Mercurial > repos > shellac > sam_consensus_v3
comparison env/lib/python3.9/site-packages/networkx/algorithms/approximation/matching.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
| author | shellac |
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| date | Mon, 22 Mar 2021 18:12:50 +0000 |
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| -1:000000000000 | 0:4f3585e2f14b |
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| 1 """ | |
| 2 ************** | |
| 3 Graph Matching | |
| 4 ************** | |
| 5 | |
| 6 Given a graph G = (V,E), a matching M in G is a set of pairwise non-adjacent | |
| 7 edges; that is, no two edges share a common vertex. | |
| 8 | |
| 9 `Wikipedia: Matching <https://en.wikipedia.org/wiki/Matching_(graph_theory)>`_ | |
| 10 """ | |
| 11 import networkx as nx | |
| 12 | |
| 13 __all__ = ["min_maximal_matching"] | |
| 14 | |
| 15 | |
| 16 def min_maximal_matching(G): | |
| 17 r"""Returns the minimum maximal matching of G. That is, out of all maximal | |
| 18 matchings of the graph G, the smallest is returned. | |
| 19 | |
| 20 Parameters | |
| 21 ---------- | |
| 22 G : NetworkX graph | |
| 23 Undirected graph | |
| 24 | |
| 25 Returns | |
| 26 ------- | |
| 27 min_maximal_matching : set | |
| 28 Returns a set of edges such that no two edges share a common endpoint | |
| 29 and every edge not in the set shares some common endpoint in the set. | |
| 30 Cardinality will be 2*OPT in the worst case. | |
| 31 | |
| 32 Notes | |
| 33 ----- | |
| 34 The algorithm computes an approximate solution fo the minimum maximal | |
| 35 cardinality matching problem. The solution is no more than 2 * OPT in size. | |
| 36 Runtime is $O(|E|)$. | |
| 37 | |
| 38 References | |
| 39 ---------- | |
| 40 .. [1] Vazirani, Vijay Approximation Algorithms (2001) | |
| 41 """ | |
| 42 return nx.maximal_matching(G) |