Covering analysis of the greedy algorithm for partial cover

Authors:
Tapio Elomaa;Jussi Kujala
Affiliations:
Department of Software Systems, Tampere University of Technology, Tampere, Finland;Department of Software Systems, Tampere University of Technology, Tampere, Finland
Venue:
Algorithms and Applications
Year:
2010

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Abstract

The greedy algorithm is known to have a guaranteed approximation performance in many variations of the well-known minimum set cover problem. We analyze the number of elements covered by the greedy algorithm for the minimum set cover problem, when executed for k rounds. This analysis quite easily yields in the p-partial cover problem over a ground set of m elements the harmonic approximation guarantee H(⌈pm⌉) for the number of required covering sets. Thus, we tie together the coverage analysis of the greedy algorithm for minimum set cover and its dual problem partial cover.