The Minimum-Entropy Set Cover Problem

We study graph orientations that minimize the entropy of the in-degree sequence. The problem of finding such an orientation is an interesting special case of the minimum entropy set cover problem previously studied by Halperin and Karp (Theoret. Comput. Sci., 2005) and by the current authors (Algorithmica, to appear). We prove that the minimum entropy orientation problem is NP-hard even if the graph is planar, and that there exists a simple linear-time algorithm that returns an approximate solution with an additive error guarantee of 1 bit. This improves on the only previously known algorithm

• Type: Conference
• Year: 2004
• Where: ICALP
• Authors: Eran Halperin, Richard M. Karp
• Keywords: Entropy Orientation Problem, Entropy Set Cover, ICALP 2004, Minimum Entropy, Theoretical Computer Science