85 lines
2.2 KiB
MiniZinc
85 lines
2.2 KiB
MiniZinc
%------------------------------------------------------------------------------%
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% Constrained Community Detection Problem
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%
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% The problem is to find communities in the graph with maximum modularity value
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% satisfying must-link and cannot-link constraints which indicate whether a
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% pair of vertices must assign to same or different communities.
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%------------------------------------------------------------------------------%
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% Includes
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include "global_cardinality_low_up.mzn";
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include "value_precede_chain.mzn";
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%------------------------------------------------------------------------------%
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% Input and Derived Parameters
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int:n;
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int:k;
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int:maxsize;
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%int:minsize;
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int: nML;
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int: nCL;
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set of int: must = 1..nML;
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set of int: cannot = 1..nCL;
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array[must,1..2] of int: ML;
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array[cannot,1..2] of int: CL;
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array[1..n,1..n] of int: W;
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array[1..n,1..n] of int: A;
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array[1..n] of int: deg;
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array[1..n] of set of 1..n: nbh =[ {j | j in 1..n where A[i,j] > 0} | i in 1..n];
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int: dum = sum(i in 1..n)(W[i,i]);
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%------------------------------------------------------------------------------%
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% Variables
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array[1..n] of var 1..k: x;
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var 1..k: kk = max(x);
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int: objub = 2*sum(i,j in 1..n where i < j)(W[i,j]) + dum;
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var 0..objub: objective;
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%------------------------------------------------------------------------------%
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% Constraints
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constraint value_precede_chain([i|i in 1..k], x);
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constraint forall(m in must)( x[ML[m,1]] = x[ML[m,2]] );
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constraint forall(c in cannot)( x[CL[c,1]] != x[CL[c,2]] );
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constraint
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global_cardinality_low_up(
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x,
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[i | i in 1..k],
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[0 | i in 1..k],
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[n | i in 1..k]
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);
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% Objective
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%
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constraint
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objective = 2 * (
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sum(i in 1..n)(
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sum(j in 1..n where j < i)(
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bool2int(x[i] = x[j]) * W[i,j]
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)
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)
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) + dum;
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%------------------------------------------------------------------------------%
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% Solve item and search
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solve
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:: int_search(x,input_order,indomain_min, complete)
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maximize objective;
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%------------------------------------------------------------------------------%
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% Output
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output [
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"x = \(x);\n",
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% "kk = \(kk);\n",
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"objective = \(objective);\n"
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];
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