A (2-c\ frac {\ log {n}}{n}) Approximation Algorithm for the Minimum Maximal Matching Problem

Zvi Gotthilf; M. Lewenstein; Elad Rainshmidt

A (2-c\ frac {\ log {n}}{n}) Approximation Algorithm for the Minimum Maximal Matching Problem

Zvi Gotthilf, M. Lewenstein, Elad Rainshmidt

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 7676. 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 2−clognn2−clog⁡nn, 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.

Original language	American English
Title of host publication	International Workshop on Approximation and Online Algorithms
Editors	Evripidis Bampis, Martin Skutella
Publisher	Springer Berlin Heidelberg
State	Published - 2008

Bibliographical note

Place of conference:Germany

Cite this

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title = "A (2-c\ frac {\ log {n}}{n}) Approximation Algorithm for the Minimum Maximal Matching Problem",

abstract = "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 7676. 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 2−clognn2−clog⁡nn, 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.",

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A (2-c\ frac {\ log {n}}{n}) Approximation Algorithm for the Minimum Maximal Matching Problem. / Gotthilf, Zvi; Lewenstein, M.; Rainshmidt, Elad.
International Workshop on Approximation and Online Algorithms. ed. / Evripidis Bampis; Martin Skutella. Springer Berlin Heidelberg, 2008.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - A (2-c\ frac {\ log {n}}{n}) Approximation Algorithm for the Minimum Maximal Matching Problem

AU - Gotthilf, Zvi

AU - Lewenstein, M.

AU - Rainshmidt, Elad

N1 - Place of conference:Germany

PY - 2008

Y1 - 2008

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 7676. 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 2−clognn2−clog⁡nn, 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 7676. 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 2−clognn2−clog⁡nn, 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.

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M3 - Conference contribution

BT - International Workshop on Approximation and Online Algorithms

A2 - Bampis, Evripidis

A2 - Skutella, Martin

PB - Springer Berlin Heidelberg

ER -

A (2-c\ frac {\ log {n}}{n}) Approximation Algorithm for the Minimum Maximal Matching Problem

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