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.
UR - http://www.scopus.com/inward/record.url?scp=84905841259&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84905841259&partnerID=8YFLogxK
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 -