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

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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 -