On the Optimality of a Class of LP-based Algorithms

TL;DR

This paper demonstrates the optimality of a simple LP-based rounding algorithm for Vertex Cover under the Unique Games Conjecture, extending the result to a broader class of CSPs.

Contribution

It proves the optimality of LP-based algorithms for Vertex Cover and related problems assuming UGC, generalizing previous results to a wider class of CSPs.

Findings

LP-based rounding for Vertex Cover is optimal under UGC

The result extends to a class of strict covering/packing CSPs

Provides theoretical limits for approximation algorithms under UGC

Abstract

In this paper we will be concerned with a class of packing and covering problems which includes Vertex Cover and Independent Set. Typically, one can write an LP relaxation and then round the solution. In this paper, we explain why the simple LP-based rounding algorithm for the \\VC problem is optimal assuming the UGC. Complementing Raghavendra's result, our result generalizes to a class of strict, covering/packing type CSPs.