Improved Analysis of a Max Cut Algorithm Based on Spectral Partitioning

TL;DR

This paper improves the approximation ratio of a spectral partitioning algorithm for Max-Cut from 0.531 to approximately 0.614, surpassing the 1/2 barrier without using semidefinite programming.

Contribution

It provides an enhanced analysis of Trevisan's spectral Max-Cut algorithm, achieving a higher approximation guarantee and extending results to the Maximum Colored Cut problem.

Findings

Approximation ratio improved to 0.614247

First non-semidefinite spectral Max-Cut algorithm with >1/2 guarantee

Extension of results to Maximum Colored Cut

Abstract

Trevisan [SICOMP 2012] presented an algorithm for Max-Cut based on spectral partitioning techniques. This is the first algorithm for Max-Cut with an approximation guarantee strictly larger than 1/2 that is not based on semidefinite programming. Trevisan showed that its approximation ratio is of at least 0.531. In this paper we improve this bound up to 0.614247. We also define and extend this result for the more general Maximum Colored Cut problem.