Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T01:26:03.937Z Has data issue: false hasContentIssue false
  • English
  • Français

Un Algorithme pour la Bipartitiond'un Graphe en Sous-graphesde Cardinalité Fixée

Published online by Cambridge University Press:  15 August 2002

Philippe Michelon ,
Stéphanie Ripeau  and
Nelson Maculan
Philippe Michelon
Affiliation:
Laboratoire d'Informatique d'Avignon, UAPV, BP. 1228, 84911 Avignon Cedex 9, France.
Stéphanie Ripeau
Affiliation:
Université de Montréal, DIRO, CP. 6128, Succursale Centre-Ville, Montréal (Québec) H3C 3J7 Canada.
Nelson Maculan
Affiliation:
Universidade Federal do Rio de Janeiro, COPPE/Sistemas, P.O. Box 68511, Rio de Janeiro, RJ 21945–790, Brésil.
Get access

Abstract

A branch-and-bound method for solving the min cut with size constraint problemis presented. At each node of the branch-and-bound tree the feasible set isapproximated by an ellipsoid and a lower bound is computed by minimizing thequadratic objective function over this ellipsoid. An upper bound is alsoobtained by a Tabu search method. Numerical results will be presented.

Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 4 , October 2001 , pp. 401 - 414
Copyright
© EDP Sciences, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barnes, E.R., An algorithm for partitioning the nodes of a graph. SIAM J. Algebraic Discrete Math. 3 (1982) 541-550. CrossRef
Barnes, E.R., Vanelli, A. et Walker, J.Q., A new heuristic for partitioning the nodes of a graph. SIAM J. Discrete Math. 1 (1988) 299-305. CrossRef
R.B. Boppana, Eigenvalues and graph bissection: An average case analysis, in Proc. of the 28 th annual symposium on computer sciences. IEEE London (1987) 280-285.
A. Billionnet et A. Faye, A lower bound for a constrained quadratic 0-1minimization problem. Discrete Appl. Math. (soumis).
Christofides, N. et Brooker, P., The optimal partitioning of graphs. SIAM J. Appl. Math. 30 (1976) 55-69. CrossRef
Donath, W.E. et Hoffman, A.J., Lower bounds for the partitioning of graphs. IBM J. Res. Developments 17 (1973) 420-425. CrossRef
Falkner, J., Rendl, F. et Wolkowicz, H., A computational study of graph partitioning. Math. Programming 66 (1994) 211-240. CrossRef
Computing, D.M. Gay optimal locally constrained steps. SIAM J. Sci. Statist. Comput. 2 (1981) 186-197.
Held, M., Wolfe, P. et Crowder, H.D., Validation of the subgradient optimization. Math. Programming 6 (1974) 62-88. CrossRef
Johnson, D.S., Aragon, C.R., McGeoch, L.A. et Schevon, C., Optimization by simulated annealing: An experimental evaluation, Part 1, Graph partitioning. Oper. Res. 37 (1989) 865-892. CrossRef
Kernighan, B.W. et Lin, S., An efficient heuristic procedure for partitioning graphs. The Bell System Technical J. 49 (1970) 291-307. CrossRef
T. Lengauer, Combinatorial algorithms for integrated circuit layout. Wiley, Chicester (1990).
Martinez, J.M., Local minimizers of quadratic functions on euclidean balls and spheres. SIAM J. Optim. 4 (1994) 159-176. CrossRef
P. Michelon, N. Brossard et N. Maculan, A branch-and-bound scheme for unconstrained 0-1 quadratic programs, Rapport Technique # 960, DIRO. Université de Montréal. SIAM J. Optim. (soumis).
Moré, J.J. et Sorensen, D.C., Computing a trust region step. SIAM J. Sci. Statist. Comput. 4 (1983) 553-572. CrossRef
G.L. Nemhauser et L.A. Wolsey, Integer and Combinatorial Optimization. Wiley, New York (1988).
Roucairol, C. et Hansen, P., Problème de la bipartition minimale d'un graphe. RAIRO: Oper. Res. 21 (1987) 325-348. CrossRef
Sorensen, D.C., Newton's method with a model trust region modification. SIAM J. Numer. Anal. 19 (1982) 406-426. CrossRef