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

TL;DR

This paper introduces memory-efficient, polynomial-time algorithms for Max-k-Cut and correlation clustering that nearly match the best approximation guarantees while significantly reducing memory usage, suitable for large-scale and streaming graphs.

Contribution

The authors develop Gaussian sampling-based algorithms that use linear memory and extend to streaming dense graphs, improving scalability of graph partitioning methods.

Findings

Algorithms use O(n+|E|) memory, reducing the memory bottleneck.

Nearly match the best approximation guarantees of SDP-based methods.

Effective for large-scale and streaming graph instances.

Abstract

Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with 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 $O(n^2)$ variables and constraints. 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.