Nonlinear formulations and improved randomized approximation algorithms for multicut problems
We introduce nonlinear formulations for the multiway cut and multicut problems. By simple linearizations of these formulations we derive several well known formulations and valid inequalities as well as several new ones. Through these formulations we establish a connection between the multiway cut and the maximum weighted independent set problem that leads to the study of the tightness of several LP formulations for the multiway cut problem through the theory of perfect graphs. We finally introduce a new randomized rounding heuristic to study the worst case bound of these formulations, obtaining a new bound of 2α(H)(1-1/k) for the multicut problem, where α(H) is the size of a maximum independent set in the demand graph H.
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- C. Berge and V. Chvátal (eds), Topics on Perfect graphs, Annals of Discrete Mathematics, 21, 1984.Google Scholar
- S. Chopra and L.H. Owen, Extended formulations for the A-cut problem, preprint, 1994.Google Scholar
- S. Chopra and M.R. Rao, On the multiway cut polyhedron, Networks, 21, 51–89, 1991.Google Scholar
- W.H. Cunningham, The optimal multiterminal cut problem, DIMACS series in Discrete Mathematics and Theoretical Computer Science, 5, 105–120, 1991.Google Scholar
- E. Dalhaus, D. Johnson, C. Papadimitriou, P. Seymour and M. Yannakakis, The complexity of the multiway cuts, 24th Annual ACM STOC, 241–251, 1992.Google Scholar
- P. Erdos and L.A. Székely, On weighted multiway cuts in trees, Mathematical Programming, 65, 93–105, 1994.Google Scholar
- N. Garg, V. Vazirani, M. Yannakakis, Approximate max-flow min-(multi) cut theorems and their applications, 26th Annual ACM STOC, 1994.Google Scholar
- M. Grötschel, L. Lovász and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer, 1988.Google Scholar
- L. Lovász and A. Schrijver, Cones of Matrices and Set-Functions and 0–1 Optimization, SIAM J. Optimization, 1, 166–190, 1991.Google Scholar
- M. Laurent and S. Poljak, On the facial structure of the set of correlation matrices, Technical report, 1994.Google Scholar
- M. Padberg, The Boolean quadric polytope: some characteristics, facets and relatives, Mathematical Programming, 45, 139–172, 1989.Google Scholar