SIAM Journal on Discrete Mathematics
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
Analysis of Approximation Algorithms for k-Set Cover Using Factor-Revealing Linear Programs
Theory of Computing Systems
An Improved Approximation Bound for Spanning Star Forest and Color Saving
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Approximating the Unweighted ${k}$-Set Cover Problem: Greedy Meets Local Search
SIAM Journal on Discrete Mathematics
Wavelength Management in WDM Rings to Maximize the Number of Connections
SIAM Journal on Discrete Mathematics
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Uniform unweighted set cover: The power of non-oblivious local search
Theoretical Computer Science
Packing-based approximation algorithm for the k-set cover problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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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.