Combinatorial optimization-Typical problem-Minimum spanning tree problem

Typical problem and execution method

Minimum spanning tree problem

When the weight of the edge $ e $ on the undirected graph $ G = (V, E) $ is $ w (e) $, the sum of the weights of the edge $ T = (V, E_T) $ on the spanning tree $ T = (V, E_T) $ Find the spanning tree that minimizes \ sum_ {e \ in E_T} {w (e)} $.

Execution method

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 data
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())

result

[(0, 1), (0, 3), (0, 4), (2, 3), (4, 5)]

python

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

python

#Random number data
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()

data

• data/node0.csv
• data/edge0.csv