# Efficient algorithms for finding maximum matching in graphs

@article{Galil1986EfficientAF, title={Efficient algorithms for finding maximum matching in graphs}, author={Zvi Galil}, journal={ACM Comput. Surv.}, year={1986}, volume={18}, pages={23-38} }

This paper surveys the techniques used for designing the most efficient algorithms for finding a maximum cardinality or weighted matching in (general or bipartite) graphs. It also lists some open problems concerning possible improvements in existing algorithms and the existence of fast parallel algorithms for these problems.

## 479 Citations

AN ALGORITHM TO FIND A MAXIMUM MATCHING OF A TRAPEZOID GRAPH

- Computer Science, Mathematics
- 2005

An efficient algorithm is presented which takes O(n²) time and O( n+m) space for a trapezoid graph, where n and m represent the number of vertices and theNumber of edges of the graph.

A Self-Stabilizing Algorithm for Maximum Matching in Trees

- Computer Science
- 2007

This paper presents a distributed, self-stabilizing algorithm for constructing a maximum matching in trees that does not require any initialization and is tolerant to transient faults.

Finding the Maximum Matching in a Bipartite Graph

- Mathematics
- 2010

A matching M of the graph G is an edge set such that no two edges of M share their endpoints. For a bipartite graph G = (V, E) maximum matching are matching whose cardinalities are maximum among all…

A New Approach to Maximum Matching in General Graphs

- Mathematics, Computer ScienceICALP
- 1990

A straightforward algorithm for maximum matching in general graphs of time complexity O(√nm) is obtained, where n is the number of nodes and m is thenumber of edges in the graph.

Fast Parallel Approximation Algorithms for Maximum Weighted Matching Problem

- Computer Science
- 2007

Two parallel approximation algorithms for matching a matching of maximum weight in a given edge-weighted graph using the total order of the weights to deal with unbounded weights on a PRAM are presented.

in Interval Graphs

- Computer Science, Mathematics
- 1997

A new parallel maximum matching algorith,ms in interval graphs by exploiting the characteristics of interval graphs is developed, which requires O(log2 w+(n log n)/w) time and O(nv2 + n) operations on the CREW PRAM.

New Approximation Results on Graph Matching and related Problems

- MathematicsWG
- 1994

This work proposes an approximate maximum cardinality matching algorithm that runs in O(e+n) sequential time yielding a matching of size at least e/n−1, improving the bound known before.

The symmetric travelling salesman problem I. New fast lower bounds for the problem of optimal 2-matching

- Computer Science
- 2009

To solve the symmetric travelling salesman problem, a lower bound is suggested—the solution of an optimal 2-matching problem that is solved not completely, but up to obtaining new stable lower bounds.

Approximation algorithms for covering a graph by vertex-disjoint paths of maximum total weight

- Computer ScienceNetworks
- 1990

This work considers the problem of covering a weighted graph G = (V, E) by a set of vertex-disjoint paths, such that the total weight of these paths is maximized, and develops an algorithm for covering undirected graphs.

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