TY - JOUR
T1 - A (2 - c log/n) approximation algorithm for the minimum maximal matching problem
AU - Gotthilf, Zvi
AU - Lewenstein, Moshe
AU - Rainshmidt, Elad
PY - 2009
Y1 - 2009
N2 - We consider the problem of finding a maximal matching of minimum size, given an unweighted general graph. This problem is a well studied and it is known to be NP-hard even for some restricted classes of graphs. Moreover, in case of general graphs, it is NP-hard to approximate the Minimum Maximal Matching (shortly MMM) within any constant factor smaller than . The current best known approximation algorithm is the straightforward algorithm which yields an approximation ratio of 2. We propose the first nontrivial algorithm yields an approximation ratio of , for an arbitrarily positive constant c. Our algorithm is based on the local search technique and utilizes an approximate solution of the Minimum Weighted Maximal Matching problem in order to achieve the desirable approximation ratio.
AB - We consider the problem of finding a maximal matching of minimum size, given an unweighted general graph. This problem is a well studied and it is known to be NP-hard even for some restricted classes of graphs. Moreover, in case of general graphs, it is NP-hard to approximate the Minimum Maximal Matching (shortly MMM) within any constant factor smaller than . The current best known approximation algorithm is the straightforward algorithm which yields an approximation ratio of 2. We propose the first nontrivial algorithm yields an approximation ratio of , for an arbitrarily positive constant c. Our algorithm is based on the local search technique and utilizes an approximate solution of the Minimum Weighted Maximal Matching problem in order to achieve the desirable approximation ratio.
UR - http://www.scopus.com/inward/record.url?scp=60349109830&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-93980-1_21
DO - 10.1007/978-3-540-93980-1_21
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.conferencearticle???
AN - SCOPUS:60349109830
SN - 0302-9743
VL - 5426 LNCS
SP - 267
EP - 278
JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
T2 - 6th International Workshop on Approximation and Online Algorithms, WAOA 2008
Y2 - 18 September 2008 through 19 September 2008
ER -