Choose Outsiders First: a mean 2-approximation random algorithm for covering problems

TL;DR

This paper introduces a novel randomized algorithm called 'Choose Outsiders First' for covering problems, achieving an expected solution size at most twice the optimal, applicable to problems like Vertex Cover and Set Cover.

Contribution

It presents a new randomized approximation algorithm with a 2-approximation ratio for a broad class of covering problems, expanding the toolkit for intractable combinatorial optimization.

Findings

The algorithm guarantees an expected solution size at most twice the optimal.

It applies to various covering problems including Vertex Cover and Set Cover.

The approach offers a simple and effective randomized method for inapproximable problems.

Abstract

A high number of discrete optimization problems, including Vertex Cover, Set Cover or Feedback Vertex Set, can be unified into the class of covering problems. Several of them were shown to be inapproximable by deterministic algorithms. This article proposes a new random approach, called Choose Outsiders First, which consists in selecting randomly ele- ments which are excluded from the cover. We show that this approach leads to random outputs which mean size is at most twice the optimal solution.