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Abstract: We study the problem of finding the minimum bisection of a graph into two parts of prescribed sizes. We formulate two lower bounds on the problem by relaxing node- and edge- incidence vectors of cuts. We prove that both relaxations provide the same bound. The main fact we prove is that the duality between the relaxed edge- and node- vectors preserves very natural cardinality constraints on cuts. We present an analogous result also for the max-cut problem, and show a relation between the edge... (Update)
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BibTeX entry: (Update)
S. Poljak and F. Rendl. Nonpolyhedral relaxations of graph-bisection problems. Technical Report 92--55, DIMACS, 1992. http://citeseer.ist.psu.edu/article/poljak92nonpolyhedral.html More
@article{ poljak95nonpolyhedral,
author = "S. Poljak and F. Rendl",
title = "Nonpolyhedral relaxations of graph-bisection problems",
journal = "SIAM Journal on Optimization",
volume = "5",
pages = "467--487",
year = "1995",
url = "citeseer.ist.psu.edu/article/poljak92nonpolyhedral.html" }
Citations (may not include all citations):88 Eigenvalues and graph bisection: an average case analysis (context) - Boppana - 1987
82 Lower bounds for the partitioning graphs (context) - Donath, Hoffman - 1973
76 A version of the Bundle idea for minimizing a nonsmooth func.. (context) - Schramm, Zowe - 1992
47 On minimizing the maximum eigenvalue of a symmetric matrix (context) - Overton - 1988
41 A projection technique for partitioning the nodes of a graph - Rendl, Wolkowicz - 1990
36 An application of combinatorial optimization to statistical .. (context) - Barahona, otschel et al. - 1988
35 Some applications of optimization in matrix theory (context) - Wolkowicz - 1981
26 A computational study of graph partitioning - Falkner, Rendl et al. - 1994
23 Solving the max-cut problem using eigenvalues (context) - Poljak, Rendl - 1991
21 The max-cut problem in graphs not contractible to K (context) - Barahona - 1983
12 Optimization over the positive semi-definite cone: Interior .. (context) - Alizadeh - 1992
10 Introduction to minimax (context) - Dem'yanov, Malozemov - 1974
10 The hypermetric cone is polyhedral (context) - Deza, Grishuchin et al. - 1993
8 personal communication (context) - Schrijver
7 Laplacian eigenvalues and the max-cut problem (context) - Delorme, Poljak - 1993
5 A Cutting Plane Algorithm for the Max-Cut Problem (context) - Rinaldi, De Simone - 1992
3 Gap inequalities (context) - Laurent, Poljak
3 the relative error of the polyhedral approximation of the ma.. (context) - Poljak, Tuza - 1991
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