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63 lines
2.1 KiB
Python
63 lines
2.1 KiB
Python
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"""
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* Author: Manuel Di Lullo (https://github.com/manueldilullo)
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* Description: Approximization algorithm for minimum vertex cover problem.
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Matching Approach. Uses graphs represented with an adjacency list
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URL: https://mathworld.wolfram.com/MinimumVertexCover.html
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URL: https://www.princeton.edu/~aaa/Public/Teaching/ORF523/ORF523_Lec6.pdf
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"""
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def matching_min_vertex_cover(graph: dict) -> set:
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"""
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APX Algorithm for min Vertex Cover using Matching Approach
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@input: graph (graph stored in an adjacency list where each vertex
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is represented as an integer)
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@example:
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>>> graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
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>>> matching_min_vertex_cover(graph)
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{0, 1, 2, 4}
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"""
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# chosen_vertices = set of chosen vertices
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chosen_vertices = set()
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# edges = list of graph's edges
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edges = get_edges(graph)
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# While there are still elements in edges list, take an arbitrary edge
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# (from_node, to_node) and add his extremity to chosen_vertices and then
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# remove all arcs adjacent to the from_node and to_node
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while edges:
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from_node, to_node = edges.pop()
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chosen_vertices.add(from_node)
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chosen_vertices.add(to_node)
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for edge in edges.copy():
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if from_node in edge or to_node in edge:
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edges.discard(edge)
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return chosen_vertices
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def get_edges(graph: dict) -> set:
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"""
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Return a set of couples that represents all of the edges.
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@input: graph (graph stored in an adjacency list where each vertex is
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represented as an integer)
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@example:
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>>> graph = {0: [1, 3], 1: [0, 3], 2: [0, 3], 3: [0, 1, 2]}
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>>> get_edges(graph)
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{(0, 1), (3, 1), (0, 3), (2, 0), (3, 0), (2, 3), (1, 0), (3, 2), (1, 3)}
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"""
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edges = set()
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for from_node, to_nodes in graph.items():
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for to_node in to_nodes:
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edges.add((from_node, to_node))
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return edges
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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# graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
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# print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")
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