Planar Bipartite Graph Perfect Matching: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Planar Bipartite Graph Perfect Matching (Maximum Cardinality Matching)}} == 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 is a planar bipartite graph. == Related Problems == Generalizations: Bipartite Graph MCM Related: General Graph MCM == Parameters == <pre>V: number of vertices E: number of...") |
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== Parameters == | == Parameters == | ||
$V$: number of vertices | |||
E: number of edges | |||
$E$: number of edges | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Micali and Vazirani ( Maximum Cardinality Matching)|Micali and Vazirani]] || 1980 || $O(V^{0.5} E)$ || $O(V)$ || || Deterministic || [https:// | | [[Micali and Vazirani ( Maximum Cardinality Matching)|Micali and Vazirani]] || 1980 || $O(V^{0.5} E)$ || $O(V)$ || || Deterministic || [https://ieeexplore.ieee.org/document/4567800 Time] & [https://link.springer.com/content/pdf/10.1007/PL00009186.pdf Space] | ||
|- | |- | ||
| [[Klein (section 5) (Planar Bipartite Graph Perfect Matching Maximum Cardinality Matching)|Klein (section 5)]] || 1997 || $O(V^{({4}/{3})$} logV) || $O(V^{({4}/{3})$})? || Exact || Deterministic || [http://theory.stanford.edu/~virgi/cs267/papers/planar-sssp.pdf Time] | | [[Klein (section 5) (Planar Bipartite Graph Perfect Matching Maximum Cardinality Matching)|Klein (section 5)]] || 1997 || $O(V^{({4}/{3})$} logV) || $O(V^{({4}/{3})$})? || Exact || Deterministic || [http://theory.stanford.edu/~virgi/cs267/papers/planar-sssp.pdf Time] | ||
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Maximum Cardinality Matching - Planar Bipartite Graph Perfect Matching - Time.png|1000px]] | [[File:Maximum Cardinality Matching - Planar Bipartite Graph Perfect Matching - Time.png|1000px]] | ||
Latest revision as of 09:07, 28 April 2023
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 is a planar bipartite graph.
Related Problems
Generalizations: Bipartite Graph MCM
Related: General Graph MCM
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 | |
| Klein (section 5) | 1997 | $O(V^{({4}/{3})$} logV) | $O(V^{({4}/{3})$})? | Exact | Deterministic | Time |
Time Complexity Graph
