# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Simple coloring problem using MIP in Google CP Solver.
Inspired by the GLPK:s model color.mod
'''
COLOR, Graph Coloring Problem
Written in GNU MathProg by Andrew Makhorin
Given an undirected loopless graph G = (V, E), where V is a set of
nodes, E <= V x V is a set of arcs, the Graph Coloring Problem is to
find a mapping (coloring) F: V -> C, where C = {1, 2, ... } is a set
of colors whose cardinality is as small as possible, such that
F(i) != F(j) for every arc (i,j) in E, that is adjacent nodes must
be assigned different colors.
'''
Compare with the MiniZinc model:
http://www.hakank.org/minizinc/coloring_ip.mzn
This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_or_tools/
"""
import sys
from ortools.linear_solver import pywraplp
def main(sol='GLPK'):
# Create the solver.
print 'Solver: ', sol
if sol == 'GLPK':
# using GLPK
solver = pywraplp.Solver('CoinsGridGLPK',
pywraplp.Solver.GLPK_MIXED_INTEGER_PROGRAMMING)
else:
# Using CBC
solver = pywraplp.Solver('CoinsGridCLP',
pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
#
# data
#
# max number of colors
# [we know that 4 suffices for normal maps]
nc = 5
# number of nodes
n = 11
# set of nodes
V = range(n)
num_edges = 20
#
# Neighbours
#
# This data correspond to the instance myciel3.col from:
# http://mat.gsia.cmu.edu/COLOR/instances.html
#
# Note: 1-based (adjusted below)
E = [[1, 2],
[1, 4],
[1, 7],
[1, 9],
[2, 3],
[2, 6],
[2, 8],
[3, 5],
[3, 7],
[3, 10],
[4, 5],
[4, 6],
[4, 10],
[5, 8],
[5, 9],
[6, 11],
[7, 11],
[8, 11],
[9, 11],
[10, 11]]
#
# declare variables
#
# x[i,c] = 1 means that node i is assigned color c
x = {}
for v in V:
for j in range(nc):
x[v, j] = solver.IntVar(0, 1, 'v[%i,%i]' % (v, j))
# u[c] = 1 means that color c is used, i.e. assigned to some node
u = [solver.IntVar(0, 1, 'u[%i]' % i) for i in range(nc)]
# number of colors used, to minimize
obj = solver.Sum(u)
#
# constraints
#
# each node must be assigned exactly one color
for i in V:
solver.Add(solver.Sum([x[i, c] for c in range(nc)]) == 1)
# adjacent nodes cannot be assigned the same color
# (and adjust to 0-based)
for i in range(num_edges):
for c in range(nc):
solver.Add(x[E[i][0] - 1, c] + x[E[i][1] - 1, c] <= u[c])
# objective
objective = solver.Minimize(obj)
#
# solution
#
solver.Solve()
print
print 'number of colors:', int(solver.Objective().Value())
print 'colors used:', [int(u[i].SolutionValue()) for i in range(nc)]
print
for v in V:
print 'v%i' % v, ' color ',
for c in range(nc):
if int(x[v, c].SolutionValue()) == 1:
print c
print
print 'WallTime:', solver.WallTime()
if sol == 'CBC':
print 'iterations:', solver.Iterations()
if __name__ == '__main__':
sol = 'GLPK'
if len(sys.argv) > 1:
sol = sys.argv[1]
if sol != 'GLPK' and sol != 'CBC':
print 'Solver must be either GLPK or CBC'
sys.exit(1)
main(sol)