Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut
摘要
The multiway-cut problem is, given a weighted graph and k >= 2 terminal nodes, to find a minimum-weight set of edges whose removal separates all the terminals. The problem is NP-hard, and even NP-hard to approximate within 1+delta for some small delta > 0. Calinescu, Karloff, and Rabani (1998) gave an algorithm with performance guarantee 3/2-1/k, based on a geometric relaxation of the problem. In this paper, we give improved randomized rounding schemes for their relaxation, yielding a 12/11-approximation algorithm for k=3 and a 1.3438-approximation algorithm in general. Our approach hinges on the observation that the problem of designing a randomized rounding scheme for a geometric relaxation is itself a linear programming problem. The paper explores computational solutions to this problem, and gives a proof that for a general class of geometric relaxations, there are always randomized rounding schemes that match the integrality gap.
引用
@article{arxiv.cs/0205051,
title = {Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut},
author = {David Karger and Phil Klein and Cliff Stein and Mikkel Thorup and Neal E. Young},
journal= {arXiv preprint arXiv:cs/0205051},
year = {2015}
}
备注
Conference version in ACM Symposium on Theory of Computing (1999). To appear in Mathematics of Operations Research