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