Approximation algorithms for the Weighted t-Uniform Sparsest Cut and some other graph partitioning problems

Abstract

We study the Weighted t-Uniform Sparsest Cut (Weighted t-USC) and other related problems. In an instance of the Weighted t-USC problem, a parameter t and an undirected graph G = (V, E) with edge-weights w : E -> 1R(>=)0 and vertex-weights : V -> R+ are given. The goal is to find a vertex set S subset of V with vertical bar S vertical bar <= t while minimizing w(S, V\S)/eta(S), where w(S, V \ S) is the total weight of the edges with exactly one endpoint in S and eta(S) = Sigma(v is an element of S) eta(v) For this problem, we present a (0 (log t), 1 + is an element of) factor bicriteria approximation lgorithm. Our algorithm outperforms the current best algorithm when t = n(o(1)). We also present better approximation algorithms for Weighted rho-Unbalanced Cut and Min-Max k-Partitioning problems. (C) 2016 Elsevier Inc. All rights reserved