% % Global constraint clique in MiniZinc. % % From Global Constraint Catalogue: % http://www.emn.fr/x-info/sdemasse/gccat/sec4.49.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. % """ include "globals.mzn"; int: num_nodes; array[1..num_nodes, 1..num_nodes] of 0..1: g; % the graph var set of 1..num_nodes: s; var int: c = card(s); % size of the clique % % clique(clique size, the clique, the graph) % % Note: I have added the clique in the parameters list. % predicate clique(var int: c, var set of int: s, array[int, int] of int: g) = let { int: n = card(index_set_1of2(g)), array[1..n] of var bool: s_bool } in link_set_to_booleans(s, s_bool) /\ forall(i,j in 1..n where i != j) ( (s_bool[i] /\ s_bool[j]) -> ( g[i,j] > 0) ) /\ c = card(s) ; solve :: set_search([s], "input_order", "indomain_min", "complete") satisfy; % solve :: set_search([s], "input_order", "indomain_min", "complete") maximize c; % solve satisfy; % solve maximize c; constraint % s = {1,2,3} % s = {2,3,5} % /\ clique(c, s, g) /\ c >= 3 ; output [ "s: ", show(s),"\n", "c: ", show(c), "\n", ]; % Two cliques: (1,2,4) and (3, 5) % num_nodes = 5; % g = % array2d(1..num_nodes, 1..num_nodes, [ % % 1 2 3 4 5 % 1, 1, 0, 1, 0, % 1 % 1, 1, 0, 1, 0, % 2 % 0, 0, 1, 0, 1, % 3 % 1, 1, 0, 1, 0, % 4 % 0, 0, 1, 0, 1 % 5 % ]); % A larger graph % The cliques are % 1,2,3 % 4,5,6 % 6,7,8,9,10 % (and their "sub cliques") % % num_nodes = 10; % g = array2d(1..num_nodes, 1..num_nodes, % % 1 2 3 4 5 6 7 8 9 10 % [ 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, % 1 % 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, % 2 % 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, % 3 % 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, % 4 % 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, % 5 % 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, % 6 % 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, % 7 % 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, % 8 % 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, % 9 % 0, 1, 0, 0, 0, 1, 1, 1, 1, 1]); % 10 % The graph from the Global Constraint catalogue % % 1 -> 2,4 % 2 -> 1,3,5 % 3 -> 2,5 % 4 -> 1,5 % 5 -> 2,3,4 % % The found clique (N=3) is {2,3,5}. % % num_nodes = 5; % g = array2d(1..num_nodes, 1..num_nodes, [ % % 1 2 3 4 5 % 1,1,0,1,0, % 1 % 1,1,1,0,1, % 2 % 0,1,1,0,1, % 3 % 1,0,0,1,1, % 4 % 0,1,1,1,1, % 5 % ]); % A random graph of size 100 % There are 3515 of size >= 3 (including sub cliques), and four of size 6. num_nodes = 100; g = array2d(1..num_nodes, 1..num_nodes, [ 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, 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