Question

我正在尝试解决最小的图形着色问题。我想解决这个问题。我正在遵循本文中概述的解决方案：

https://manas.tech/blog/2010/09/16/modelling-graph-coloring-with-integer-linear-programming.html

我认为我定义j的方式可能存在问题：

j = int（first_line [0]）

我将其定义为节点数，因为我认为既然x和w是二进制变量，它们可能具有最大维数，但是我在下面定义的约束将迫使它们的条目数最少为1。谁能告诉我是否在下面正确设置了问题，还是需要让我的j值从最小值开始并增加？如果是这样，有人可以建议我应该如何设置我的j值？我还在学习cvxpy。

此帖子还与我之前发表的帖子有关：

Define CVXPY variables for graph coloring problem

代码：

input_data
# '4 3\n0 1\n1 2\n1 3\n'


# parse the input
lines = input_data.split('\n')

first_line = lines[0].split()
node_count = int(first_line[0])
edge_count = int(first_line[1])

edges = []
for i in range(1, edge_count + 1):
    line = lines[i]
    parts = line.split()
    edges.append((int(parts[0]), int(parts[1])))



import numpy as np
import cvxpy

from collections import namedtuple


# binary variable if at least one node is color j

j=int(first_line[0])



# w=1 if at least one node has color j
w = cvxpy.Variable(j, boolean=True)

# x=1 if node i is color j

x = cvxpy.Variable((j,j), boolean=True)


# constraints

# 1 color per node

node_color=cvxpy.sum(x,axis=1)==1

# for adjacent nodes at most 1 node has color
diff_col = []

for edge in edges:
    for k in range(node_count):
        diff_col += [
            x[edge[0],k]+x[edge[1],k]<=1

        ]



# w is upper bound for color of node x<=w

upper_bound = []

for i in range(j):
    for k in range(j):
        upper_bound += [
            x[k,i]<=w[i]
        ]


# constraints
constraints=[node_color]+diff_col+upper_bound



# Objective function
# minimize number of colors needed

obj=cvxpy.sum(w,axis=0)



# solving problem

# cvxpy must be passed as a list
graph_problem = cvxpy.Problem(cvxpy.Minimize(obj), constraints)

# Solving the problem
graph_problem.solve(solver=cvxpy.GLPK_MI)

value2=int(graph_problem.solve(solver=cvxpy.GLPK_MI))

taken2=[int(i) for i in w.value.tolist()]

# prepare the solution in the specified output format
output_data2 = str(value2) + ' ' + str(0) + '\n'
output_data2 += ' '.join(map(str, taken2))



# Objective function after solving

value2
# 2

 # Solution node colors

x.value.tolist()

# [[1.0, 0.0, 0.0, 0.0],
#  [0.0, 0.0, 1.0, 0.0],
#  [1.0, 0.0, 0.0, 0.0],
#  [1.0, 0.0, 0.0, 0.0]]

在图形着色问题中定义选择变量

0 个答案: