## A Simple Approximation Algorithm for the Weighted Matching Problem (2003)

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Venue: | Information Processing Letters |

Citations: | 35 - 4 self |

### BibTeX

@ARTICLE{Drake03asimple,

author = {Doratha E. Drake and Stefan Hougardy},

title = {A Simple Approximation Algorithm for the Weighted Matching Problem},

journal = {Information Processing Letters},

year = {2003},

volume = {85},

pages = {211--213}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present a linear time approximation algorithm with a performance ratio of 1/2 for nding a maximum weight matching in an arbitrary graph. Such a result is already known and is due to Preis [7].

### Citations

671 | An Introduction to Parallel Algorithms - JAJA - 1992 |

151 |
Data structures for weighted matching and nearest common ancestors with linking
- Gabow
- 1990
(Show Context)
Citation Context ...e). Now the weighted matching problem is tosnd a matching M in G that has maximum weight. The fastest algorithm known today for solving the weighted matching problem in general graphs is due to Gabow =-=[2]-=- and has a running time of O(jV jjEj+ jV j 2 log jV j). Under the assumption that all edge weights are integers in the range [1 : : : N ] Gabow and Tarjan [3] presented an algorithm with running time ... |

91 | Faster scaling algorithms for general graphmatching problems
- Gabow, Tarjan
- 1991
(Show Context)
Citation Context ...problem in general graphs is due to Gabow [2] and has a running time of O(jV jjEj+ jV j 2 log jV j). Under the assumption that all edge weights are integers in the range [1 : : : N ] Gabow and Tarjan =-=[-=-3] presented an algorithm with running time O( p jV j log(jV j)(jEj; jV j)jEj log(N jV j), where is the inverse of Ackermann's Greedy Matching (G = (V; E); w : E ! R+ ) 1 M := ; 2 while E 6= ; do beg... |

90 | Computing minimum-weight perfect matchings
- COOK, ROHE
- 1999
(Show Context)
Citation Context ...running time. One other reason why one is interested in simple approximation algorithms, is that implementing polynomial time exact algorithms for the weighted matching problem is a very tedious task =-=[1]-=-. The quality of an approximation algorithm for solving the weighted matching problem is measured by its so called performance ratio. An approximation algorithm has a performance ratio of c, if for al... |

51 | The Analysis of Algorithms - Purdom, Brown - 1985 |

46 | A theory of alternating paths and blossoms for proving correctness of the O( √ V E) maximum matching algorithm
- Vazirani
- 1994
(Show Context)
Citation Context ...f maximum size in a graph is a fundamental problem in algorithmic graph theory which has many applications. The fastest algorithm known today for solving this problem is due to Micali and Vazirani [4]=-=[8-=-] and has a running time of O( p jV jjEj). In this paper we are interested in algorithms for the weighted matching problem. The problem is dened as follows: Let G = (V; E) be a graph and w : E ! R+ be... |

40 | Matching is as easy as matrix inversion, Combinatorica 7 - Mulmuley, Vazirani, et al. - 1987 |

38 | Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs,” ser
- Preis
- 2001
(Show Context)
Citation Context ...bstract. We present a linear time approximation algorithm with a performance ratio of 1/2 forsnding a maximum weight matching in an arbitrary graph. Such a result is already known and is due to Preis =-=[7]-=-. Our algorithm uses a new approach which is much simpler than the one given in [7] and needs no amortized analysis for its running time. Keywords. approximation algorithms, analysis of algorithms, gr... |

36 | A new parallel algorithm for the maximal independent set problem - Goldberg, Spencer - 1989 |

30 | Quality matching and local improvement for multilevel graph-partitioning
- Monien, Preis, et al.
- 1999
(Show Context)
Citation Context ...tchings. function. For many practical problems involving very large graphs such running times can be too costly. Examples are the renement of FEM nets [5] and the partitioning problem in VLSI-Design [=-=6]-=-. Therefore one is interested in approximation algorithms for the weighted matching problem which ideally have linear running time. One other reason why one is interested in simple approximation algor... |

27 | Fast Parallel Algorithms for Graph Matching Problems - Karpinski, Rytter - 1998 |

19 | Improved linear time approximation algorithms for weighted matchings
- Drake, Hougardy
- 2003
(Show Context)
Citation Context ... possible weight. In 1999 Preis [16] presented a linear time algorithm also achieving a factor 1/2 approximation. Another such algorithm which is much simpler was presented in [3]. Drake and Hougardy =-=[4]-=- improved this result in 2004 by presenting a linear time algorithm which achieves a 2/3 − ɛ approximation factor for arbitrarily small ɛ. Pettie and Sanders [15] presented another such algorithm whit... |

18 | Constructing a perfect matching - Karp, Upfal, et al. - 1986 |

13 |
An O( |V |·|E|) Algorithm for Finding Maximum Matching
- Micali, Vazirani
- 1980
(Show Context)
Citation Context ...g of maximum size in a graph is a fundamental problem in algorithmic graph theory which has many applications. The fastest algorithm known today for solving this problem is due to Micali and Vazirani =-=[4-=-][8] and has a running time of O( p jV jjEj). In this paper we are interested in algorithms for the weighted matching problem. The problem is dened as follows: Let G = (V; E) be a graph and w : E ! R+... |

11 | A Las Vegas RNC algorithm for maximum matching - Karloff - 1986 |

9 |
Maximum matching and a polyhedron with (0
- Edmonds
- 1965
(Show Context)
Citation Context ...ysis of algorithms, graph algorithms, maximum weight matching 1 Introduction The weighted matching problem in graphs is to find a matching of maximum weight in an edge weighted graph. In 1965 Edmonds =-=[5]-=- presented the first polynomial time algorithm for this problem. The running time of his algorithm was improved over the years and the fastest algorithm currently known for the weighted matching probl... |

6 |
A simpler linear time 2/3 − ε approximation for maximum weight matching
- Pettie, Sanders
(Show Context)
Citation Context ...s presented in [3]. Drake and Hougardy [4] improved this result in 2004 by presenting a linear time algorithm which achieves a 2/3 − ɛ approximation factor for arbitrarily small ɛ. Pettie and Sanders =-=[15]-=- presented another such algorithm whith better dependence of the running time on ɛ. No other constant factor approximation algorithms for the weighted matching problem are known that are faster than G... |

3 |
Linear Time Local Improvements for Weighted
- Drake, Hougardy
- 2003
(Show Context)
Citation Context ...ir gain. □ Let M be a matching and e ∈ M. Then using the data structure of armsx one can easily find an augmentation in A2 with e as a center that achieves the maximum gain. This was already shown in =-=[1]-=-. Here we extend this result in the following: 73/4-Matching: G =(V, E),w : E → R+, l ∈ N, matching M Output: matching M ′ 1 ALG = ∅ 2 while M ̸= ∅ do 3 compute Ai(⃗e) for all e ∈ M, i ≥ 0 and both o... |

1 |
Complexity and modeling aspects of mesh re into quadrilaterals
- ohring, H, et al.
- 1997
(Show Context)
Citation Context ...The greedy algorithm forsnding maximum weight matchings. function. For many practical problems involving very large graphs such running times can be too costly. Examples are the renement of FEM nets [=-=5]-=- and the partitioning problem in VLSI-Design [6]. Therefore one is interested in approximation algorithms for the weighted matching problem which ideally have linear running time. One other reason why... |