An extended formulation approach to the edge-weighted maximal clique problem

European Journal of Operational Research

Volumn 95, Issue 3, 1996, Pages 671-682

  Park, Kyungchul ^a   Lee, Kyungsik ^a   Park, Sungsoo ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Cutting plane facet generation algorithm; Extended formulation; Integer programming; Maximal clique problem

Indexed keywords

EID: 0042541622     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-2217(95)00299-5     Document Type: Article

References (16)

1. Balas E. and Pulleyblank, W.R. (1983). The perfectly matchable subgraph polytope of a bipartite graph. Networks 13, 495-516.
2. Boros, E. and Hammer, P.L. (1993). Cut-polytopes, boolean quadric polytopes and nonnegative quadratic pseudo-boolean functions. Mathematics of Operations Research 18, 245-253.
3. De Simone (1989). The cut polytope and the boolean quadric polytope. Discrete Mathematics 79, 71-75.
4. Deza, M. and Laurent, M. (1992a). Facets for the cut cone I. Mathematical Programming 56, 121-160.
5. Deza, M. and Laurent, M. (1992b). Facets for the cut cone II: clique-web inequalities. Mathematical Programming 56, 161-188.
6. Dijkhuizen, G. and Faigle, U. (1993). A cutting-plane approach to the edge-weighted maximal clique problem. European Journal of Operational Research 69, 121-130.
7. Eppen, G.D. and Martin, R.K. (1987). Solving multi-item capacitated lot-sizing problems using variable redefinition. Operations Research 35, 832-848.
8. Fischetti, M., Hamacher, H.W., Jornsten, K. and Maffioli, F. (1994). Weighted k-cardinality trees: complexity and polyhedral structure. Networks 24, 11-21.
9. Johnson, E.L., Mehrotra, A. and Nemhauser, G.L. (1993). Min-cut clustering. Mathematical Programming 62, 133-151.
10. Nemhauser, G.L. and Wolsey, L.A. (1988). Integer and Combinatorial Optimization, Wiley, N.Y.
11. Padberg, M. (1989). The boolean quadric polytope: some characteristics, facets and relatives. Mathematical Programming (Series B) 45, 139-172.
12. Park, K., Lee, K. and Park S. (1994), An extended formulation approach to the edge-weighted maximal clique problem. Working paper, Department of Industrial Eng., Korea Advanced Institue of Science and Technology.
13. Park, K., Lee, K., Park, S. and Lee, H., in preparation. Modeling and solving the clustering problem in the broadband network design.
14. Ravi, S.S., Rosenkrantz, D.J. and Tayi, G.K. (1994). Heuristic and special case algorithms for dispersion problem. Operations Research 42, 299-310.
15. Sigismondi, G.C. (1989). A constraint generation algorithm for node packing. Ph.D. Dissertation, Cornell University.
16. Späth, H. (1985). Heuristic determining cliques of given cardinality and with minimal costs within weighted complete graphs. Zeitschrift für Operations Research 29, 125-131.