Memory-Efficient Approximation Algorithms for Max-k-Cut and Correlation Clustering

Abstract

Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph G = (V, E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering involve solving SDPs with O(n 2 ) constraints and variables. Large-scale instances of SDPs, thus, present a memory bottleneck. In this paper, we develop simple polynomial-time Gaussian sampling-based algorithms for these two problems that use O(n + |E|) memory and nearly achieve the best existing approximation guarantees. For dense graphs arriving in a stream, we eliminate the dependence on |E| in the storage complexity at the cost of a slightly worse approximation ratio by combining our approach with sparsification.