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annotate env/lib/python3.7/site-packages/networkx/utils/rcm.py @ 2:6af9afd405e9 draft

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"planemo upload commit 0a63dd5f4d38a1f6944587f52a8cd79874177fc1"
author shellac
date Thu, 14 May 2020 14:56:58 -0400 (2020-05-14)
parents 26e78fe6e8c4
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1 """
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2 Cuthill-McKee ordering of graph nodes to produce sparse matrices
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3 """
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4 # Copyright (C) 2011-2014 by
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5 # Aric Hagberg <aric.hagberg@gmail.com>
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6 # All rights reserved.
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7 # BSD license.
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8 from collections import deque
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9 from operator import itemgetter
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10
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11 import networkx as nx
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12 from ..utils import arbitrary_element
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13
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14 __author__ = """\n""".join(['Aric Hagberg <aric.hagberg@gmail.com>'])
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15 __all__ = ['cuthill_mckee_ordering',
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16 'reverse_cuthill_mckee_ordering']
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17
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18
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19 def cuthill_mckee_ordering(G, heuristic=None):
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20 """Generate an ordering (permutation) of the graph nodes to make
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21 a sparse matrix.
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22
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23 Uses the Cuthill-McKee heuristic (based on breadth-first search) [1]_.
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24
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25 Parameters
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26 ----------
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27 G : graph
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28 A NetworkX graph
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29
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30 heuristic : function, optional
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31 Function to choose starting node for RCM algorithm. If None
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32 a node from a pseudo-peripheral pair is used. A user-defined function
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33 can be supplied that takes a graph object and returns a single node.
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34
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35 Returns
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36 -------
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37 nodes : generator
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38 Generator of nodes in Cuthill-McKee ordering.
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39
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40 Examples
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41 --------
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42 >>> from networkx.utils import cuthill_mckee_ordering
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43 >>> G = nx.path_graph(4)
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44 >>> rcm = list(cuthill_mckee_ordering(G))
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45 >>> A = nx.adjacency_matrix(G, nodelist=rcm) # doctest: +SKIP
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46
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47 Smallest degree node as heuristic function:
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48
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49 >>> def smallest_degree(G):
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50 ... return min(G, key=G.degree)
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51 >>> rcm = list(cuthill_mckee_ordering(G, heuristic=smallest_degree))
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52
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53
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54 See Also
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55 --------
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56 reverse_cuthill_mckee_ordering
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57
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58 Notes
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59 -----
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60 The optimal solution the the bandwidth reduction is NP-complete [2]_.
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61
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62
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63 References
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64 ----------
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65 .. [1] E. Cuthill and J. McKee.
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66 Reducing the bandwidth of sparse symmetric matrices,
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67 In Proc. 24th Nat. Conf. ACM, pages 157-172, 1969.
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68 http://doi.acm.org/10.1145/800195.805928
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69 .. [2] Steven S. Skiena. 1997. The Algorithm Design Manual.
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70 Springer-Verlag New York, Inc., New York, NY, USA.
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71 """
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72 for c in nx.connected_components(G):
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73 for n in connected_cuthill_mckee_ordering(G.subgraph(c), heuristic):
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74 yield n
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75
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76
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77 def reverse_cuthill_mckee_ordering(G, heuristic=None):
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78 """Generate an ordering (permutation) of the graph nodes to make
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79 a sparse matrix.
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80
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81 Uses the reverse Cuthill-McKee heuristic (based on breadth-first search)
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82 [1]_.
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83
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84 Parameters
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85 ----------
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86 G : graph
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87 A NetworkX graph
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88
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89 heuristic : function, optional
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90 Function to choose starting node for RCM algorithm. If None
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91 a node from a pseudo-peripheral pair is used. A user-defined function
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92 can be supplied that takes a graph object and returns a single node.
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93
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94 Returns
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95 -------
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96 nodes : generator
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97 Generator of nodes in reverse Cuthill-McKee ordering.
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98
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99 Examples
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100 --------
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101 >>> from networkx.utils import reverse_cuthill_mckee_ordering
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102 >>> G = nx.path_graph(4)
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103 >>> rcm = list(reverse_cuthill_mckee_ordering(G))
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104 >>> A = nx.adjacency_matrix(G, nodelist=rcm) # doctest: +SKIP
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105
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106 Smallest degree node as heuristic function:
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107
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108 >>> def smallest_degree(G):
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109 ... return min(G, key=G.degree)
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110 >>> rcm = list(reverse_cuthill_mckee_ordering(G, heuristic=smallest_degree))
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111
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112
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113 See Also
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114 --------
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115 cuthill_mckee_ordering
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116
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117 Notes
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118 -----
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119 The optimal solution the the bandwidth reduction is NP-complete [2]_.
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120
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121 References
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122 ----------
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123 .. [1] E. Cuthill and J. McKee.
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124 Reducing the bandwidth of sparse symmetric matrices,
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125 In Proc. 24th Nat. Conf. ACM, pages 157-72, 1969.
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126 http://doi.acm.org/10.1145/800195.805928
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127 .. [2] Steven S. Skiena. 1997. The Algorithm Design Manual.
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128 Springer-Verlag New York, Inc., New York, NY, USA.
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129 """
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130 return reversed(list(cuthill_mckee_ordering(G, heuristic=heuristic)))
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131
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132
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133 def connected_cuthill_mckee_ordering(G, heuristic=None):
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134 # the cuthill mckee algorithm for connected graphs
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135 if heuristic is None:
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136 start = pseudo_peripheral_node(G)
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137 else:
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138 start = heuristic(G)
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139 visited = {start}
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140 queue = deque([start])
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141 while queue:
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142 parent = queue.popleft()
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143 yield parent
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144 nd = sorted(list(G.degree(set(G[parent]) - visited)),
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145 key=itemgetter(1))
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146 children = [n for n, d in nd]
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147 visited.update(children)
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148 queue.extend(children)
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149
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150
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151 def pseudo_peripheral_node(G):
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152 # helper for cuthill-mckee to find a node in a "pseudo peripheral pair"
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153 # to use as good starting node
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154 u = arbitrary_element(G)
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155 lp = 0
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156 v = u
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157 while True:
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158 spl = dict(nx.shortest_path_length(G, v))
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159 l = max(spl.values())
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160 if l <= lp:
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161 break
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162 lp = l
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163 farthest = (n for n, dist in spl.items() if dist == l)
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164 v, deg = min(G.degree(farthest), key=itemgetter(1))
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165 return v