Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/coloring/greedy_coloring.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 Greedy graph coloring using various strategies. |
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3 """ |
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4 from collections import defaultdict, deque |
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5 import itertools |
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6 |
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7 import networkx as nx |
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8 from networkx.utils import arbitrary_element |
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9 from networkx.utils import py_random_state |
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10 from . import greedy_coloring_with_interchange as _interchange |
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11 |
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12 __all__ = [ |
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13 "greedy_color", |
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14 "strategy_connected_sequential", |
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15 "strategy_connected_sequential_bfs", |
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16 "strategy_connected_sequential_dfs", |
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17 "strategy_independent_set", |
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18 "strategy_largest_first", |
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19 "strategy_random_sequential", |
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20 "strategy_saturation_largest_first", |
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21 "strategy_smallest_last", |
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22 ] |
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23 |
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24 |
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25 def strategy_largest_first(G, colors): |
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26 """Returns a list of the nodes of ``G`` in decreasing order by |
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27 degree. |
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28 |
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29 ``G`` is a NetworkX graph. ``colors`` is ignored. |
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30 |
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31 """ |
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32 return sorted(G, key=G.degree, reverse=True) |
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33 |
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34 |
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35 @py_random_state(2) |
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36 def strategy_random_sequential(G, colors, seed=None): |
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37 """Returns a random permutation of the nodes of ``G`` as a list. |
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38 |
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39 ``G`` is a NetworkX graph. ``colors`` is ignored. |
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40 |
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41 seed : integer, random_state, or None (default) |
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42 Indicator of random number generation state. |
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43 See :ref:`Randomness<randomness>`. |
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44 """ |
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45 nodes = list(G) |
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46 seed.shuffle(nodes) |
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47 return nodes |
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48 |
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49 |
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50 def strategy_smallest_last(G, colors): |
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51 """Returns a deque of the nodes of ``G``, "smallest" last. |
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52 |
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53 Specifically, the degrees of each node are tracked in a bucket queue. |
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54 From this, the node of minimum degree is repeatedly popped from the |
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55 graph, updating its neighbors' degrees. |
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56 |
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57 ``G`` is a NetworkX graph. ``colors`` is ignored. |
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58 |
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59 This implementation of the strategy runs in $O(n + m)$ time |
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60 (ignoring polylogarithmic factors), where $n$ is the number of nodes |
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61 and $m$ is the number of edges. |
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62 |
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63 This strategy is related to :func:`strategy_independent_set`: if we |
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64 interpret each node removed as an independent set of size one, then |
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65 this strategy chooses an independent set of size one instead of a |
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66 maximal independent set. |
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67 |
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68 """ |
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69 H = G.copy() |
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70 result = deque() |
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71 |
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72 # Build initial degree list (i.e. the bucket queue data structure) |
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73 degrees = defaultdict(set) # set(), for fast random-access removals |
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74 lbound = float("inf") |
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75 for node, d in H.degree(): |
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76 degrees[d].add(node) |
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77 lbound = min(lbound, d) # Lower bound on min-degree. |
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78 |
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79 def find_min_degree(): |
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80 # Save time by starting the iterator at `lbound`, not 0. |
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81 # The value that we find will be our new `lbound`, which we set later. |
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82 return next(d for d in itertools.count(lbound) if d in degrees) |
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83 |
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84 for _ in G: |
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85 # Pop a min-degree node and add it to the list. |
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86 min_degree = find_min_degree() |
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87 u = degrees[min_degree].pop() |
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88 if not degrees[min_degree]: # Clean up the degree list. |
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89 del degrees[min_degree] |
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90 result.appendleft(u) |
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91 |
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92 # Update degrees of removed node's neighbors. |
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93 for v in H[u]: |
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94 degree = H.degree(v) |
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95 degrees[degree].remove(v) |
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96 if not degrees[degree]: # Clean up the degree list. |
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97 del degrees[degree] |
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98 degrees[degree - 1].add(v) |
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99 |
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100 # Finally, remove the node. |
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101 H.remove_node(u) |
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102 lbound = min_degree - 1 # Subtract 1 in case of tied neighbors. |
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103 |
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104 return result |
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105 |
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106 |
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107 def _maximal_independent_set(G): |
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108 """Returns a maximal independent set of nodes in ``G`` by repeatedly |
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109 choosing an independent node of minimum degree (with respect to the |
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110 subgraph of unchosen nodes). |
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111 |
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112 """ |
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113 result = set() |
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114 remaining = set(G) |
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115 while remaining: |
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116 G = G.subgraph(remaining) |
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117 v = min(remaining, key=G.degree) |
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118 result.add(v) |
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119 remaining -= set(G[v]) | {v} |
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120 return result |
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121 |
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122 |
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123 def strategy_independent_set(G, colors): |
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124 """Uses a greedy independent set removal strategy to determine the |
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125 colors. |
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126 |
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127 This function updates ``colors`` **in-place** and return ``None``, |
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128 unlike the other strategy functions in this module. |
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129 |
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130 This algorithm repeatedly finds and removes a maximal independent |
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131 set, assigning each node in the set an unused color. |
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132 |
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133 ``G`` is a NetworkX graph. |
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134 |
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135 This strategy is related to :func:`strategy_smallest_last`: in that |
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136 strategy, an independent set of size one is chosen at each step |
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137 instead of a maximal independent set. |
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138 |
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139 """ |
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140 remaining_nodes = set(G) |
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141 while len(remaining_nodes) > 0: |
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142 nodes = _maximal_independent_set(G.subgraph(remaining_nodes)) |
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143 remaining_nodes -= nodes |
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144 yield from nodes |
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145 |
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146 |
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147 def strategy_connected_sequential_bfs(G, colors): |
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148 """Returns an iterable over nodes in ``G`` in the order given by a |
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149 breadth-first traversal. |
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150 |
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151 The generated sequence has the property that for each node except |
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152 the first, at least one neighbor appeared earlier in the sequence. |
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153 |
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154 ``G`` is a NetworkX graph. ``colors`` is ignored. |
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155 |
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156 """ |
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157 return strategy_connected_sequential(G, colors, "bfs") |
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158 |
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159 |
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160 def strategy_connected_sequential_dfs(G, colors): |
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161 """Returns an iterable over nodes in ``G`` in the order given by a |
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162 depth-first traversal. |
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163 |
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164 The generated sequence has the property that for each node except |
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165 the first, at least one neighbor appeared earlier in the sequence. |
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166 |
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167 ``G`` is a NetworkX graph. ``colors`` is ignored. |
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168 |
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169 """ |
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170 return strategy_connected_sequential(G, colors, "dfs") |
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171 |
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172 |
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173 def strategy_connected_sequential(G, colors, traversal="bfs"): |
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174 """Returns an iterable over nodes in ``G`` in the order given by a |
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175 breadth-first or depth-first traversal. |
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176 |
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177 ``traversal`` must be one of the strings ``'dfs'`` or ``'bfs'``, |
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178 representing depth-first traversal or breadth-first traversal, |
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179 respectively. |
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180 |
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181 The generated sequence has the property that for each node except |
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182 the first, at least one neighbor appeared earlier in the sequence. |
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183 |
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184 ``G`` is a NetworkX graph. ``colors`` is ignored. |
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185 |
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186 """ |
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187 if traversal == "bfs": |
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188 traverse = nx.bfs_edges |
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189 elif traversal == "dfs": |
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190 traverse = nx.dfs_edges |
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191 else: |
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192 raise nx.NetworkXError( |
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193 "Please specify one of the strings 'bfs' or" |
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194 " 'dfs' for connected sequential ordering" |
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195 ) |
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196 for component in nx.connected_components(G): |
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197 source = arbitrary_element(component) |
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198 # Yield the source node, then all the nodes in the specified |
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199 # traversal order. |
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200 yield source |
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201 for (_, end) in traverse(G.subgraph(component), source): |
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202 yield end |
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203 |
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204 |
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205 def strategy_saturation_largest_first(G, colors): |
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206 """Iterates over all the nodes of ``G`` in "saturation order" (also |
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207 known as "DSATUR"). |
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208 |
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209 ``G`` is a NetworkX graph. ``colors`` is a dictionary mapping nodes of |
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210 ``G`` to colors, for those nodes that have already been colored. |
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211 |
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212 """ |
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213 distinct_colors = {v: set() for v in G} |
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214 for i in range(len(G)): |
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215 # On the first time through, simply choose the node of highest degree. |
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216 if i == 0: |
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217 node = max(G, key=G.degree) |
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218 yield node |
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219 # Add the color 0 to the distinct colors set for each |
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220 # neighbors of that node. |
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221 for v in G[node]: |
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222 distinct_colors[v].add(0) |
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223 else: |
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224 # Compute the maximum saturation and the set of nodes that |
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225 # achieve that saturation. |
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226 saturation = { |
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227 v: len(c) for v, c in distinct_colors.items() if v not in colors |
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228 } |
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229 # Yield the node with the highest saturation, and break ties by |
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230 # degree. |
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231 node = max(saturation, key=lambda v: (saturation[v], G.degree(v))) |
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232 yield node |
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233 # Update the distinct color sets for the neighbors. |
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234 color = colors[node] |
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235 for v in G[node]: |
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236 distinct_colors[v].add(color) |
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237 |
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238 |
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239 #: Dictionary mapping name of a strategy as a string to the strategy function. |
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240 STRATEGIES = { |
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241 "largest_first": strategy_largest_first, |
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242 "random_sequential": strategy_random_sequential, |
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243 "smallest_last": strategy_smallest_last, |
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244 "independent_set": strategy_independent_set, |
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245 "connected_sequential_bfs": strategy_connected_sequential_bfs, |
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246 "connected_sequential_dfs": strategy_connected_sequential_dfs, |
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247 "connected_sequential": strategy_connected_sequential, |
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248 "saturation_largest_first": strategy_saturation_largest_first, |
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249 "DSATUR": strategy_saturation_largest_first, |
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250 } |
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251 |
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252 |
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253 def greedy_color(G, strategy="largest_first", interchange=False): |
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254 """Color a graph using various strategies of greedy graph coloring. |
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255 |
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256 Attempts to color a graph using as few colors as possible, where no |
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257 neighbours of a node can have same color as the node itself. The |
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258 given strategy determines the order in which nodes are colored. |
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259 |
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260 The strategies are described in [1]_, and smallest-last is based on |
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261 [2]_. |
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262 |
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263 Parameters |
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264 ---------- |
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265 G : NetworkX graph |
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266 |
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267 strategy : string or function(G, colors) |
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268 A function (or a string representing a function) that provides |
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269 the coloring strategy, by returning nodes in the ordering they |
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270 should be colored. ``G`` is the graph, and ``colors`` is a |
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271 dictionary of the currently assigned colors, keyed by nodes. The |
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272 function must return an iterable over all the nodes in ``G``. |
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273 |
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274 If the strategy function is an iterator generator (that is, a |
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275 function with ``yield`` statements), keep in mind that the |
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276 ``colors`` dictionary will be updated after each ``yield``, since |
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277 this function chooses colors greedily. |
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278 |
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279 If ``strategy`` is a string, it must be one of the following, |
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280 each of which represents one of the built-in strategy functions. |
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281 |
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282 * ``'largest_first'`` |
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283 * ``'random_sequential'`` |
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284 * ``'smallest_last'`` |
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285 * ``'independent_set'`` |
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286 * ``'connected_sequential_bfs'`` |
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287 * ``'connected_sequential_dfs'`` |
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288 * ``'connected_sequential'`` (alias for the previous strategy) |
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289 * ``'saturation_largest_first'`` |
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290 * ``'DSATUR'`` (alias for the previous strategy) |
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291 |
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292 interchange: bool |
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293 Will use the color interchange algorithm described by [3]_ if set |
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294 to ``True``. |
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295 |
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296 Note that ``saturation_largest_first`` and ``independent_set`` |
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297 do not work with interchange. Furthermore, if you use |
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298 interchange with your own strategy function, you cannot rely |
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299 on the values in the ``colors`` argument. |
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300 |
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301 Returns |
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302 ------- |
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303 A dictionary with keys representing nodes and values representing |
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304 corresponding coloring. |
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305 |
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306 Examples |
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307 -------- |
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308 >>> G = nx.cycle_graph(4) |
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309 >>> d = nx.coloring.greedy_color(G, strategy="largest_first") |
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310 >>> d in [{0: 0, 1: 1, 2: 0, 3: 1}, {0: 1, 1: 0, 2: 1, 3: 0}] |
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311 True |
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312 |
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313 Raises |
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314 ------ |
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315 NetworkXPointlessConcept |
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316 If ``strategy`` is ``saturation_largest_first`` or |
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317 ``independent_set`` and ``interchange`` is ``True``. |
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318 |
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319 References |
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320 ---------- |
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321 .. [1] Adrian Kosowski, and Krzysztof Manuszewski, |
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322 Classical Coloring of Graphs, Graph Colorings, 2-19, 2004. |
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323 ISBN 0-8218-3458-4. |
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324 .. [2] David W. Matula, and Leland L. Beck, "Smallest-last |
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325 ordering and clustering and graph coloring algorithms." *J. ACM* 30, |
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326 3 (July 1983), 417–427. <https://doi.org/10.1145/2402.322385> |
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327 .. [3] Maciej M. Sysło, Marsingh Deo, Janusz S. Kowalik, |
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328 Discrete Optimization Algorithms with Pascal Programs, 415-424, 1983. |
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329 ISBN 0-486-45353-7. |
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330 |
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331 """ |
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332 if len(G) == 0: |
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333 return {} |
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334 # Determine the strategy provided by the caller. |
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335 strategy = STRATEGIES.get(strategy, strategy) |
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336 if not callable(strategy): |
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337 raise nx.NetworkXError( |
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338 "strategy must be callable or a valid string. " f"{strategy} not valid." |
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339 ) |
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340 # Perform some validation on the arguments before executing any |
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341 # strategy functions. |
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342 if interchange: |
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343 if strategy is strategy_independent_set: |
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344 msg = "interchange cannot be used with independent_set" |
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345 raise nx.NetworkXPointlessConcept(msg) |
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346 if strategy is strategy_saturation_largest_first: |
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347 msg = "interchange cannot be used with" " saturation_largest_first" |
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348 raise nx.NetworkXPointlessConcept(msg) |
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349 colors = {} |
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350 nodes = strategy(G, colors) |
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351 if interchange: |
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352 return _interchange.greedy_coloring_with_interchange(G, nodes) |
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353 for u in nodes: |
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354 # Set to keep track of colors of neighbours |
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355 neighbour_colors = {colors[v] for v in G[u] if v in colors} |
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356 # Find the first unused color. |
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357 for color in itertools.count(): |
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358 if color not in neighbour_colors: |
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359 break |
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360 # Assign the new color to the current node. |
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361 colors[u] = color |
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362 return colors |