Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/bipartite/covering.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 """ Functions related to graph covers.""" |
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2 |
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3 from networkx.utils import not_implemented_for |
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4 from networkx.algorithms.bipartite.matching import hopcroft_karp_matching |
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5 from networkx.algorithms.covering import min_edge_cover as _min_edge_cover |
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6 |
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7 __all__ = ["min_edge_cover"] |
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8 |
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9 |
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10 @not_implemented_for("directed") |
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11 @not_implemented_for("multigraph") |
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12 def min_edge_cover(G, matching_algorithm=None): |
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13 """Returns a set of edges which constitutes |
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14 the minimum edge cover of the graph. |
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15 |
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16 The smallest edge cover can be found in polynomial time by finding |
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17 a maximum matching and extending it greedily so that all nodes |
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18 are covered. |
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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 An undirected bipartite graph. |
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24 |
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25 matching_algorithm : function |
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26 A function that returns a maximum cardinality matching in a |
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27 given bipartite graph. The function must take one input, the |
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28 graph ``G``, and return a dictionary mapping each node to its |
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29 mate. If not specified, |
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30 :func:`~networkx.algorithms.bipartite.matching.hopcroft_karp_matching` |
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31 will be used. Other possibilities include |
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32 :func:`~networkx.algorithms.bipartite.matching.eppstein_matching`, |
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33 |
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34 Returns |
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35 ------- |
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36 set |
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37 A set of the edges in a minimum edge cover of the graph, given as |
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38 pairs of nodes. It contains both the edges `(u, v)` and `(v, u)` |
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39 for given nodes `u` and `v` among the edges of minimum edge cover. |
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40 |
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41 Notes |
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42 ----- |
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43 An edge cover of a graph is a set of edges such that every node of |
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44 the graph is incident to at least one edge of the set. |
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45 A minimum edge cover is an edge covering of smallest cardinality. |
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46 |
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47 Due to its implementation, the worst-case running time of this algorithm |
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48 is bounded by the worst-case running time of the function |
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49 ``matching_algorithm``. |
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50 """ |
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51 if G.order() == 0: # Special case for the empty graph |
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52 return set() |
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53 if matching_algorithm is None: |
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54 matching_algorithm = hopcroft_karp_matching |
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55 return _min_edge_cover(G, matching_algorithm=matching_algorithm) |