%% s_max_clique.sp -- SPARC solution (using cr-rules) to additional exercise for
%% Chapter 6, finding a maximum clique in a graph.
%% Last Modified: 4/11/14
%% A clique is a subset of a graph such that each of its vertices
%% is connected by an edge to all the other vertices in the clique.
%% Note that each node of a graph is a clique of size 1 and that the empty
%% set is also a clique.
%% A maximum clique is a clique of the largest possible size in a given graph.
%% Write a SPARC program which finds a maximum clique in a given undirected
%% graph.
%% Suggested invocation:
%% java -jar sparc.jar s_max_clique.sp -A -solveropts "-pfilter=in_clique"
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#const n = 5.
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sorts
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#node = 1..n.
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predicates
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edge(#node,#node).
in_clique(#node).
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rules
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in_clique(N) :-
not -in_clique(N).
-in_clique(N) :+.
:- in_clique(N1),
in_clique(N2),
N1 != N2,
not edge(N1,N2).
%% ----------------------------------------------
%% Description of a patricular, undirected graph:
%% (Change at will.)
edge(N1,N2) :-
edge(N2,N1).
edge(1,2).
edge(2,3).
edge(3,4).
edge(3,5).
edge(4,5).
edge(2,5).
edge(2,4).