조합 최적화 - 일반적인 문제 - 최대 매칭 문제

일반적인 문제와 실행 방법

최대 매칭 문제

무향 그래프 $G=(V,E)$에 대해 변의 개수가 최대의 매칭을 구하라.

실행 방법

usage

Signature: nx.max_weight_matching(G, maxcardinality=False)
Docstring:
Compute a maximum-weighted matching of G.

A matching is a subset of edges in which no node occurs more than once.
The cardinality of a matching is the number of matched edges.
The weight of a matching is the sum of the weights of its edges.

파이썬

# CSVデータ
import pandas as pd, networkx as nx, matplotlib.pyplot as plt
from ortoolpy import graph_from_table, networkx_draw
tbn = pd.read_csv('data/node0.csv')
tbe = pd.read_csv('data/edge0.csv')
g = graph_from_table(tbn, tbe)[0]
for i, j in g.edges():
    del g.adj[i][j]['weight']
d = nx.max_weight_matching(g)
pos = networkx_draw(g)
nx.draw_networkx_edges(g, pos, width=3, edgelist=[(i, j) for i, j in d])
plt.show()
print(d)

결과

{5: 0, 0: 5, 4: 3, 3: 4, 2: 1, 1: 2}

파이썬

# pandas.DataFrame
from ortoolpy.optimization import MaxMatching
MaxMatching('data/edge0.csv')

node1
node2
capacity
weight




0
0
5
2
4


1
1
2
2
5


2
3
4
2
4



파이썬

# 乱数データ
import networkx as nx, matplotlib.pyplot as plt
from ortoolpy import networkx_draw
g = nx.random_graphs.fast_gnp_random_graph(10, 0.3, 1)
d = nx.max_weight_matching(g)
pos = networkx_draw(g, nx.spring_layout(g))
nx.draw_networkx_edges(g, pos, width=3, edgelist=[(i, j) for i, j in d])
plt.show()

데이터

data/node0.csv

data/edge0.csv