Steiner trees and polyhedra

Discrete Applied Mathematics

Volumn 112, Issue 1-3, 2001, Pages 101-120

  Didi Biha, M ^a   Kerivin, H ^b   Mahjoub, A R ^b  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^b UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

Facet; Polytope; Series parallel graph; Steiner connected subgraph; Steiner tree

Indexed keywords

EID: 0035885272     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(00)00311-5     Document Type: Article

References (33)

1. Balas E., Fischetti M. On the monotonization of polyhedra. Math. Programming. 78:1997;59-84.
2. Chopra S. Polyhedra of the equivalent subgraph problem and some edge connectivity problems. SIAM J. Discrte Math. 5:1992;321-337.
3. Chopra S., Gorres E. On the node weighted Steiner tree problem. 1990;Working paper, New York University.
4. Chopra S., Rao M.R. The Steiner tree problem I: formulations, compositions and extension of facets. Math. Programming. 64:1994;209-229.
5. Chopra S., Rao M.R. The Steiner tree problem II: properties and classes of facets. Math. Programming. 64:1994;231-246.
6. Cornuéjols G., Fonlupt J., Naddef D. The travelling salesman problem on a graph and some related integer polyhedra. Math. Programming 33. 1985:1-27.
7. E. Dahlhaus, D. Johnson, C. Papadimitriou, P. Seymour, M. Yannakakis, The complexity of multiway cuts extended abstract, 1983.
8. Dahlhaus E., Johnson D., Papadimitriou C., Seymour P., Yannakakis M. The Complexity of multiterminals cuts. SIAM J. Comput. 23:1994;864-894.
9. M. Didi Biha, Graphes k-arête connexes et polyèdres, Ph.D. Thesis, Université de Bretagne Occidentale, Brest, France, 1998.
10. Duffin R.J. Topology of series-parallel networks. J. Math. Anal. Appl. 10:1965;303-318.
11. Duin C.W., Volgenant A. Reduction test for the Steiner problem in graphs. Network. 19:1989;549-567.
12. Garey M.R., Johnson D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness. 1979;Freeman, San Francisco.
13. Goemans M.X. Arborescence polytopes for series-parallel graphes. Discrete Appl. Math. 51:1994;277-289.
14. Goemans M.X. The Steiner tree polytope and related polyhedra. Math. Programming. 63:1994;157-182.
15. Goemans M.X., Bertsimas D.J. Survivable networks, linear programming and the parsimonious property. Math. Programming. 60:1993;145-166.
16. Goemans M.X., Myungt Y.-S. A catalog of Steiner tree formulations. Networks. 23:1993;19-28.
17. Grötschel M., Monma C.L., Stoer M. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Oper. Res. 40:1992;309-330.
18. F.W. Hwang, D.S. Richards, P. Winter, The Steiner Tree Problem, Ann. Discrete Mathematics vol. 53, North Holland, Amsterdam, 1992.
19. Lawler E.L. Combinatorial Optimization: Networks and Matroids. 1976;Holt Rinejart and Winston, New York.
20. Margot F., Prodon A., Liebling T.M. Tree polytope on 2-trees. Mathe. Programming. 63:1994;183-191.
21. T. Polzin, S.V. Daneshmand, A comparison of steiner tree relaxations, Technical Report, Mannheim University, 1998.
22. T. Polzin, S.V. Daneshmand, Improved algorithms for the Steiner problem in networks, Technical Report, Mannheim University, 1998.
23. A. Prodon, T.M. Liebling, H. Gröflin, Steiner's problem on two-trees preprint, 1985.
24. A. Prodon, A polyhedron for Steiner trees in series parallel graphs, Département de Mathématiques, École Polytechnique Fédérale de Lausanne, 1985.
25. A. Segev, The node-weighted Steiner tree problem, Technical Report, School of Business Administration, University of California, Berkeley, CA, 1985.
26. Stoer M. Design of Survivable Networks. Lecture Notes in Mathematics. Vol. 1531:1992;Springer, Berlin.
27. S. Vo ß , Steiner-Probleme in Graphen, Hain, Frankfurt/Main, 1990.
28. Vo ß S. Steiner's problem in graphs : heuristic methods. Discrete Appl. Math. 40:1992;45-72.
29. Wald J., Colbourn C.J. Steiner trees, partial 2-trees, and minimum IFI networks. Networks. 13:1983;159-167.
30. Winter P. Steiner problem in networks: a survey. Networks. 17:1987;129-167.
31. Winter P., MacGregor Smith J. Path-distance heuristics for the Steiner problem in undirected networks. Algorithmica. 7:1992;309-327.
32. Zelikovski A.Z. A faster algorithm for the Steiner tree problem. Inform. Process. Lett. 46:1993;79-83.
33. Zelikovski A.Z. New approximation algorithm for the Steiner tree problem. J. Conbin. Optim. 1:1997;47-65.