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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.
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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

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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