20.1 Introduction 20.2 the Multicut Problem

Last time we covered the s-t MinCut problem and the Multiway Cut problem, for which we gave a 2(1− 1 k )-approximation via an LP relaxation and showed that the integrality gap was 2(1− 1 k ). Today we will cover the MultiCut problem, and approximation algorithms for the problem using a techniques called low-diameter random decomposition (LDRD) and region growing. The MultiCut problem is related to the Sparsest Cut problem in which a roughly balanced separator is sought in a graph. Being able to find a sparse cut can help with divide and conquer algorithms because it implies we can divide the graph into two roughly equal-sized pieces with little “interaction” (i.e., edges crossing between the two pieces). Ideas similar to the ones in today’s lecture come from [1, 2, 3, 4, 5].