Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/flow/utils.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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 Utility classes and functions for network flow algorithms. |
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3 """ |
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4 |
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5 from collections import deque |
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6 import networkx as nx |
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7 |
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8 __all__ = [ |
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9 "CurrentEdge", |
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10 "Level", |
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11 "GlobalRelabelThreshold", |
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12 "build_residual_network", |
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13 "detect_unboundedness", |
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14 "build_flow_dict", |
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15 ] |
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16 |
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17 |
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18 class CurrentEdge: |
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19 """Mechanism for iterating over out-edges incident to a node in a circular |
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20 manner. StopIteration exception is raised when wraparound occurs. |
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21 """ |
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22 |
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23 __slots__ = ("_edges", "_it", "_curr") |
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24 |
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25 def __init__(self, edges): |
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26 self._edges = edges |
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27 if self._edges: |
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28 self._rewind() |
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29 |
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30 def get(self): |
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31 return self._curr |
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32 |
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33 def move_to_next(self): |
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34 try: |
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35 self._curr = next(self._it) |
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36 except StopIteration: |
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37 self._rewind() |
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38 raise |
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39 |
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40 def _rewind(self): |
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41 self._it = iter(self._edges.items()) |
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42 self._curr = next(self._it) |
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43 |
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44 |
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45 class Level: |
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46 """Active and inactive nodes in a level. |
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47 """ |
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48 |
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49 __slots__ = ("active", "inactive") |
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50 |
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51 def __init__(self): |
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52 self.active = set() |
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53 self.inactive = set() |
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54 |
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55 |
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56 class GlobalRelabelThreshold: |
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57 """Measurement of work before the global relabeling heuristic should be |
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58 applied. |
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59 """ |
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60 |
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61 def __init__(self, n, m, freq): |
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62 self._threshold = (n + m) / freq if freq else float("inf") |
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63 self._work = 0 |
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64 |
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65 def add_work(self, work): |
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66 self._work += work |
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67 |
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68 def is_reached(self): |
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69 return self._work >= self._threshold |
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70 |
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71 def clear_work(self): |
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72 self._work = 0 |
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73 |
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74 |
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75 def build_residual_network(G, capacity): |
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76 """Build a residual network and initialize a zero flow. |
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77 |
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78 The residual network :samp:`R` from an input graph :samp:`G` has the |
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79 same nodes as :samp:`G`. :samp:`R` is a DiGraph that contains a pair |
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80 of edges :samp:`(u, v)` and :samp:`(v, u)` iff :samp:`(u, v)` is not a |
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81 self-loop, and at least one of :samp:`(u, v)` and :samp:`(v, u)` exists |
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82 in :samp:`G`. |
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83 |
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84 For each edge :samp:`(u, v)` in :samp:`R`, :samp:`R[u][v]['capacity']` |
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85 is equal to the capacity of :samp:`(u, v)` in :samp:`G` if it exists |
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86 in :samp:`G` or zero otherwise. If the capacity is infinite, |
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87 :samp:`R[u][v]['capacity']` will have a high arbitrary finite value |
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88 that does not affect the solution of the problem. This value is stored in |
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89 :samp:`R.graph['inf']`. For each edge :samp:`(u, v)` in :samp:`R`, |
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90 :samp:`R[u][v]['flow']` represents the flow function of :samp:`(u, v)` and |
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91 satisfies :samp:`R[u][v]['flow'] == -R[v][u]['flow']`. |
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92 |
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93 The flow value, defined as the total flow into :samp:`t`, the sink, is |
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94 stored in :samp:`R.graph['flow_value']`. If :samp:`cutoff` is not |
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95 specified, reachability to :samp:`t` using only edges :samp:`(u, v)` such |
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96 that :samp:`R[u][v]['flow'] < R[u][v]['capacity']` induces a minimum |
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97 :samp:`s`-:samp:`t` cut. |
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98 |
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99 """ |
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100 if G.is_multigraph(): |
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101 raise nx.NetworkXError("MultiGraph and MultiDiGraph not supported (yet).") |
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102 |
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103 R = nx.DiGraph() |
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104 R.add_nodes_from(G) |
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105 |
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106 inf = float("inf") |
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107 # Extract edges with positive capacities. Self loops excluded. |
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108 edge_list = [ |
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109 (u, v, attr) |
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110 for u, v, attr in G.edges(data=True) |
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111 if u != v and attr.get(capacity, inf) > 0 |
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112 ] |
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113 # Simulate infinity with three times the sum of the finite edge capacities |
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114 # or any positive value if the sum is zero. This allows the |
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115 # infinite-capacity edges to be distinguished for unboundedness detection |
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116 # and directly participate in residual capacity calculation. If the maximum |
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117 # flow is finite, these edges cannot appear in the minimum cut and thus |
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118 # guarantee correctness. Since the residual capacity of an |
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119 # infinite-capacity edge is always at least 2/3 of inf, while that of an |
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120 # finite-capacity edge is at most 1/3 of inf, if an operation moves more |
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121 # than 1/3 of inf units of flow to t, there must be an infinite-capacity |
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122 # s-t path in G. |
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123 inf = ( |
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124 3 |
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125 * sum( |
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126 attr[capacity] |
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127 for u, v, attr in edge_list |
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128 if capacity in attr and attr[capacity] != inf |
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129 ) |
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130 or 1 |
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131 ) |
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132 if G.is_directed(): |
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133 for u, v, attr in edge_list: |
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134 r = min(attr.get(capacity, inf), inf) |
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135 if not R.has_edge(u, v): |
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136 # Both (u, v) and (v, u) must be present in the residual |
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137 # network. |
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138 R.add_edge(u, v, capacity=r) |
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139 R.add_edge(v, u, capacity=0) |
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140 else: |
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141 # The edge (u, v) was added when (v, u) was visited. |
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142 R[u][v]["capacity"] = r |
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143 else: |
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144 for u, v, attr in edge_list: |
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145 # Add a pair of edges with equal residual capacities. |
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146 r = min(attr.get(capacity, inf), inf) |
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147 R.add_edge(u, v, capacity=r) |
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148 R.add_edge(v, u, capacity=r) |
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149 |
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150 # Record the value simulating infinity. |
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151 R.graph["inf"] = inf |
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152 |
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153 return R |
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154 |
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155 |
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156 def detect_unboundedness(R, s, t): |
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157 """Detect an infinite-capacity s-t path in R. |
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158 """ |
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159 q = deque([s]) |
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160 seen = {s} |
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161 inf = R.graph["inf"] |
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162 while q: |
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163 u = q.popleft() |
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164 for v, attr in R[u].items(): |
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165 if attr["capacity"] == inf and v not in seen: |
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166 if v == t: |
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167 raise nx.NetworkXUnbounded( |
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168 "Infinite capacity path, flow unbounded above." |
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169 ) |
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170 seen.add(v) |
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171 q.append(v) |
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172 |
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173 |
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174 def build_flow_dict(G, R): |
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175 """Build a flow dictionary from a residual network. |
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176 """ |
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177 flow_dict = {} |
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178 for u in G: |
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179 flow_dict[u] = {v: 0 for v in G[u]} |
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180 flow_dict[u].update( |
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181 (v, attr["flow"]) for v, attr in R[u].items() if attr["flow"] > 0 |
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182 ) |
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183 return flow_dict |