Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/community/kernighan_lin.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 for computing the Kernighan–Lin bipartition algorithm.""" |
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2 |
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3 import networkx as nx |
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4 from itertools import count |
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5 from networkx.utils import not_implemented_for, py_random_state, BinaryHeap |
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6 from networkx.algorithms.community.community_utils import is_partition |
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7 |
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8 __all__ = ["kernighan_lin_bisection"] |
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9 |
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10 |
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11 def _kernighan_lin_sweep(edges, side): |
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12 """ |
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13 This is a modified form of Kernighan-Lin, which moves single nodes at a |
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14 time, alternating between sides to keep the bisection balanced. We keep |
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15 two min-heaps of swap costs to make optimal-next-move selection fast. |
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16 """ |
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17 costs0, costs1 = costs = BinaryHeap(), BinaryHeap() |
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18 for u, side_u, edges_u in zip(count(), side, edges): |
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19 cost_u = sum(w if side[v] else -w for v, w in edges_u) |
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20 costs[side_u].insert(u, cost_u if side_u else -cost_u) |
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21 |
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22 def _update_costs(costs_x, x): |
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23 for y, w in edges[x]: |
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24 costs_y = costs[side[y]] |
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25 cost_y = costs_y.get(y) |
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26 if cost_y is not None: |
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27 cost_y += 2 * (-w if costs_x is costs_y else w) |
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28 costs_y.insert(y, cost_y, True) |
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29 |
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30 i = totcost = 0 |
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31 while costs0 and costs1: |
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32 u, cost_u = costs0.pop() |
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33 _update_costs(costs0, u) |
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34 v, cost_v = costs1.pop() |
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35 _update_costs(costs1, v) |
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36 totcost += cost_u + cost_v |
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37 yield totcost, i, (u, v) |
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38 |
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39 |
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40 @py_random_state(4) |
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41 @not_implemented_for("directed") |
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42 def kernighan_lin_bisection(G, partition=None, max_iter=10, weight="weight", seed=None): |
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43 """Partition a graph into two blocks using the Kernighan–Lin |
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44 algorithm. |
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45 |
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46 This algorithm partitions a network into two sets by iteratively |
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47 swapping pairs of nodes to reduce the edge cut between the two sets. The |
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48 pairs are chosen according to a modified form of Kernighan-Lin, which |
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49 moves node individually, alternating between sides to keep the bisection |
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50 balanced. |
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51 |
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52 Parameters |
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53 ---------- |
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54 G : graph |
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55 |
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56 partition : tuple |
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57 Pair of iterables containing an initial partition. If not |
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58 specified, a random balanced partition is used. |
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59 |
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60 max_iter : int |
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61 Maximum number of times to attempt swaps to find an |
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62 improvemement before giving up. |
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63 |
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64 weight : key |
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65 Edge data key to use as weight. If None, the weights are all |
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66 set to one. |
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67 |
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68 seed : integer, random_state, or None (default) |
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69 Indicator of random number generation state. |
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70 See :ref:`Randomness<randomness>`. |
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71 Only used if partition is None |
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72 |
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73 Returns |
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74 ------- |
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75 partition : tuple |
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76 A pair of sets of nodes representing the bipartition. |
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77 |
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78 Raises |
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79 ------- |
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80 NetworkXError |
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81 If partition is not a valid partition of the nodes of the graph. |
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82 |
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83 References |
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84 ---------- |
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85 .. [1] Kernighan, B. W.; Lin, Shen (1970). |
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86 "An efficient heuristic procedure for partitioning graphs." |
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87 *Bell Systems Technical Journal* 49: 291--307. |
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88 Oxford University Press 2011. |
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89 |
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90 """ |
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91 n = len(G) |
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92 labels = list(G) |
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93 seed.shuffle(labels) |
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94 index = {v: i for i, v in enumerate(labels)} |
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95 |
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96 if partition is None: |
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97 side = [0] * (n // 2) + [1] * ((n + 1) // 2) |
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98 else: |
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99 try: |
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100 A, B = partition |
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101 except (TypeError, ValueError) as e: |
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102 raise nx.NetworkXError("partition must be two sets") from e |
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103 if not is_partition(G, (A, B)): |
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104 raise nx.NetworkXError("partition invalid") |
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105 side = [0] * n |
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106 for a in A: |
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107 side[a] = 1 |
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108 |
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109 if G.is_multigraph(): |
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110 edges = [ |
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111 [ |
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112 (index[u], sum(e.get(weight, 1) for e in d.values())) |
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113 for u, d in G[v].items() |
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114 ] |
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115 for v in labels |
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116 ] |
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117 else: |
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118 edges = [ |
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119 [(index[u], e.get(weight, 1)) for u, e in G[v].items()] for v in labels |
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120 ] |
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121 |
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122 for i in range(max_iter): |
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123 costs = list(_kernighan_lin_sweep(edges, side)) |
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124 min_cost, min_i, _ = min(costs) |
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125 if min_cost >= 0: |
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126 break |
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127 |
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128 for _, _, (u, v) in costs[: min_i + 1]: |
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129 side[u] = 1 |
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130 side[v] = 0 |
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131 |
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132 A = {u for u, s in zip(labels, side) if s == 0} |
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133 B = {u for u, s in zip(labels, side) if s == 1} |
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134 return A, B |