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組合せ最適化 - 典型問題 - 最大マッチング問題

Last updated at Posted at 2015-07-10

典型問題と実行方法

最大マッチング問題

無向グラフ$G=(V,E)$に対し辺の本数が最大のマッチングを求めよ。

実行方法

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.
python
# 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)
結果
{5: 0, 0: 5, 4: 3, 3: 4, 2: 1, 1: 2}

image.png

python
# 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
python
# 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()

mwm.png

データ

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