# Maximum-Weight Matching (Maximum-Weight Matching)

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## Description

In computer science, the maximum weight matching problem is the problem of finding, in a weighted graph, a matching in which the sum of weights is maximized. Here, the graph is unrestricted; i.e. can be any general graph.

## Related Problems

Subproblem: Bipartite Maximum-Weight Matching

## Parameters

$n$: number of vertices

$m$: number of edges

$N$: largest weight magnitude

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Hungarian algorithm | 1955 | $O(n^{4})$ | $O(n^{2})$ | Exact | Deterministic | Time |

Edmonds | 1965 | $O(mn^{2})$ | $O(mn^{2})$?? | Exact | Deterministic | Time |

Micali; Vazirani | 1980 | $O(n^{3} \log n)$ | Exact | Deterministic | Time | |

Mucha and Sankowski | 2004 | $O(n^{3})$ | Exact | Deterministic | Time |