153 lines
4.9 KiB
Python
153 lines
4.9 KiB
Python
# -*- coding: utf-8 -*-
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"""Maximum flow algorithms test suite on large graphs.
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"""
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__author__ = """Loïc Séguin-C. <loicseguin@gmail.com>"""
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# Copyright (C) 2010 Loïc Séguin-C. <loicseguin@gmail.com>
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# All rights reserved.
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# BSD license.
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import os
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import networkx as nx
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from networkx.algorithms.flow import build_flow_dict, build_residual_network
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from networkx.algorithms.flow import boykov_kolmogorov
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from networkx.algorithms.flow import dinitz
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from networkx.algorithms.flow import edmonds_karp
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from networkx.algorithms.flow import preflow_push
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from networkx.algorithms.flow import shortest_augmenting_path
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from networkx.testing import almost_equal
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flow_funcs = [
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boykov_kolmogorov,
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dinitz,
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edmonds_karp,
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preflow_push,
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shortest_augmenting_path,
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]
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msg = "Assertion failed in function: {0}"
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def gen_pyramid(N):
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# This graph admits a flow of value 1 for which every arc is at
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# capacity (except the arcs incident to the sink which have
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# infinite capacity).
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G = nx.DiGraph()
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for i in range(N - 1):
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cap = 1. / (i + 2)
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for j in range(i + 1):
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G.add_edge((i, j), (i + 1, j),
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capacity=cap)
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cap = 1. / (i + 1) - cap
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G.add_edge((i, j), (i + 1, j + 1),
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capacity=cap)
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cap = 1. / (i + 2) - cap
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for j in range(N):
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G.add_edge((N - 1, j), 't')
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return G
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def read_graph(name):
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dirname = os.path.dirname(__file__)
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path = os.path.join(dirname, name + '.gpickle.bz2')
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return nx.read_gpickle(path)
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def validate_flows(G, s, t, soln_value, R, flow_func):
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flow_value = R.graph['flow_value']
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flow_dict = build_flow_dict(G, R)
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assert soln_value == flow_value, msg.format(flow_func.__name__)
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assert set(G) == set(flow_dict), msg.format(flow_func.__name__)
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for u in G:
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assert set(G[u]) == set(flow_dict[u]), msg.format(flow_func.__name__)
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excess = {u: 0 for u in flow_dict}
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for u in flow_dict:
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for v, flow in flow_dict[u].items():
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assert flow <= G[u][v].get('capacity', float('inf')), msg.format(flow_func.__name__)
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assert flow >= 0, msg.format(flow_func.__name__)
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excess[u] -= flow
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excess[v] += flow
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for u, exc in excess.items():
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if u == s:
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assert exc == -soln_value, msg.format(flow_func.__name__)
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elif u == t:
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assert exc ==soln_value, msg.format(flow_func.__name__)
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else:
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assert exc == 0, msg.format(flow_func.__name__)
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class TestMaxflowLargeGraph:
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def test_complete_graph(self):
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N = 50
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G = nx.complete_graph(N)
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nx.set_edge_attributes(G, 5, 'capacity')
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R = build_residual_network(G, 'capacity')
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kwargs = dict(residual=R)
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for flow_func in flow_funcs:
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kwargs['flow_func'] = flow_func
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flow_value = nx.maximum_flow_value(G, 1, 2, **kwargs)
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assert flow_value == 5 * (N - 1), msg.format(flow_func.__name__)
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def test_pyramid(self):
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N = 10
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# N = 100 # this gives a graph with 5051 nodes
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G = gen_pyramid(N)
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R = build_residual_network(G, 'capacity')
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kwargs = dict(residual=R)
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for flow_func in flow_funcs:
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kwargs['flow_func'] = flow_func
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flow_value = nx.maximum_flow_value(G, (0, 0), 't', **kwargs)
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assert almost_equal(flow_value, 1.), msg.format(flow_func.__name__)
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def test_gl1(self):
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G = read_graph('gl1')
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s = 1
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t = len(G)
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R = build_residual_network(G, 'capacity')
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kwargs = dict(residual=R)
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# do one flow_func to save time
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flow_func = flow_funcs[0]
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validate_flows(G, s, t, 156545, flow_func(G, s, t, **kwargs),
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flow_func)
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# for flow_func in flow_funcs:
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# validate_flows(G, s, t, 156545, flow_func(G, s, t, **kwargs),
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# flow_func)
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def test_gw1(self):
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G = read_graph('gw1')
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s = 1
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t = len(G)
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R = build_residual_network(G, 'capacity')
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kwargs = dict(residual=R)
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for flow_func in flow_funcs:
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validate_flows(G, s, t, 1202018, flow_func(G, s, t, **kwargs),
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flow_func)
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def test_wlm3(self):
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G = read_graph('wlm3')
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s = 1
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t = len(G)
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R = build_residual_network(G, 'capacity')
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kwargs = dict(residual=R)
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# do one flow_func to save time
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flow_func = flow_funcs[0]
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validate_flows(G, s, t, 11875108, flow_func(G, s, t, **kwargs),
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flow_func)
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# for flow_func in flow_funcs:
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# validate_flows(G, s, t, 11875108, flow_func(G, s, t, **kwargs),
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# flow_func)
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def test_preflow_push_global_relabel(self):
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G = read_graph('gw1')
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R = preflow_push(G, 1, len(G), global_relabel_freq=50)
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assert R.graph['flow_value'] == 1202018
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