""" Global constraint clique in cpmpy. From Globals constraint catalogue: http://www.emn.fr/x-info/sdemasse/gccat/Cclique.html ''' Consider a digraph G described by the NODES collection: to the ith item of the NODES collection corresponds the ith vertex of G; To each value j of the ith succ variable corresponds an arc from the ith vertex to the jth vertex. Select a subset S of the vertices of G that forms a clique of size SIZE_CLIQUE (i.e., there is an arc between each pair of distinct vertices of S). Example [The graph is 1 -> 2,4 2 -> 1,3,5 3 -> 2,5 4 -> 1,5 5 -> 2,3,4 ] (3,< index-1 succ-{}, index-2 succ-{3,5}, index-3 succ-{2,5}, index-4 succ-{}, index-5 succ-{2,3} > ) The clique constraint holds since the NODES collection depicts a clique involving 3 vertices (namely vertices 2, 3 and 5) and since its first argument SIZE_CLIQUE is set to the number of vertices of this clique. ''' Model created by Hakan Kjellerstrand, hakank@hakank.com See also my cpmpy page: http://www.hakank.org/cpmpy/ """ import sys, random import numpy as np from cpmpy import * from cpmpy.solvers import * from cpmpy_hakank import * def check_clique(graph,type="all",card1=None): n = len(graph) # variables x = boolvar(shape=n,name="x") card = intvar(0,n,name="card") if type == "max": model = Model(maximize=card) else: model = Model() # constraints if card1 != None: model += (card == card1) model += (clique(graph,x, card)) ss = CPM_ortools(model) # ss.ort_solver.parameters.num_search_workers = 12 # Don't work together with SearchForAllSolutions ss.ort_solver.parameters.search_branching = ort.PORTFOLIO_SEARCH # ss.ort_solver.parameters.cp_model_presolve = False ss.ort_solver.parameters.linearization_level = 0 ss.ort_solver.parameters.cp_model_probing_level = 0 num_solutions = 0 max_card = 0 while ss.solve(): num_solutions += 1 print("card:", card.value(), "x :", [i for i in range(n) if x[i].value() == 1]) max_card = card.value() if type == "max": return max_card else: ss += [any([t.value() != t for t in x])] print("num_solutions:", num_solutions) return max_card # # make a symmetric random graph (0/1) of size # def random_graph(n): g = {} for i in range(n): for j in range(n): if i == j: g[(i,j)] = 1 else: g[(i,j)] = random.randint(0,1) g[(j,i)] = g[i,j] # Translate return [ [g[(i,j)] for j in range(n) ] for i in range(n)] # Two cliques: (0,1,3) and (2,4) graph1 = [[1, 1, 0, 1, 0], # 0,1,3 [1, 1, 0, 1, 0], # 0,1,3 [0, 0, 1, 0, 1], # 2,4 [1, 1, 0, 1, 0], # 0,1,3 [0, 0, 1, 0, 1]] # 2,4 # # A larger graph # The cliques are # 0,1,2 # 3,4,5 # 5,6,7,8,9 # (and their sub cliques) # graph2 =[[1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1], [0, 0, 1, 0, 0, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 0, 1, 1, 1, 1, 1]] # The graph from the Global Constraint catalogue (the example above) # # 1 -> 1,3 # 2 -> 0,2,4 # 3 -> 1,4 # 4 -> 0,4 # 5 -> 1,2,3 # # The found (maximal) clique (N=3) is {1,2,4}. # graph3 = [[1,1,0,1,0], [1,1,1,0,1], [0,1,1,0,1], [1,0,0,1,1], [0,1,1,1,1]] # # A random graph of size 100 (generated by another program). # There are 3515 clique of size >= 3 (including sub cliques], # and four of size 6. # graph4 = [[0,0,1,0,1,0,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,1,1,0,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,1,1,1,1,1], [1,0,0,1,1,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,0,1,0,1], 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[1,0,0,1,0,0,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0], [1,0,1,0,0,0,0,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]] graph_random = random_graph(120) graphs = [graph1,graph2,graph3,graph4,graph_random] for graph in graphs: n = len(graph) print("size:",n) if n <= 10: print("all cliques and sub cliques") check_clique(graph,"all") print("\nsearch for max card clique") max_card = check_clique(graph,"max") print("all cliques of size", max_card) check_clique(graph,"all",max_card) print()