## Simple distributed weighted matchings (2004)

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Venue: | In eprint cs.DC/0410047 |

Citations: | 9 - 1 self |

### BibTeX

@INPROCEEDINGS{Hoepman04simpledistributed,

author = {Jaap-henk Hoepman},

title = {Simple distributed weighted matchings},

booktitle = {In eprint cs.DC/0410047},

year = {2004}

}

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### Abstract

Wattenhofer et al. [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the obvious sequential greedy algorithm [Pre99], that computes a weighted matching at most a factor 2 away from the maximum, is easily distributed. This yields the best known distributed approximation algorithm for this problem so far. 1

### Citations

142 |
An O( √|v|·|E|) algorithm for finding maximum matching in general graphs
- Micali, Vazirani
- 1980
(Show Context)
Citation Context ... weighted matching M(G) with approximation ratio 5, i.e., such that w(M(G)) > 1 5 w(M ∗ (G)). For sequential algorithms, the problem is much better studied. For unweighted graphs, Micali and Vazirani =-=[MV80]-=- present an O( � |V ||E|) time algorithm that computes a maximal matching. For weighted graphs Gabow [Gab90] gives an O(|V ||E|+|V | 2 log |V |) time algorithm, computing the maximum weighted matching... |

138 |
Data structures for weighted matching and nearest common ancestors with linking
- Gabow
- 1990
(Show Context)
Citation Context ...l algorithms, the problem is much better studied. For unweighted graphs, Micali and Vazirani [MV80] present an O( � |V ||E|) time algorithm that computes a maximal matching. For weighted graphs Gabow =-=[Gab90]-=- gives an O(|V ||E|+|V | 2 log |V |) time algorithm, computing the maximum weighted matching. Both return an exact solution, and not approximations. Recently, there have improvements in the performanc... |

52 | A fast and simple randomized parallel algorithm for maximal matching, preprint
- ISRAELI, ITAI
- 1984
(Show Context)
Citation Context ... unweighted graphs, there are deterministic distributed algorithms computing the maximal matching in trees [KS00], and bipartite and general graphs [CHS02]. Randomised algorithms for the general case =-=[II86]-=- also exist. For weighted graphs, Uehara et al. [UC00] present a constant time distributed algorithm that computes a weighted matching that is O(∆) away ∗ Id: weighted-matchings.tex,v 1.3 2004/10/19 0... |

51 |
A survey of heuristics for the weighted matching problem
- Avis
- 1983
(Show Context)
Citation Context ...rithms. The obvious greedy sequential algorithm (that each time adds the remaining heaviest edge) computes a weighted matching at most a factor 2 away from the maximum, in running time O(|E|log |V |) =-=[Avi83]-=-. Preis [Pre99] showed that selecting locally heaviest edges instead of globally heavy edges achieves the same approximation, improving the running time to O(|E|). Using a path-growing algorithm, Drak... |

35 | Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs
- Preis
- 1999
(Show Context)
Citation Context ...a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the obvious sequential greedy algorithm =-=[Pre99]-=-, that computes a weighted matching at most a factor 2 away from the maximum, is easily distributed. This yields the best known distributed approximation algorithm for this problem so far. 1 Introduct... |

32 | A simple approximation algorithm for the weighted matching problem
- Drake, Hougardy
- 2003
(Show Context)
Citation Context ...Pre99] showed that selecting locally heaviest edges instead of globally heavy edges achieves the same approximation, improving the running time to O(|E|). Using a path-growing algorithm, Drake et al. =-=[DH03b]-=- achieve the same running time and performance ratio. Later, Drake et al. [DH03a] improved the approximation to 3/2 + ǫ, using a slowly converging algorithm using the concept of augmenting paths. Pett... |

26 | Distributed Weighted Matching
- Wattenhofer, Wattenhofer
- 2004
(Show Context)
Citation Context ...ijmegen Institute for Computing and Information Sciences (NIII) Radboud University Nijmegen P.O. Box 9010, 6500 GL Nijmegen, the Netherlands jhh@cs.ru.nl 1st February 2008 Abstract Wattenhofer et al. =-=[WW04]-=- derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show tha... |

14 | Parallel approximation algorithms for maximum weighted matching
- Uehara, Chen
- 2000
(Show Context)
Citation Context ...d algorithms computing the maximal matching in trees [KS00], and bipartite and general graphs [CHS02]. Randomised algorithms for the general case [II86] also exist. For weighted graphs, Uehara et al. =-=[UC00]-=- present a constant time distributed algorithm that computes a weighted matching that is O(∆) away ∗ Id: weighted-matchings.tex,v 1.3 2004/10/19 08:30:12 jhh Exp 1sM(G) = ∅ while E �= ∅ do pick locall... |

10 |
A simpler linear time 2/3 − ɛ approximation to maximum weight matching
- Pettie, Sanders
- 2004
(Show Context)
Citation Context ...he same running time and performance ratio. Later, Drake et al. [DH03a] improved the approximation to 3/2 + ɛ, using a slowly converging algorithm using the concept of augmenting paths. Pettie et al. =-=[PS04]-=- present both a deterministic and a randomised algorithm achieving the same approximation in running time O(|E| log 1 ɛ ). In this paper, we show that Preis’s algorithm is easily distributed determini... |

9 |
Dynamic and self-stabilizing distributed matching
- Chattopadhyay, Higham, et al.
- 2002
(Show Context)
Citation Context ...d matching of the communication graph are known. For unweighted graphs, there are deterministic distributed algorithms computing the maximal matching in trees [KS00], and bipartite and general graphs =-=[CHS02]-=-. Randomised algorithms for the general case [II86] also exist. For weighted graphs, Uehara et al. [UC00] present a constant time distributed algorithm that computes a weighted matching that is O(∆) a... |

8 |
A distributed self-stabilizing algorithm for finding maximum matching
- Karaata, Saleh
- 2000
(Show Context)
Citation Context ...(an approximation of) the maximum weighted matching of the communication graph are known. For unweighted graphs, there are deterministic distributed algorithms computing the maximal matching in trees =-=[KS00]-=-, and bipartite and general graphs [CHS02]. Randomised algorithms for the general case [II86] also exist. For weighted graphs, Uehara et al. [UC00] present a constant time distributed algorithm that c... |

8 |
A simpler linear time 2/3 - ǫ approximation for maximum weight matching
- Pettie, Sanders
- 2004
(Show Context)
Citation Context ...he same running time and performance ratio. Later, Drake et al. [DH03a] improved the approximation to 3/2 + ǫ, using a slowly converging algorithm using the concept of augmenting paths. Pettie et al. =-=[PS04]-=- present both a deterministic and a randomised algorithm achieving the same approximation in running time O(|E|log 1 ǫ ). In this paper, we show that Preis’s algorithm is easily distributed determinis... |

1 |
Improved linear time approximation algrotihms for weighted matchings
- Drake, Hougardy
(Show Context)
Citation Context ...es achieves the same approximation, improving the running time to O(|E|). Using a path-growing algorithm, Drake et al. [DH03b] achieve the same running time and performance ratio. Later, Drake et al. =-=[DH03a]-=- improved the approximation to 3/2 + ǫ, using a slowly converging algorithm using the concept of augmenting paths. Pettie et al. [PS04] present both a deterministic and a randomised algorithm achievin... |