Improved approximation algorithms for low-density instances of the Minimum Entropy Set Cover Problem

TL;DR

This paper investigates the approximability of the minimum entropy set cover problem, proposing a hybrid algorithm that improves approximation guarantees for instances with low average element frequency, especially below the value of e.

Contribution

It introduces a novel hybrid algorithm combining greedy and biased approaches, with optimal parameter tuning around the average density e, enhancing approximation for low-density instances.

Findings

Improved approximation guarantees for instances with average density less than e.

Identification of a phase transition in algorithm performance around the density e.

Hybrid algorithm outperforms traditional methods in low-density scenarios.

Abstract

We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased towards large sets. The algorithm is controled by the percentage of elements to which we apply the biased approach. The optimal parameter choice has a phase transition around average density $e$ and leads to improved approximation guarantees when average element frequency is less than $e$.