Greedy differential approximations for min set cover

Authors:
C. Bazgan;J. Monnot;V. Th. Paschos;F. Serrière
Affiliations:
LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France;LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France;LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France;LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France
Venue:
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Year:
2005

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Abstract

We present in this paper differential approximation results for min set cover and min weighted set cover. We first show that the differential approximation ratio of the natural greedy algorithm for min set cover is bounded below by 1.365/$\it \Delta$ and above by 4/($\it \Delta$ + 1), where $\it \Delta$ is the maximum set-cardinality in the min set cover-instance. Next, we study an approximation algorithm for min weighted set cover and provide a tight lower bound of 1/$\it \Delta$.