TY - GEN

T1 - Approximating the k-Set Packing problem by local improvements

AU - Fürer, Martin

AU - Yu, Huiwen

N1 - Funding Information:
Research supported in part by NSF Grant CCF-0964655 and CCF-1320814.

PY - 2014

Y1 - 2014

N2 - We study algorithms based on local improvements for the k-Set Packing problem. The well-known local improvement algorithm by Hurkens and Schrijver [14] has been improved by Sviridenko and Ward [15] from to k/2 + ∈ to k+2/3, and by Cygan [7] to k+1/3 + ∈ for any ∈ > 0. In this paper, we achieve the approximation ratio k+1/3 + ∈ for the k-Set Packing problem using a simple polynomial-time algorithm based on the method by Sviridenko and Ward [15]. With the same approximation guarantee, our algorithm runs in time singly exponential in 1/∈2, while the running time of Cygan's algorithm [7] is doubly exponential in 1/∈. On the other hand, we construct an instance with locality gap k+1/3 for any algorithm using local improvements of size O(n1/5), where is the total number of sets. Thus, our approximation guarantee is optimal with respect to results achievable by algorithms based on local improvements.

AB - We study algorithms based on local improvements for the k-Set Packing problem. The well-known local improvement algorithm by Hurkens and Schrijver [14] has been improved by Sviridenko and Ward [15] from to k/2 + ∈ to k+2/3, and by Cygan [7] to k+1/3 + ∈ for any ∈ > 0. In this paper, we achieve the approximation ratio k+1/3 + ∈ for the k-Set Packing problem using a simple polynomial-time algorithm based on the method by Sviridenko and Ward [15]. With the same approximation guarantee, our algorithm runs in time singly exponential in 1/∈2, while the running time of Cygan's algorithm [7] is doubly exponential in 1/∈. On the other hand, we construct an instance with locality gap k+1/3 for any algorithm using local improvements of size O(n1/5), where is the total number of sets. Thus, our approximation guarantee is optimal with respect to results achievable by algorithms based on local improvements.

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U2 - 10.1007/978-3-319-09174-7_35

DO - 10.1007/978-3-319-09174-7_35

M3 - Conference contribution

AN - SCOPUS:84905841259

SN - 9783319091730

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 408

EP - 420

BT - Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers

PB - Springer Verlag

T2 - 3rd International Symposium on Combinatorial Optimization, ISCO 2014

Y2 - 5 March 2014 through 7 March 2014

ER -