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We study the approximability of instances of the minimum entropy set coverproblem, parameterized by the average frequency of a random element in thecovering sets. We analyze an algorithm combining a greedy approach with anotherone biased towards large sets. The algorithm is controled by the percentage ofelements to which we apply the biased approach. The optimal parameter choicehas a phase transition around average density $e$ and leads to improvedapproximation guarantees when average element frequency is less than $e$.

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