## A parallel approximation algorithm for the weighted maximum matching problem (2007)

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Venue: | In Proc. Seventh Int. Conf. on Parallel Processing and Applied Mathematics (PPAM |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Manne07aparallel,

author = {Fredrik Manne and Rob H. Bisseling},

title = {A parallel approximation algorithm for the weighted maximum matching problem},

booktitle = {In Proc. Seventh Int. Conf. on Parallel Processing and Applied Mathematics (PPAM},

year = {2007}

}

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### Abstract

Abstract. We consider the problem of computing a weighted edge matching in a large graph using a parallel algorithm. This problem has application in several areas of combinatorial scientific computing. Since an exact algorithm for the weighted matching problem is both fairly expensive to compute and hard to parallelise we instead consider fast approximation algorithms. We analyse a distributed algorithm due to Hoepman [8] and show how this can be turned into a parallel algorithm. Through experiments using both complete as well as sparse graphs we show that our new parallel algorithm scales well using up to 32 processors. 1

### Citations

378 | A simple parallel algorithm for the maximal independent set problem
- Luby
- 1986
(Show Context)
Citation Context ... the work by Preis and returns the same solution as this algorithm. We present and analyse the algorithm by Hoepman and show that this can in fact be phrased as a variant of Luby’s parallel algorithm =-=[10]-=- for finding an independent set in a graph. Next, we explain how it is possible to turn Hoepmans algorithm into an efficient parallel algorithm suitable for distributed-memory computers. This algorith... |

317 | The university of florida sparse matrix collection. http://www.cise.ufl.edu/research/sparse/matrices/index.html
- Davis
(Show Context)
Citation Context ...rigin 3800 using up to 32 processors. For our input data we have used complete graphs with random weights on the edges as well as sparse graphs from the University of Florida sparse matrix collection =-=[3]-=-. The top chart of Figure 1 displays the running time for a complete graph on 5000 vertices with random edge weights, as different numbers of processors are applied. As one can see, the running time d... |

305 | Metis, a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices.” http://www-users.cs.umn.edu/ karypis/metis/metis/download.html
- Karypis, Kumar
- 1998
(Show Context)
Citation Context ...mation from N(v). In the case of a complete graph we use a regular block partition where each processor gets n/p vertices and in the case of a sparse graph we use the Metissgraph partitioning library =-=[9]-=- to achieve an even partition where the number of crossing edges is kept small. In our implementation, we have used ghost-vertices to make handling of crossing edges easier. Thus, if a vertex v is ass... |

74 | The design and use of algorithms for permuting large entries to the diagonal of sparse matrices
- Duff, Koster
- 1999
(Show Context)
Citation Context ... element aij has been chosen no other element in row i or column j can be used as a pivot again. The typical strategy is then to choose pivots in a greedy fashion. But as was shown by Duff and Koster =-=[5,6]-=-, this can lead to sub-optimal results and they demonstrate that better results can be achieved by modelling the pivoting problem as computing a weighted matching in a bipartite graph. This is done by... |

68 |
Parallel Scientific Computation: A Structured Approach using BSP and MPI
- Bisseling
- 2004
(Show Context)
Citation Context ... is continued until the set D is empty on each processor. We note that this separation of computation and communication into distinct, rather than intermingled, stages results in a BSP-type algorithm =-=[2]-=-. The parallelism in the algorithm is obtained from the assumption that each processor will have a large number of local matches to perform between the communication rounds. However, it is not difficu... |

53 |
A survey of heuristics for the weighted matching problem
- Avis
- 1983
(Show Context)
Citation Context ...GM) algorithm where eligible edges are chosen by declining weight, obtains an approximation ratio of 1 2 but requires a global sorting of the edges, thus resulting in a running time of O(|E| log |E|) =-=[1]-=-. Preis [12] has shown how one can avoid the sorting in the GM algorithm, thus getting the time complexity down to O(|E|). The algorithm by Preis depends on finding dominating edges, i.e., edges that ... |

38 | Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs,” ser
- Preis
- 2001
(Show Context)
Citation Context ...hm where eligible edges are chosen by declining weight, obtains an approximation ratio of 1 2 but requires a global sorting of the edges, thus resulting in a running time of O(|E| log |E|) [1]. Preis =-=[12]-=- has shown how one can avoid the sorting in the GM algorithm, thus getting the time complexity down to O(|E|). The algorithm by Preis depends on finding dominating edges, i.e., edges that are heavier ... |

34 | A simple approximation algorithm for the weighted matching problem, Information Processing letters 85
- Drake, Hougardy
- 2003
(Show Context)
Citation Context ...ng can be computed in polynomial time the time complexity of doing this is still high. However, the last years has seen a number of new fast approximation algorithms for the weighted matching problem =-=[2, 3, 8, 9]-=-. As an extension of this Hoepman [6] presented a distributed version of the algorithm by Preis [9]. Our works builds on the work by Hoepman and show how this can be turned into an efficient parallel ... |

16 | A linear-time approximation algorithm for weighted matchings in graphs
- Vinkemeier, Hougardy
- 2005
(Show Context)
Citation Context ...edges that are heavier than their incident edges, and adding these to the matching. Since the work of Preis, linear-time algorithms that get the approximation ratio up to 2 3 − ǫ have been introduced =-=[4, 11]-=-. Common to these algorithms is that they are inherently sequential. Thus, they are unpractical to use if the graph is distributed, as is often the case for scientific applications running on parallel... |

10 |
A simpler linear time 2/3 − ɛ approximation to maximum weight matching
- Pettie, Sanders
- 2004
(Show Context)
Citation Context ...ng can be computed in polynomial time the time complexity of doing this is still high. However, the last years has seen a number of new fast approximation algorithms for the weighted matching problem =-=[2, 3, 8, 9]-=-. As an extension of this Hoepman [6] presented a distributed version of the algorithm by Preis [9]. Our works builds on the work by Hoepman and show how this can be turned into an efficient parallel ... |

9 | Simple distributed weighted matchings
- Hoepman
- 2004
(Show Context)
Citation Context ...ithm for the weighted matching problem is both fairly expensive to compute and hard to parallelise we instead consider fast approximation algorithms. We analyse a distributed algorithm due to Hoepman =-=[8]-=- and show how this can be turned into a parallel algorithm. Through experiments using both complete as well as sparse graphs we show that our new parallel algorithm scales well using up to 32 processo... |

8 |
A simpler linear time 2/3-ǫ approximation for maximum weight matching
- Pettie, Sanders
(Show Context)
Citation Context ...edges that are heavier than their incident edges, and adding these to the matching. Since the work of Preis, linear-time algorithms that get the approximation ratio up to 2 3 − ǫ have been introduced =-=[4, 11]-=-. Common to these algorithms is that they are inherently sequential. Thus, they are unpractical to use if the graph is distributed, as is often the case for scientific applications running on parallel... |

1 |
A simpler linear time 2=3 e approximation for maximum weight matching
- PETTIE, SANDERS
(Show Context)
Citation Context ...ing can be computed in polynomial time the time complexity of doing this is still high.However, the last years has seen a number of new fast approximation algorithms for the weighted matching problem =-=[2, 3, 8, 9]-=-.As an extension of this Hoepman [6] presented a distributed version of the algorithm by Preis [9].Our works builds on the work by Hoepman and show how this can be turned into an efficient parallel al... |