Analysis of approximation algorithms for k-set cover using factor-revealing linear programs

Authors:
Stavros Athanassopoulos;Ioannis Caragiannis;Christos Kaklamanis
Affiliations:
Research Academic Computer Technology Institute & Department of Computer Engineering and Informatics, University of Patras, Rio, Greece;Research Academic Computer Technology Institute & Department of Computer Engineering and Informatics, University of Patras, Rio, Greece;Research Academic Computer Technology Institute & Department of Computer Engineering and Informatics, University of Patras, Rio, Greece
Venue:
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Year:
2007

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Abstract

We present new combinatorial approximation algorithms for k-set cover. Previous approaches are based on extending the greedy algorithm by efficiently handling small sets. The new algorithms further extend them by utilizing the natural idea of computing large packings of elements into sets of large size. Our results improve the previously best approximation bounds for the k-set cover problem for all values of k ≥ 6. The analysis technique could be of independent interest; the upper bound on the approximation factor is obtained by bounding the objective value of a factor-revealing linear program.