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Copy pathutil.py
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390 lines (351 loc) · 13.3 KB
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import math
import random
import collections
import sympy as sym
from sympy import FiniteSet
def normalizeEntry(entry):
_min = entry[0]
_index = 0
for i in range(len(entry)):
if entry[i] < _min:
_min = entry[i]
_index = i
return entry[_index:] + entry[0:_index]
def generateFirstPath(h):
#
numNewEntries = 8*h-2
first = [1,2,4*h]
seed = first + [3]
result = [first,seed]
counter = 0
#
for t in range(4*h-4):
newEntry = [t for t in result[-1]]
if counter % 2 == 0:
newEntry[1] = (newEntry[1] + 2)%(4*h)
else:
newEntry[3] = (newEntry[3] + 2)%(4*h)
result.append(newEntry)
counter+=1
#
mid1 = [1,4*h,4*h-1]
result.append(mid1)
##########################
#
mid2 = [1,4*h,2]
result.append(mid2)
seed = mid2 + [4*h-1]
result.append(seed)
counter = 0
for t in range(4*h-4):
newEntry = [t for t in result[-1]]
if counter % 2 == 0:
newEntry[1] = (newEntry[1] - 2)%(4*h)
else:
newEntry[3] = (newEntry[3] - 2)%(4*h)
result.append(newEntry)
counter+=1
#
last = [1,2,3]
result.append(last)
return [normalizeEntry(t) for t in result]
def step(t,h,m):
result = (t+2)%m
return 4*h if result == 0 else result
def processEntry(entry, h, m):
return [step(t,h,m) for t in entry]
def generateAllPaths(h):
numPaths = 2*h
modulo = 4*h
paths = []
#first path
firstPath = generateFirstPath(h)
paths = []
paths.append(firstPath)
#
for i in range(1,numPaths):
prevPath = paths[i-1]
newPath = [processEntry(t,h,modulo) for t in prevPath]
paths.append([normalizeEntry(t) for t in newPath])
#
return paths
####################################################
def getSign(num):
return ('+' if num == 1 else '-')
def getVariableName(indices):
newIndices = indices
return 'xa_%d_%d' % (newIndices[0],newIndices[1])
def constraintToString(constraint):
signs = [getSign(t) for t in constraint['signs']]
variables = [getVariableName(t) for t in constraint['variables']]
aux = ''
for i in range(len(signs)):
aux += (signs[i] + ' ' + variables[i] + ' ')
if constraint['entryType'] == 3:
i = constraint['variables'][0][0]
j = constraint['variables'][1][0]
k = constraint['variables'][2][0]
aux += '+ xo_%d_%d_%d ' % (i,j,k)
elif constraint['entryType'] == 2:
i = constraint['variables'][0][0]
j = constraint['variables'][0][1]
aux += '+ xo_%d_%d ' % (i,j)
else:
i = constraint['variables'][0][0]
j = constraint['variables'][1][0]
k = constraint['variables'][2][0]
l = constraint['variables'][3][0]
aux += '+ xo_%d_%d_%d_%d ' % (i,j,k,l)
return constraint['name'] + ': ' + aux + ' <= ' + str(constraint['rightSide'])
import collections
def generateConstraints (path,h):
inequalities = collections.OrderedDict()
for entry in path:
if len(entry) == 3:
i = entry[0]
j = entry[1]
k = entry[2]
#yuijkn0: + xij + xjk + xki + xoijk <= 2
name = "yu_%d_%d_%dn0" % (i,j,k)
inequalities[name] = {'name':name,"type":"CD","entryType":3,"variables":[[i,j],[j,k],[k,i]],"signs":[1,1,1],"rightSide":2}
#yuijkp1: + xij - xjk - xki + xoijk <= 0
name = "yu_%d_%d_%dp1" % (i,j,k)
inequalities[name] = {'name':name,"type":"CD","entryType":3,"variables":[[i,j],[j,k],[k,i]],"signs":[1,-1,-1],"rightSide":0}
#yuijkp2: - xij + xjk - xki + xoijk <= 0
name = "yu_%d_%d_%dp2" % (i,j,k)
inequalities[name] = {'name':name,"type":"CD","entryType":3,"variables":[[i,j],[j,k],[k,i]],"signs":[-1,1,-1],"rightSide":0}
#yuijkp3: - xij - xjk + xki + xoijk <= 0
name = "yu_%d_%d_%dp3" % (i,j,k)
inequalities[name] = {'name':name,"type":"CD","entryType":3,"variables":[[i,j],[j,k],[k,i]],"signs":[-1,-1,1],"rightSide":0}
else:
i = entry[0]
j = entry[1]
k = entry[2]
l = entry[3]
#yuijkln1: - xij + xjk + xkl + xli + xoijkl <= 2
name = "yu_%d_%d_%d_%dn1" % (i,j,k,l)
inequalities[name] = {'name':name,"type":"CD","entryType":4,"variables":[[i,j],[j,k],[k,l],[l,i]],"signs":[-1,1,1,1],"rightSide":2}
#yuijkln2: + xij - xjk + xkl + xli + xoijkl <= 2
name = "yu_%d_%d_%d_%dn2" % (i,j,k,l)
inequalities[name] = {'name':name,"type":"CD","entryType":4,"variables":[[i,j],[j,k],[k,l],[l,i]],"signs":[1,-1,1,1],"rightSide":2}
#yuijkln3: + xij + xjk - xkl + xli + xoijkl <= 2
name = "yu_%d_%d_%d_%dn3" % (i,j,k,l)
inequalities[name] = {'name':name,"type":"CD","entryType":4,"variables":[[i,j],[j,k],[k,l],[l,i]],"signs":[1,1,-1,1],"rightSide":2}
#yuijkln4: + xij + xjk + xkl - xli + xoijkl <= 2
name = "yu_%d_%d_%d_%dn4" % (i,j,k,l)
inequalities[name] = {'name':name,"type":"CD","entryType":4,"variables":[[i,j],[j,k],[k,l],[l,i]],"signs":[1,1,1,-1],"rightSide":2}
#yuijklp1: +xij - xjk - xkl - xli + xoijkl <= 0
name = "yu_%d_%d_%d_%dp1" % (i,j,k,l)
inequalities[name] = {'name':name,"type":"CD","entryType": 4, "variables": [[i,j],[j,k],[k,l],[l,i]], "signs": [1,-1,-1,-1], "rightSide": 0}
#yuijklp2: -xij + xjk - xkl - xli + xoijkl <= 0
name = "yu_%d_%d_%d_%dp2" % (i,j,k,l)
inequalities[name] = {'name':name,"type":"CD","entryType": 4, "variables": [[i,j],[j,k],[k,l],[l,i]], "signs": [-1,1,-1,-1], "rightSide": 0}
#yuijklp3: -xij - xjk + xkl - xli + xoijkl <= 0
name = "yu_%d_%d_%d_%dp3" % (i,j,k,l)
inequalities[name] = {'name':name,"type":"CD","entryType": 4, "variables": [[i,j],[j,k],[k,l],[l,i]], "signs": [-1,-1,1,-1], "rightSide": 0}
#yuijklp4: -xij - xjk - xkl + xli + xoijkl <= 0
name = "yu_%d_%d_%d_%dp4" % (i,j,k,l)
inequalities[name] = {'name':name,"type":"CD","entryType": 4, "variables": [[i,j],[j,k],[k,l],[l,i]], "signs": [-1,-1,-1,1], "rightSide": 0}
#central triangles
for pp in range(4*h):
i = (pp+1)%(4*h)
i = 4*h if i == 0 else i
j = 4*h+1
k = (i+1)%(4*h)
k = 4*h if k == 0 else k
indices = normalizeEntry([i,j,k])
i,j,k = indices
#yuijkn0: + xij + xjk + xki + xoijk <= 2
name = "yu_%d_%d_%dn0" % (i,j,k)
inequalities[name] = {'name':name,"type":"tripla","entryType":3,"variables":[[i,j],[j,k],[k,i]],"signs":[1,1,1],"rightSide":2}
#yuijkp1: + xij - xjk - xki + xoijk <= 0
name = "yu_%d_%d_%dp1" % (i,j,k)
inequalities[name] = {'name':name,"type":"tripla","entryType":3,"variables":[[i,j],[j,k],[k,i]],"signs":[1,-1,-1],"rightSide":0}
#yuijkp2: - xij + xjk - xki + xoijk <= 0
name = "yu_%d_%d_%dp2" % (i,j,k)
inequalities[name] = {'name':name,"type":"tripla","entryType":3,"variables":[[i,j],[j,k],[k,i]],"signs":[-1,1,-1],"rightSide":0}
#yuijkp3: - xij - xjk + xki + xoijk <= 0
name = "yu_%d_%d_%dp3" % (i,j,k)
inequalities[name] = {'name':name,"type":"tripla","entryType":3,"variables":[[i,j],[j,k],[k,i]],"signs":[-1,-1,1],"rightSide":0}
#centrail digonos
if False: #removendo digonos
for i in range(4*h):
#
name = "yu_" + str(i+1) + '_' + str(4*h+1) +"p1"
inequalities[name] = {'name':name,"type":"digonos","entryType": 2, "variables": [[i+1,4*h+1],[4*h+1,i+1]], "signs": [1,-1], "rightSide": 0}
#
name = name = "yu_" + str(i+1) + '_' + str(4*h+1) +"n1"
inequalities[name] = {'name':name,"type":"digonos","entryType": 2, "variables": [[i+1,4*h+1],[4*h+1,i+1]], "signs": [-1,1], "rightSide": 0}
#
return inequalities
def generateXos(constraints):
variables = {}
for key in constraints:
constraint = constraints[key]
#
if constraint['entryType'] == 3:
i = constraint['variables'][0][0]
j = constraint['variables'][1][0]
k = constraint['variables'][2][0]
name = 'xo_%d_%d_%d' % (i,j,k)
if not (name in variables):
variables[name] = 1
elif constraint['entryType'] == 2:
i = constraint['variables'][0][0]
j = constraint['variables'][0][1]
name = 'xo_%d_%d' % (i,j)
if not (name in variables):
variables[name] = 1
else:
i = constraint['variables'][0][0]
j = constraint['variables'][1][0]
k = constraint['variables'][2][0]
l = constraint['variables'][3][0]
name = 'xo_%d_%d_%d_%d' % (i,j,k,l)
if not (name in variables):
variables[name] = 1
return variables.keys()
def generateBounds(constraints):
variables = {}
resultXa = [];
resultXo = []
for key in constraints:
constraint = constraints[key]
for variable in constraint['variables']:
name = getVariableName(variable)
if not (name in variables):
variables[name] = 1
resultXa.append(name + ' free')
#
if constraint['entryType'] == 3:
i = constraint['variables'][0][0]
j = constraint['variables'][1][0]
k = constraint['variables'][2][0]
name = 'xo_%d_%d_%d' % (i,j,k)
if not (name in variables):
variables[name] = 1
resultXo.append('xo_%d_%d_%d >= 0' % (i,j,k))
elif constraint['entryType'] == 2:
i = constraint['variables'][0][0]
j = constraint['variables'][0][1]
name = 'xo_%d_%d' % (i,j)
if not (name in variables):
variables[name] = 1
resultXo.append('xo_%d_%d >= 0' % (i,j))
else:
i = constraint['variables'][0][0]
j = constraint['variables'][1][0]
k = constraint['variables'][2][0]
l = constraint['variables'][3][0]
name = 'xo_%d_%d_%d_%d' % (i,j,k,l)
if not (name in variables):
variables[name] = 1
resultXo.append('xo_%d_%d_%d_%d >= 0' % (i,j,k,l))
return (resultXa,resultXo)
def testConstraints(h):
paths = generateAllPaths(h)
constraints = {}
for path in paths:
result = generateConstraints(path,h)
for key in result:
constraints[key] = result[key]
constraintStrings = [constraintToString(constraints[key]) for key in constraints]
print(len(paths),len(constraints))
if False:
for t in (constraintStrings):
print(t)
print('\n')
print('bounds')
print('\n')
bounds = generateBounds(constraints)
for t in bounds[0]:
print(t)
for t in bounds[1]:
print(t)
def generateRandomGraph(numVertices,density):
edges = []
for i in range(numVertices):
for j in range(i+1,numVertices):
if random.random() <= density:
edges.append([i+1,j+1])
return edges
def getObjectiveFunctionStr(graph,xos):
names = [getVariableName(t) for t in graph]
objective = " + ".join(names + xos)
return objective
def generateLPStr(graph,numVertices):
h = math.ceil((numVertices-1)/4.0)
#
paths = generateAllPaths(h)
constraints = {}
for path in paths:
result = generateConstraints(path,h)
for key in result:
constraints[key] = result[key]
#
constraintStrings1 = [constraintToString(constraints[key]) for key in constraints if constraints[key]['type'] == "CD"]
constraintStrings2 = [constraintToString(constraints[key]) for key in constraints if constraints[key]['type'] == "tripla"]
constraintStrings3 = [constraintToString(constraints[key]) for key in constraints if constraints[key]['type'] == "digonos"]
constraintStrings = constraintStrings1 + constraintStrings2 + constraintStrings3
xos = list(generateXos(constraints))
#
getObjectiveFunctionStr(graph,xos)
#
print("Maximize "+ getObjectiveFunctionStr(graph,xos))
print('\n')
print('subject to')
print('\n')
for t in (constraintStrings):
print(t)
print('\n')
print('\n')
print('bounds')
print('\n')
bounds = generateBounds(constraints)
for t in bounds[0]:
print(t)
for t in bounds[1]:
print(t)
print('end')
def generateLPFile(graph,numVertices, outputFilename):
h = math.ceil((numVertices-1)/4.0)
#
paths = generateAllPaths(h)
constraints = {}
for path in paths:
result = generateConstraints(path,h)
for key in result:
constraints[key] = result[key]
#
constraintStrings1 = [constraintToString(constraints[key]) for key in constraints if constraints[key]['type'] == "CD"]
constraintStrings2 = [constraintToString(constraints[key]) for key in constraints if constraints[key]['type'] == "tripla"]
constraintStrings3 = [constraintToString(constraints[key]) for key in constraints if constraints[key]['type'] == "digonos"]
constraintStrings = constraintStrings1 + constraintStrings2 + constraintStrings3
xos = list(generateXos(constraints))
#
getObjectiveFunctionStr(graph,xos)
#
outFile = open(outputFilename,'w')
outFile.write("Maximize "+ getObjectiveFunctionStr(graph,xos))
outFile.write('\n')
outFile.write('subject to')
outFile.write('\n')
for t in (constraintStrings):
outFile.write(t)
outFile.write('\n')
outFile.write('\n')
outFile.write('\n')
outFile.write('bounds')
outFile.write('\n')
bounds = generateBounds(constraints)
for t in bounds[0]:
outFile.write(t)
outFile.write('\n')
for t in bounds[1]:
outFile.write(t)
outFile.write('\n')
outFile.write('end')
outFile.write('\n')
outFile.close()
if __name__ == '__main__':
testConstraints(2)