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組合せ最適化 - 典型問題 - 最小全域木問題

Last updated at Posted at 2015-07-10

典型問題と実行方法

最小全域木問題

無向グラフ$G=(V, E)$上の辺$e$の重みを$w(e)$とするとき、全域木$T=(V,E_T)$上の辺の重みの総和$\sum_{e \in E_T}{w(e)}$が最小になる全域木を求めよ。

実行方法

usage
Signature: nx.minimum_spanning_tree(G, weight='weight')
Docstring:
Return a minimum spanning tree or forest of an undirected
weighted graph.

A minimum spanning tree is a subgraph of the graph (a tree) with
the minimum sum of edge weights.
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]
t = nx.minimum_spanning_tree(g)
pos = networkx_draw(g)
nx.draw_networkx_edges(t, pos, width=3)
plt.show()
print(t.edges())
結果
[(0, 1), (0, 3), (0, 4), (2, 3), (4, 5)]

mst2.png

python
# pandas.DataFrame
from ortoolpy.optimization import MinimumSpanningTree
MinimumSpanningTree('data/edge0.csv')
node1 node2 capacity weight
0 0 1 2 1
1 0 3 2 2
2 0 4 2 2
3 2 3 2 3
4 4 5 2 1
python
# 乱数データ
import math, networkx as nx, matplotlib.pyplot as plt
from ortoolpy import networkx_draw
g = nx.random_graphs.fast_gnp_random_graph(10, 0.3, 1)
pos = nx.spring_layout(g)
for i, j in g.edges():
    g.adj[i][j]['weight'] = math.sqrt(sum((pos[i] - pos[j])**2))
t = nx.minimum_spanning_tree(g)
pos = networkx_draw(g, nx.spring_layout(g))
nx.draw_networkx_edges(t, pos, width=3)
plt.show()

mst.png

データ

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