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Nonlinear formulations and improved randomized approximation algorithms for multiway and multicut problems
TL;DR: In this article, the authors introduce nonlinear formulations of the multiway cut and multicut problems and derive several well known formulations and valid inequalities as well as several new ones by simple linearizations of these formulations.
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Abstract: We introduce nonlinear formulations of 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 also introduce a new randomized rounding argument to study the worst case bound of these formulations, obtaining a new bound of 2a(H)(1 - ) for the multicut problem, where ac(H) is the size of a maximum independent set in the demand graph H.
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Citations
Semidefinite Relaxations, Multivariate Normal Distributions, and Order Statistics
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TL;DR: In this paper, the authors considered the quadratic programming problem with linear and boolean constraints and showed that the constraint x j 2 = 1 will force x j = 1 or x j= −1, making it a boolean variable.
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On approximation algorithms for the minimum satisfiability problem
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TL;DR: An approximation-preserving reduction from MINSAT to the minimum vertex cover (MINVC) problem is presented, and it is observed thatMINSAT remains NP-complete even when restricted to planar instances.
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On Dependent Randomized Rounding Algorithms
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- 03 Jun 1996
TL;DR: A class of rounding methods is described that exploits the structure and geometry of the underlying problem to round fractional solution to 0–1 solution and can be used to establish the integrality of several classical polyhedra.
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