Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/community/lukes.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 """Lukes Algorithm for exact optimal weighted tree partitioning.""" |
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2 |
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3 from copy import deepcopy |
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4 from functools import lru_cache |
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5 from random import choice |
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6 |
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7 import networkx as nx |
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8 from networkx.utils import not_implemented_for |
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9 |
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10 __all__ = ["lukes_partitioning"] |
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11 |
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12 D_EDGE_W = "weight" |
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13 D_EDGE_VALUE = 1.0 |
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14 D_NODE_W = "weight" |
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15 D_NODE_VALUE = 1 |
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16 PKEY = "partitions" |
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17 CLUSTER_EVAL_CACHE_SIZE = 2048 |
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18 |
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19 |
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20 def _split_n_from(n: int, min_size_of_first_part: int): |
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21 # splits j in two parts of which the first is at least |
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22 # the second argument |
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23 assert n >= min_size_of_first_part |
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24 for p1 in range(min_size_of_first_part, n + 1): |
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25 yield p1, n - p1 |
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26 |
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27 |
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28 def lukes_partitioning(G, max_size: int, node_weight=None, edge_weight=None) -> list: |
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29 |
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30 """Optimal partitioning of a weighted tree using the Lukes algorithm. |
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31 |
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32 This algorithm partitions a connected, acyclic graph featuring integer |
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33 node weights and float edge weights. The resulting clusters are such |
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34 that the total weight of the nodes in each cluster does not exceed |
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35 max_size and that the weight of the edges that are cut by the partition |
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36 is minimum. The algorithm is based on LUKES[1]. |
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37 |
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38 Parameters |
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39 ---------- |
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40 G : graph |
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41 |
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42 max_size : int |
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43 Maximum weight a partition can have in terms of sum of |
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44 node_weight for all nodes in the partition |
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45 |
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46 edge_weight : key |
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47 Edge data key to use as weight. If None, the weights are all |
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48 set to one. |
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49 |
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50 node_weight : key |
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51 Node data key to use as weight. If None, the weights are all |
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52 set to one. The data must be int. |
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53 |
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54 Returns |
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55 ------- |
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56 partition : list |
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57 A list of sets of nodes representing the clusters of the |
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58 partition. |
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59 |
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60 Raises |
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61 ------- |
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62 NotATree |
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63 If G is not a tree. |
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64 TypeError |
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65 If any of the values of node_weight is not int. |
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66 |
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67 References |
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68 ---------- |
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69 .. Lukes, J. A. (1974). |
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70 "Efficient Algorithm for the Partitioning of Trees." |
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71 IBM Journal of Research and Development, 18(3), 217–224. |
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72 |
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73 """ |
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74 # First sanity check and tree preparation |
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75 if not nx.is_tree(G): |
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76 raise nx.NotATree("lukes_partitioning works only on trees") |
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77 else: |
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78 if nx.is_directed(G): |
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79 root = [n for n, d in G.in_degree() if d == 0] |
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80 assert len(root) == 1 |
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81 root = root[0] |
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82 t_G = deepcopy(G) |
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83 else: |
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84 root = choice(list(G.nodes)) |
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85 # this has the desirable side effect of not inheriting attributes |
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86 t_G = nx.dfs_tree(G, root) |
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87 |
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88 # Since we do not want to screw up the original graph, |
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89 # if we have a blank attribute, we make a deepcopy |
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90 if edge_weight is None or node_weight is None: |
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91 safe_G = deepcopy(G) |
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92 if edge_weight is None: |
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93 nx.set_edge_attributes(safe_G, D_EDGE_VALUE, D_EDGE_W) |
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94 edge_weight = D_EDGE_W |
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95 if node_weight is None: |
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96 nx.set_node_attributes(safe_G, D_NODE_VALUE, D_NODE_W) |
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97 node_weight = D_NODE_W |
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98 else: |
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99 safe_G = G |
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100 |
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101 # Second sanity check |
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102 # The values of node_weight MUST BE int. |
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103 # I cannot see any room for duck typing without incurring serious |
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104 # danger of subtle bugs. |
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105 all_n_attr = nx.get_node_attributes(safe_G, node_weight).values() |
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106 for x in all_n_attr: |
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107 if not isinstance(x, int): |
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108 raise TypeError( |
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109 "lukes_partitioning needs integer " |
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110 f"values for node_weight ({node_weight})" |
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111 ) |
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112 |
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113 # SUBROUTINES ----------------------- |
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114 # these functions are defined here for two reasons: |
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115 # - brevity: we can leverage global "safe_G" |
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116 # - caching: signatures are hashable |
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117 |
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118 @not_implemented_for("undirected") |
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119 # this is intended to be called only on t_G |
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120 def _leaves(gr): |
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121 for x in gr.nodes: |
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122 if not nx.descendants(gr, x): |
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123 yield x |
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124 |
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125 @not_implemented_for("undirected") |
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126 def _a_parent_of_leaves_only(gr): |
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127 tleaves = set(_leaves(gr)) |
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128 for n in set(gr.nodes) - tleaves: |
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129 if all([x in tleaves for x in nx.descendants(gr, n)]): |
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130 return n |
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131 |
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132 @lru_cache(CLUSTER_EVAL_CACHE_SIZE) |
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133 def _value_of_cluster(cluster: frozenset): |
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134 valid_edges = [e for e in safe_G.edges if e[0] in cluster and e[1] in cluster] |
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135 return sum([safe_G.edges[e][edge_weight] for e in valid_edges]) |
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136 |
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137 def _value_of_partition(partition: list): |
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138 return sum([_value_of_cluster(frozenset(c)) for c in partition]) |
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139 |
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140 @lru_cache(CLUSTER_EVAL_CACHE_SIZE) |
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141 def _weight_of_cluster(cluster: frozenset): |
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142 return sum([safe_G.nodes[n][node_weight] for n in cluster]) |
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143 |
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144 def _pivot(partition: list, node): |
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145 ccx = [c for c in partition if node in c] |
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146 assert len(ccx) == 1 |
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147 return ccx[0] |
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148 |
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149 def _concatenate_or_merge(partition_1: list, partition_2: list, x, i, ref_weigth): |
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150 |
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151 ccx = _pivot(partition_1, x) |
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152 cci = _pivot(partition_2, i) |
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153 merged_xi = ccx.union(cci) |
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154 |
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155 # We first check if we can do the merge. |
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156 # If so, we do the actual calculations, otherwise we concatenate |
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157 if _weight_of_cluster(frozenset(merged_xi)) <= ref_weigth: |
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158 cp1 = list(filter(lambda x: x != ccx, partition_1)) |
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159 cp2 = list(filter(lambda x: x != cci, partition_2)) |
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160 |
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161 option_2 = [merged_xi] + cp1 + cp2 |
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162 return option_2, _value_of_partition(option_2) |
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163 else: |
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164 option_1 = partition_1 + partition_2 |
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165 return option_1, _value_of_partition(option_1) |
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166 |
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167 # INITIALIZATION ----------------------- |
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168 leaves = set(_leaves(t_G)) |
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169 for lv in leaves: |
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170 t_G.nodes[lv][PKEY] = dict() |
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171 slot = safe_G.nodes[lv][node_weight] |
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172 t_G.nodes[lv][PKEY][slot] = [{lv}] |
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173 t_G.nodes[lv][PKEY][0] = [{lv}] |
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174 |
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175 for inner in [x for x in t_G.nodes if x not in leaves]: |
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176 t_G.nodes[inner][PKEY] = dict() |
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177 slot = safe_G.nodes[inner][node_weight] |
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178 t_G.nodes[inner][PKEY][slot] = [{inner}] |
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179 |
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180 # CORE ALGORITHM ----------------------- |
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181 while True: |
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182 x_node = _a_parent_of_leaves_only(t_G) |
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183 weight_of_x = safe_G.nodes[x_node][node_weight] |
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184 best_value = 0 |
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185 best_partition = None |
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186 bp_buffer = dict() |
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187 x_descendants = nx.descendants(t_G, x_node) |
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188 for i_node in x_descendants: |
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189 for j in range(weight_of_x, max_size + 1): |
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190 for a, b in _split_n_from(j, weight_of_x): |
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191 if ( |
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192 a not in t_G.nodes[x_node][PKEY].keys() |
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193 or b not in t_G.nodes[i_node][PKEY].keys() |
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194 ): |
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195 # it's not possible to form this particular weight sum |
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196 continue |
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197 |
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198 part1 = t_G.nodes[x_node][PKEY][a] |
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199 part2 = t_G.nodes[i_node][PKEY][b] |
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200 part, value = _concatenate_or_merge(part1, part2, x_node, i_node, j) |
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201 |
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202 if j not in bp_buffer.keys() or bp_buffer[j][1] < value: |
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203 # we annotate in the buffer the best partition for j |
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204 bp_buffer[j] = part, value |
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205 |
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206 # we also keep track of the overall best partition |
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207 if best_value <= value: |
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208 best_value = value |
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209 best_partition = part |
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210 |
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211 # as illustrated in Lukes, once we finished a child, we can |
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212 # discharge the partitions we found into the graph |
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213 # (the key phrase is make all x == x') |
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214 # so that they are used by the subsequent children |
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215 for w, (best_part_for_vl, vl) in bp_buffer.items(): |
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216 t_G.nodes[x_node][PKEY][w] = best_part_for_vl |
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217 bp_buffer.clear() |
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218 |
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219 # the absolute best partition for this node |
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220 # across all weights has to be stored at 0 |
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221 t_G.nodes[x_node][PKEY][0] = best_partition |
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222 t_G.remove_nodes_from(x_descendants) |
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223 |
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224 if x_node == root: |
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225 # the 0-labeled partition of root |
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226 # is the optimal one for the whole tree |
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227 return t_G.nodes[root][PKEY][0] |