最大流問題
グラフ$G=(V,E)$の各辺$e_{ij}=(v_i,v_j)\in E$が容量$c_{ij}$をもつとき、始点$v_s \in V$(ソース)から終点$v_t \in V$(シンク)への総流量が最大となるフローを求めよ。
実行方法
usage
Signature: nx.maximum_flow(G, s, t, capacity='capacity', flow_func=None, **kwargs)
Docstring:
Find a maximum single-commodity flow.
python
# CSVデータ
import pandas as pd, networkx as nx
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.maximum_flow(g, 5, 2)
pos = networkx_draw(g)
nx.draw_networkx_edges(g, pos, width=3, edgelist
=[(k1, k2) for k1, d in t[1].items() for k2, v in d.items() if v])
plt.show()
for i, d in t[1].items():
for j, f in d.items():
if f: print((i, j), f)
結果
(0, 2) 2
(0, 3) 2
(1, 2) 2
(3, 2) 2
(4, 0) 2
(5, 0) 2
(5, 1) 2
(5, 4) 2
python
# pandas.DataFrame
from ortoolpy.optimization import MaximumFlow
MaximumFlow('data/edge0.csv', 5, 2)[1]
| node1 | node2 | capacity | weight | flow | |
|---|---|---|---|---|---|
| 0 | 0 | 2 | 2 | 4 | 2 |
| 1 | 0 | 3 | 2 | 2 | 2 |
| 2 | 0 | 4 | 2 | 2 | 2 |
| 3 | 0 | 5 | 2 | 4 | 2 |
| 4 | 1 | 2 | 2 | 5 | 2 |
| 5 | 1 | 5 | 2 | 5 | 2 |
| 6 | 2 | 3 | 2 | 3 | 2 |
| 7 | 4 | 5 | 2 | 1 | 2 |
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)
for i, j in g.edges():
g.adj[i][j]['capacity'] = 1
t = nx.maximum_flow(g, 5, 6)
pos = networkx_draw(g, nx.spring_layout(g))
nx.draw_networkx_edges(g, pos, width=3, edgelist
=[(k1, k2) for k1, d in t[1].items() for k2, v in d.items() if v])
plt.show()
