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Tight approximation bounds for combinatorial frugal coverage algorithms

Author

Listed:
  • Ioannis Caragiannis

    (University of Patras)

  • Christos Kaklamanis

    (University of Patras)

  • Maria Kyropoulou

    (University of Patras)

Abstract

We consider the frugal coverage problem, an interesting variation of set cover defined as follows. Instances of the problem consist of a universe of elements and a collection of sets over these elements; the objective is to compute a subcollection of sets so that the number of elements it covers plus the number of sets not chosen is maximized. The problem was introduced and studied by Huang and Svitkina (Proceedings of the 29th IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS), pp. 227–238, 2009) due to its connections to the donation center location problem. We prove that the greedy algorithm has approximation ratio at least 0.782, improving a previous bound of 0.731 in Huang and Svitkina (Proceedings of the 29th IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS), pp. 227–238, 2009). We also present a further improvement that is obtained by adding a simple corrective phase at the end of the execution of the greedy algorithm. The approximation ratio achieved in this way is at least 0.806. Finally, we consider a packing based algorithm that uses semi-local optimization, and show that its approximation ratio is not less than 0.872. Our analysis is based on the use of linear programs which capture the behavior of the algorithms in worst-case examples. The obtained bounds are proved to be tight.

Suggested Citation

  • Ioannis Caragiannis & Christos Kaklamanis & Maria Kyropoulou, 2013. "Tight approximation bounds for combinatorial frugal coverage algorithms," Journal of Combinatorial Optimization, Springer, vol. 26(2), pages 292-309, August.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:2:d:10.1007_s10878-012-9464-0
    DOI: 10.1007/s10878-012-9464-0
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    Cited by:

    1. Jihong Yan & Wenliang Cheng & Chengyu Wang & Jun Liu & Ming Gao & Aoying Zhou, 2015. "Optimizing word set coverage for multi-event summarization," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 996-1015, November.

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