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

Nimita Rajendra Shinde, Vishnu Narayanan, James Saunderson

Keywords: Semidefinite programming, Max-k-Cut, correlation clustering, Convex optimization, Gaussian sampling

TL;DR: We generate approximation solutions to Max-k-Cut and correlation clustering using memory linear in the size of the input graph

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 $\mathcal{O}(n^2)$ 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 $\mathcal{O}(n+|E|)$ 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.

Code Of Conduct: I certify that all co-authors of this work have read and commit to adhering to the NeurIPS Statement on Ethics, Fairness, Inclusivity, and Code of Conduct.