On Approximation of Robust Max-Cut and Related Problems using Randomized Rounding Algorithms

TL;DR

This paper extends the randomized rounding approach of Goemans and Williamson to robust and distributionally robust versions of the Max-Cut problem, maintaining the same approximation bounds.

Contribution

It demonstrates that the 0.878 approximation bound applies to robust Max-Cut and related problems using the same randomized projection framework.

Findings

Robust Max-Cut achieves a 0.878 approximation bound.

The approximation bounds for related problems are preserved in their robust versions.

The randomized rounding framework is effective for robust optimization problems.

Abstract

Goemans and Williamson proposed a randomized rounding algorithm for the MAX-CUT problem with a 0.878 approximation bound in expectation. The 0.878 approximation bound remains the best-known approximation bound for this APX-hard problem. Their approach was subsequently applied to other related problems such as Max-DiCut, MAX-SAT, and Max-2SAT, etc. We show that the randomized rounding algorithm can also be used to achieve a 0.878 approximation bound for the robust and distributionally robust counterparts of the max-cut problem. We also show that the approximation bounds for the other problems are maintained for their robust and distributionally robust counterparts if the randomization projection framework is used.