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Diffstat (limited to '.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/tests/test_matching.py')
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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/tests/test_matching.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/tests/test_matching.py new file mode 100644 index 00000000..c24659ea --- /dev/null +++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/tests/test_matching.py @@ -0,0 +1,327 @@ +"""Unit tests for the :mod:`networkx.algorithms.bipartite.matching` module.""" + +import itertools + +import pytest + +import networkx as nx +from networkx.algorithms.bipartite.matching import ( + eppstein_matching, + hopcroft_karp_matching, + maximum_matching, + minimum_weight_full_matching, + to_vertex_cover, +) + + +class TestMatching: + """Tests for bipartite matching algorithms.""" + + def setup_method(self): + """Creates a bipartite graph for use in testing matching algorithms. + + The bipartite graph has a maximum cardinality matching that leaves + vertex 1 and vertex 10 unmatched. The first six numbers are the left + vertices and the next six numbers are the right vertices. + + """ + self.simple_graph = nx.complete_bipartite_graph(2, 3) + self.simple_solution = {0: 2, 1: 3, 2: 0, 3: 1} + + edges = [(0, 7), (0, 8), (2, 6), (2, 9), (3, 8), (4, 8), (4, 9), (5, 11)] + self.top_nodes = set(range(6)) + self.graph = nx.Graph() + self.graph.add_nodes_from(range(12)) + self.graph.add_edges_from(edges) + + # Example bipartite graph from issue 2127 + G = nx.Graph() + G.add_nodes_from( + [ + (1, "C"), + (1, "B"), + (0, "G"), + (1, "F"), + (1, "E"), + (0, "C"), + (1, "D"), + (1, "I"), + (0, "A"), + (0, "D"), + (0, "F"), + (0, "E"), + (0, "H"), + (1, "G"), + (1, "A"), + (0, "I"), + (0, "B"), + (1, "H"), + ] + ) + G.add_edge((1, "C"), (0, "A")) + G.add_edge((1, "B"), (0, "A")) + G.add_edge((0, "G"), (1, "I")) + G.add_edge((0, "G"), (1, "H")) + G.add_edge((1, "F"), (0, "A")) + G.add_edge((1, "F"), (0, "C")) + G.add_edge((1, "F"), (0, "E")) + G.add_edge((1, "E"), (0, "A")) + G.add_edge((1, "E"), (0, "C")) + G.add_edge((0, "C"), (1, "D")) + G.add_edge((0, "C"), (1, "I")) + G.add_edge((0, "C"), (1, "G")) + G.add_edge((0, "C"), (1, "H")) + G.add_edge((1, "D"), (0, "A")) + G.add_edge((1, "I"), (0, "A")) + G.add_edge((1, "I"), (0, "E")) + G.add_edge((0, "A"), (1, "G")) + G.add_edge((0, "A"), (1, "H")) + G.add_edge((0, "E"), (1, "G")) + G.add_edge((0, "E"), (1, "H")) + self.disconnected_graph = G + + def check_match(self, matching): + """Asserts that the matching is what we expect from the bipartite graph + constructed in the :meth:`setup` fixture. + + """ + # For the sake of brevity, rename `matching` to `M`. + M = matching + matched_vertices = frozenset(itertools.chain(*M.items())) + # Assert that the maximum number of vertices (10) is matched. + assert matched_vertices == frozenset(range(12)) - {1, 10} + # Assert that no vertex appears in two edges, or in other words, that + # the matching (u, v) and (v, u) both appear in the matching + # dictionary. + assert all(u == M[M[u]] for u in range(12) if u in M) + + def check_vertex_cover(self, vertices): + """Asserts that the given set of vertices is the vertex cover we + expected from the bipartite graph constructed in the :meth:`setup` + fixture. + + """ + # By Konig's theorem, the number of edges in a maximum matching equals + # the number of vertices in a minimum vertex cover. + assert len(vertices) == 5 + # Assert that the set is truly a vertex cover. + for u, v in self.graph.edges(): + assert u in vertices or v in vertices + # TODO Assert that the vertices are the correct ones. + + def test_eppstein_matching(self): + """Tests that David Eppstein's implementation of the Hopcroft--Karp + algorithm produces a maximum cardinality matching. + + """ + self.check_match(eppstein_matching(self.graph, self.top_nodes)) + + def test_hopcroft_karp_matching(self): + """Tests that the Hopcroft--Karp algorithm produces a maximum + cardinality matching in a bipartite graph. + + """ + self.check_match(hopcroft_karp_matching(self.graph, self.top_nodes)) + + def test_to_vertex_cover(self): + """Test for converting a maximum matching to a minimum vertex cover.""" + matching = maximum_matching(self.graph, self.top_nodes) + vertex_cover = to_vertex_cover(self.graph, matching, self.top_nodes) + self.check_vertex_cover(vertex_cover) + + def test_eppstein_matching_simple(self): + match = eppstein_matching(self.simple_graph) + assert match == self.simple_solution + + def test_hopcroft_karp_matching_simple(self): + match = hopcroft_karp_matching(self.simple_graph) + assert match == self.simple_solution + + def test_eppstein_matching_disconnected(self): + with pytest.raises(nx.AmbiguousSolution): + match = eppstein_matching(self.disconnected_graph) + + def test_hopcroft_karp_matching_disconnected(self): + with pytest.raises(nx.AmbiguousSolution): + match = hopcroft_karp_matching(self.disconnected_graph) + + def test_issue_2127(self): + """Test from issue 2127""" + # Build the example DAG + G = nx.DiGraph() + G.add_edge("A", "C") + G.add_edge("A", "B") + G.add_edge("C", "E") + G.add_edge("C", "D") + G.add_edge("E", "G") + G.add_edge("E", "F") + G.add_edge("G", "I") + G.add_edge("G", "H") + + tc = nx.transitive_closure(G) + btc = nx.Graph() + + # Create a bipartite graph based on the transitive closure of G + for v in tc.nodes(): + btc.add_node((0, v)) + btc.add_node((1, v)) + + for u, v in tc.edges(): + btc.add_edge((0, u), (1, v)) + + top_nodes = {n for n in btc if n[0] == 0} + matching = hopcroft_karp_matching(btc, top_nodes) + vertex_cover = to_vertex_cover(btc, matching, top_nodes) + independent_set = set(G) - {v for _, v in vertex_cover} + assert {"B", "D", "F", "I", "H"} == independent_set + + def test_vertex_cover_issue_2384(self): + G = nx.Graph([(0, 3), (1, 3), (1, 4), (2, 3)]) + matching = maximum_matching(G) + vertex_cover = to_vertex_cover(G, matching) + for u, v in G.edges(): + assert u in vertex_cover or v in vertex_cover + + def test_vertex_cover_issue_3306(self): + G = nx.Graph() + edges = [(0, 2), (1, 0), (1, 1), (1, 2), (2, 2)] + G.add_edges_from([((i, "L"), (j, "R")) for i, j in edges]) + + matching = maximum_matching(G) + vertex_cover = to_vertex_cover(G, matching) + for u, v in G.edges(): + assert u in vertex_cover or v in vertex_cover + + def test_unorderable_nodes(self): + a = object() + b = object() + c = object() + d = object() + e = object() + G = nx.Graph([(a, d), (b, d), (b, e), (c, d)]) + matching = maximum_matching(G) + vertex_cover = to_vertex_cover(G, matching) + for u, v in G.edges(): + assert u in vertex_cover or v in vertex_cover + + +def test_eppstein_matching(): + """Test in accordance to issue #1927""" + G = nx.Graph() + G.add_nodes_from(["a", 2, 3, 4], bipartite=0) + G.add_nodes_from([1, "b", "c"], bipartite=1) + G.add_edges_from([("a", 1), ("a", "b"), (2, "b"), (2, "c"), (3, "c"), (4, 1)]) + matching = eppstein_matching(G) + assert len(matching) == len(maximum_matching(G)) + assert all(x in set(matching.keys()) for x in set(matching.values())) + + +class TestMinimumWeightFullMatching: + @classmethod + def setup_class(cls): + pytest.importorskip("scipy") + + def test_minimum_weight_full_matching_incomplete_graph(self): + B = nx.Graph() + B.add_nodes_from([1, 2], bipartite=0) + B.add_nodes_from([3, 4], bipartite=1) + B.add_edge(1, 4, weight=100) + B.add_edge(2, 3, weight=100) + B.add_edge(2, 4, weight=50) + matching = minimum_weight_full_matching(B) + assert matching == {1: 4, 2: 3, 4: 1, 3: 2} + + def test_minimum_weight_full_matching_with_no_full_matching(self): + B = nx.Graph() + B.add_nodes_from([1, 2, 3], bipartite=0) + B.add_nodes_from([4, 5, 6], bipartite=1) + B.add_edge(1, 4, weight=100) + B.add_edge(2, 4, weight=100) + B.add_edge(3, 4, weight=50) + B.add_edge(3, 5, weight=50) + B.add_edge(3, 6, weight=50) + with pytest.raises(ValueError): + minimum_weight_full_matching(B) + + def test_minimum_weight_full_matching_square(self): + G = nx.complete_bipartite_graph(3, 3) + G.add_edge(0, 3, weight=400) + G.add_edge(0, 4, weight=150) + G.add_edge(0, 5, weight=400) + G.add_edge(1, 3, weight=400) + G.add_edge(1, 4, weight=450) + G.add_edge(1, 5, weight=600) + G.add_edge(2, 3, weight=300) + G.add_edge(2, 4, weight=225) + G.add_edge(2, 5, weight=300) + matching = minimum_weight_full_matching(G) + assert matching == {0: 4, 1: 3, 2: 5, 4: 0, 3: 1, 5: 2} + + def test_minimum_weight_full_matching_smaller_left(self): + G = nx.complete_bipartite_graph(3, 4) + G.add_edge(0, 3, weight=400) + G.add_edge(0, 4, weight=150) + G.add_edge(0, 5, weight=400) + G.add_edge(0, 6, weight=1) + G.add_edge(1, 3, weight=400) + G.add_edge(1, 4, weight=450) + G.add_edge(1, 5, weight=600) + G.add_edge(1, 6, weight=2) + G.add_edge(2, 3, weight=300) + G.add_edge(2, 4, weight=225) + G.add_edge(2, 5, weight=290) + G.add_edge(2, 6, weight=3) + matching = minimum_weight_full_matching(G) + assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1} + + def test_minimum_weight_full_matching_smaller_top_nodes_right(self): + G = nx.complete_bipartite_graph(3, 4) + G.add_edge(0, 3, weight=400) + G.add_edge(0, 4, weight=150) + G.add_edge(0, 5, weight=400) + G.add_edge(0, 6, weight=1) + G.add_edge(1, 3, weight=400) + G.add_edge(1, 4, weight=450) + G.add_edge(1, 5, weight=600) + G.add_edge(1, 6, weight=2) + G.add_edge(2, 3, weight=300) + G.add_edge(2, 4, weight=225) + G.add_edge(2, 5, weight=290) + G.add_edge(2, 6, weight=3) + matching = minimum_weight_full_matching(G, top_nodes=[3, 4, 5, 6]) + assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1} + + def test_minimum_weight_full_matching_smaller_right(self): + G = nx.complete_bipartite_graph(4, 3) + G.add_edge(0, 4, weight=400) + G.add_edge(0, 5, weight=400) + G.add_edge(0, 6, weight=300) + G.add_edge(1, 4, weight=150) + G.add_edge(1, 5, weight=450) + G.add_edge(1, 6, weight=225) + G.add_edge(2, 4, weight=400) + G.add_edge(2, 5, weight=600) + G.add_edge(2, 6, weight=290) + G.add_edge(3, 4, weight=1) + G.add_edge(3, 5, weight=2) + G.add_edge(3, 6, weight=3) + matching = minimum_weight_full_matching(G) + assert matching == {1: 4, 2: 6, 3: 5, 4: 1, 5: 3, 6: 2} + + def test_minimum_weight_full_matching_negative_weights(self): + G = nx.complete_bipartite_graph(2, 2) + G.add_edge(0, 2, weight=-2) + G.add_edge(0, 3, weight=0.2) + G.add_edge(1, 2, weight=-2) + G.add_edge(1, 3, weight=0.3) + matching = minimum_weight_full_matching(G) + assert matching == {0: 3, 1: 2, 2: 1, 3: 0} + + def test_minimum_weight_full_matching_different_weight_key(self): + G = nx.complete_bipartite_graph(2, 2) + G.add_edge(0, 2, mass=2) + G.add_edge(0, 3, mass=0.2) + G.add_edge(1, 2, mass=1) + G.add_edge(1, 3, mass=2) + matching = minimum_weight_full_matching(G, weight="mass") + assert matching == {0: 3, 1: 2, 2: 1, 3: 0} |