"""
* Author: Manuel Di Lullo (https://github.com/manueldilullo)
* Description: Approximization algorithm for minimum vertex cover problem.
Greedy Approach. Uses graphs represented with an adjacency list
URL: https://mathworld.wolfram.com/MinimumVertexCover.html
URL: https://cs.stackexchange.com/questions/129017/greedy-algorithm-for-vertex-cover
"""
import heapq
def greedy_min_vertex_cover(graph: dict) -> set[int]:
"""
Greedy APX Algorithm for min Vertex Cover
@input: graph (graph stored in an adjacency list where each vertex
is represented with an integer)
@example:
>>> graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
>>> greedy_min_vertex_cover(graph)
{0, 1, 2, 4}
"""
queue: list[list] = []
for key, value in graph.items():
heapq.heappush(queue, [-1 * len(value), (key, value)])
chosen_vertices = set()
while queue and queue[0][0] != 0:
argmax = heapq.heappop(queue)[1][0]
chosen_vertices.add(argmax)
for elem in queue:
if elem[0] == 0:
continue
if argmax in elem[1][1]:
index = elem[1][1].index(argmax)
del elem[1][1][index]
elem[0] += 1
heapq.heapify(queue)
return chosen_vertices
if __name__ == "__main__":
import doctest
doctest.testmod()
graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
print(f"Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}")