Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/approximation/ramsey.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 Ramsey numbers. |
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3 """ |
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4 import networkx as nx |
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5 from ...utils import arbitrary_element |
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6 |
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7 __all__ = ["ramsey_R2"] |
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8 |
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9 |
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10 def ramsey_R2(G): |
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11 r"""Compute the largest clique and largest independent set in `G`. |
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12 |
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13 This can be used to estimate bounds for the 2-color |
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14 Ramsey number `R(2;s,t)` for `G`. |
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15 |
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16 This is a recursive implementation which could run into trouble |
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17 for large recursions. Note that self-loop edges are ignored. |
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18 |
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19 Parameters |
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20 ---------- |
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21 G : NetworkX graph |
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22 Undirected graph |
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23 |
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24 Returns |
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25 ------- |
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26 max_pair : (set, set) tuple |
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27 Maximum clique, Maximum independent set. |
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28 """ |
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29 if not G: |
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30 return set(), set() |
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31 |
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32 node = arbitrary_element(G) |
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33 nbrs = (nbr for nbr in nx.all_neighbors(G, node) if nbr != node) |
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34 nnbrs = nx.non_neighbors(G, node) |
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35 c_1, i_1 = ramsey_R2(G.subgraph(nbrs).copy()) |
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36 c_2, i_2 = ramsey_R2(G.subgraph(nnbrs).copy()) |
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37 |
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38 c_1.add(node) |
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39 i_2.add(node) |
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40 # Choose the larger of the two cliques and the larger of the two |
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41 # independent sets, according to cardinality. |
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42 return max(c_1, c_2, key=len), max(i_1, i_2, key=len) |