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組合せ最適化 - 典型問題 - 最大安定集合問題

Last updated at Posted at 2015-07-10

典型問題と実行方法

最大安定集合問題

無向グラフ$G=(V, E)$において、重みの和が最大の安定集合(互いに隣接していない節点の集合)を求めよ。

実行方法

usage
Signature: maximum_stable_set(g, weight='weight')
Docstring:
最大安定集合問題
入力
    g: グラフ(node:weight)
    weight: 重みの属性文字
出力
    最大安定集合の重みの合計と頂点番号リスト
python
# CSVデータ
import pandas as pd, networkx as nx, matplotlib.pyplot as plt
from ortoolpy import graph_from_table, networkx_draw, maximum_stable_set
tbn = pd.read_csv('data/node0.csv')
tbe = pd.read_csv('data/edge0.csv')
g = graph_from_table(tbn, tbe)[0]
t = maximum_stable_set(g)
pos = networkx_draw(g, node_color='white')
nx.draw_networkx_nodes(g, pos, nodelist=t[1])
plt.show()
print(t)
結果
(5.0, [1, 4])

mss2.png

python
# pandas.DataFrame
from ortoolpy.optimization import MaximumStableSet
MaximumStableSet('data/node0.csv','data/edge0.csv')
id x y demand weight
1 1 5 8 1 3
4 4 2 2 1 2
python
# 乱数データ
import networkx as nx, matplotlib.pyplot as plt
from ortoolpy import networkx_draw, maximum_stable_set
g = nx.random_graphs.fast_gnp_random_graph(10, 0.3, 1)
t = maximum_stable_set(g)
pos = networkx_draw(g, nx.spring_layout(g), node_color='white')
nx.draw_networkx_nodes(g, pos, nodelist=t[1])
plt.show()

mss.png

データ

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