. Stoer Design of survivable networks Lecture Notes in Mathematics 1531 1992 Springer Berlin
26. W.T. Tutte On the problem of decomposing a graph into n connected factors J. London Math. Soc. 36 1961 221 230