Steiner 2-edge connected subgraph polytopes on series-parallel graphs

SIAM Journal on Discrete Mathematics

Volumn 10, Issue 3, 1997, Pages 505-514

  Baïou, Mourad ^a   Mahjoub, Ali Ridha ^a  

^a UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

Author keywords

Polytopes; Series parallel graphs; Steiner 2 edge connected subgraphs

Indexed keywords

EID: 0037910900     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480193259813     Document Type: Article

References (29)

1. M. BAÏOU, Le problème du sous graphe Steiner 2-arête connexe: Approche polyédrale, Ph.D. dissertation, N 1639, Université de Rennes 1, Rennes, France, 1993.
2. F. BARAHONA AND A. R. MAHJOUB, On two-connected subgraph polytopes, Discrete Math., 147 (1995), pp. 19-34.
3. D. BIENSTOCK, E. F. BRICKELL, AND C. L. MONMA, On the structure of minimum weight k-connected spanning networks, SIAM J. Discrete Math., 3 (1990), pp. 320-329.
4. S. CHOPRA, The k-edge connected spanning subgraph polyhedron, SIAM J. Discrete Math., 7 (1994), pp. 245-259.
5. N. CHRISTOFIDES AND C. A. WHITLOCK, Network synthesis with connectivity constraints-A survey, in Oper. Res., 81, J. P. Brans, ed., North-Holland, Amsterdam, 1981, pp. 705-723.
6. G. CORNUÉJOLS, J. FONLUPT, AND D. NADDEF, The traveling salesman problem on a graph and some related integer polyhedra, Math. Programming, 33 (1985), pp. 1-27.
7. R. COULLARD, A. RAIS, R. L. RARDIN, AND D. K. WAGNER. The 2-Connected-Steiner Subgraph Polytope for Series-Parallel Graphs, Report CC-91-23, School of Industrial Engineering, Purdue University, West Lafayette, IN, 1991.
8. R. COULLARD, A. RAIS, R. L. RARDIN, AND D. K. WAGNER, Linear-Time Algorithm for the 2-Connected Steiner Subgraph Problem on Special Classes of Graphs, Report 91-25, School of Industrial Engineering, Purdue University, West Lafayette, IN, 1991.
9. 4-Free Graphs, Report 91-28, School of Industrial Engineering, Purdue University, West Lafayette, IN, 1991.
10. E. A. DINITS, Algorithm for solution of a problem of maximum flow in a network with power estimation, Soviet Math. Dokl, 11 (1970), pp. 1277-1280.
11. R. J. DUFFIN, Topology of series-parallel networks, J. Math. Anal. Appl., 10 (1965), pp. 303-318.
12. J. EDMONDS AND R. M. KARP, Theoretical improvement in algorithm efficiency for network flow problems, J. Assoc. Comput. Mach., 19 (1972), pp. 248-264.
13. J. FONLUPT AND D. NADDEF, The traveling salesman problem in graphs with some excluded minors, Math. Programming, 53 (1992), pp. 147-172.
14. L. R. FORD AND D. R. FULKERSON, Maximal flow through a network, Can. J. Math., 8 (1956), pp. 399-404.
15. G. N. FREDERICKSON AND J. JA'JA', On the relationship between the biconnectivity augmentations and traveling salesman problem, Theoret. Comput. Sci., 13 (1982), pp. 189-201.
16. M. X. GOEMANS AND D. J. BERTSIMAS, Survivable networks, linear programming and the parsimonious property, Math. Programming, 60 (1993), pp. 145-166.
17. M. GROTSCHEL, L. LOVÁSZ, AND A. SCHRIJVER, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1 (1981), pp. 70-89.
18. M. GRÖTSCHEL AND C. MONMA, Integer polyhedra arising from certain network design problems with connectivity constraints, SIAM J. Discrete Math., 3 (1990), pp. 502-523.
19. M. GRÖTSCHEL, C. MONMA, AND M. STOER, Facets for polyhedra arising in the design of communication networks with low-connectivity constraints, SIAM J. Optim., 2 (1992), pp. 474-504.
20. M. GRÖTSCHEL, C. MONMA, AND M. STOER, Polyhedral approaches to network survivability, in Reliability of Computer and Communication Networks, F. Roberts, F. Hwang, and C. L. Monma, eds., Discrete Mathematics and Computer Science, Vol. 5, AMS/ACM, Providence, RI, 1991, pp. 121-141.
21. M. GRÖTSCHEL, C. MONMA, AND M. STOER, Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints, Oper. Res., 40 (1992), pp. 309-330.
22. A. R. MAHJOUB, Two-edge connected spanning subgraphs and polyhedra, Math. Programming, 64 (1994), pp. 199-208.
23. C. L. MONMA, B. S. MUNSON, AND W. R. PULLEYBLANK, Minimum-weight two connected spanning networks, Math. Programming, 46 (1990), pp. 153-171.
24. C. L. MONMA AND J. B. SIDNEY, Sequencing with series-parallel precedence constraints, Math. Oper. Res., 4 (1979), pp. 215-224.
25. K. STEIGLITZ, P. WEINER, AND D. J. KLEITMAN, The design of minimum cost survivable networks, IEEE Transactions and Circuit Theory, 16 (1969), pp. 455-460.
26. M. STOER, Design of survivable networks, Lecture Notes in Mathematics 1531, Springer-Verlag, New York, 1992.
27. J. A. WALD AND C. J. COLBOURN, Steiner trees in outerplanar graphs, Congressus Numeratum, 36 (1982), pp. 15-22.
28. P. WINTER, Generalized Steiner problem in Halin networks, in Proc. 12th International Symposium on Mathematical Programming, MIT, Cambridge, MA, 1985.
29. P. WINTER, Generalized Steiner problem in series-parallel networks, J. Algorithms, 7 (1986), pp. 549-566.