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

•We study the Minimum Entropy Set Cover Problem, parameterized by average element frequency.•We analyze the performance of an approximation algorithm that combine a greedy approach with one biased towards large sets.•For average density f

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 controlled by the percentage of elements to which we apply the biased approach. The optimal parameter choice leads to improved approximation guarantees when average element frequency is less than e.