General Graph MCM (Maximum Cardinality Matching)
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Description
The goal of maximum cardinality matching is to find a matching with as many edges as possible (equivalently: a matching that covers as many vertices as possible). Here, the graph can be any general graph.
Related Problems
Subproblem: Bipartite Graph MCM
Related: Planar Bipartite Graph Perfect Matching
Parameters
V: number of vertices
E: number of edges
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Micali and Vazirani | 1980 | $O(V^{0.5} E)$ | $O(V)$ | Deterministic | Time & Space | |
| Blum | 1990 | $O((V^{0.5})$E) | $O(E)$ auxiliary?? | Exact | Deterministic | Time |
| Gabow; Tarjan | 1991 | $O((V^{0.5})$E) | $O(E)$ auxiliary? | Exact | Deterministic | Time & Space |
| Mucha, Sankowski (general) | 2004 | $O(V^{2.{37}6})$ | $O(V^{2})$?? | Exact | Randomized | Time |
Time Complexity Graph
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Space Complexity Graph
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Time-Space Tradeoff
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