32 lines
No EOL
902 B
Python
32 lines
No EOL
902 B
Python
from pulp import *
|
|
|
|
def min_vertexcover(nodes, edges):
|
|
#Problemdefinition
|
|
prob = LpProblem("Kleinste Knotenüberdeckung", LpMinimize)
|
|
|
|
#Binäre Variablen
|
|
x = {v: LpVariable(f"x_{v}", cat=LpBinary) for v in nodes}
|
|
|
|
#Zielfunktion
|
|
prob += lpSum(x[v] for v in nodes)
|
|
|
|
#Nebenbedingung
|
|
for u,v in edges:
|
|
prob += x[u] + x[v] >=1, f"Kante_{u}_{v}"
|
|
|
|
#Lösen mit gurobi
|
|
prob.solve(GUROBI())
|
|
|
|
#Ergebnis
|
|
status = LpStatus[prob.status]
|
|
vertex_cover = [v for v in nodes if value(x[v]) == 1]
|
|
|
|
return status, vertex_cover, value(prob.objective)
|
|
|
|
nodes_test = ['A', 'B', 'C', 'D', 'E']
|
|
edges_test = [('A', 'B'), ('A', 'C'), ('B', 'C'), ('B', 'D'), ('C', 'D'), ('D', 'E')]
|
|
|
|
status, cover, size = min_vertexcover(nodes_test, edges_test)
|
|
print(f"Status: {status}")
|
|
print(f"Minimale Knotenüberdeckung: {cover}")
|
|
print(f"Größe der Überdeckung: {size}") |