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65 lines
2.3 KiB
Python
65 lines
2.3 KiB
Python
"""
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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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Greedy 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://cs.stackexchange.com/questions/129017/greedy-algorithm-for-vertex-cover
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"""
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import heapq
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def greedy_min_vertex_cover(graph: dict) -> set[int]:
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"""
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Greedy APX Algorithm for min Vertex Cover
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@input: graph (graph stored in an adjacency list where each vertex
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is represented with 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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>>> greedy_min_vertex_cover(graph)
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{0, 1, 2, 4}
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"""
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# queue used to store nodes and their rank
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queue: list[list] = []
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# for each node and his adjacency list add them and the rank of the node to queue
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# using heapq module the queue will be filled like a Priority Queue
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# heapq works with a min priority queue, so I used -1*len(v) to build it
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for key, value in graph.items():
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# O(log(n))
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heapq.heappush(queue, [-1 * len(value), (key, value)])
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# chosen_vertices = set of chosen vertices
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chosen_vertices = set()
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# while queue isn't empty and there are still edges
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# (queue[0][0] is the rank of the node with max rank)
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while queue and queue[0][0] != 0:
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# extract vertex with max rank from queue and add it to chosen_vertices
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argmax = heapq.heappop(queue)[1][0]
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chosen_vertices.add(argmax)
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# Remove all arcs adjacent to argmax
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for elem in queue:
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# if v haven't adjacent node, skip
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if elem[0] == 0:
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continue
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# if argmax is reachable from elem
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# remove argmax from elem's adjacent list and update his rank
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if argmax in elem[1][1]:
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index = elem[1][1].index(argmax)
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del elem[1][1][index]
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elem[0] += 1
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# re-order the queue
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heapq.heapify(queue)
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return chosen_vertices
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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"Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}")
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