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package samples.integer;
import org.kohsuke.args4j.Option;
import org.slf4j.LoggerFactory;
import samples.AbstractProblem;
import solver.Solver;
import solver.constraints.IntConstraintFactory;
import solver.search.strategy.IntStrategyFactory;
import solver.variables.BoolVar;
import solver.variables.IntVar;
import solver.variables.VariableFactory;
import util.ESat;
import util.tools.ArrayUtils;
/**
* CSPLib prob028:<br/>
* "A Balanced Incomplete Block Design (BIBD) is defined as an arrangement of
* v distinct objects into b blocks such that
* each block contains exactly k distinct objects,
* each object occurs in exactly r different blocks,
* and every two distinct objects occur together in exactly lambda blocks.
* <br/>
* Another way of defining a BIBD is in terms of its incidence matrix,
* which is a v by b binary matrix with exactly r ones per row,
* k ones per column,
* and with a scalar product of lambda between any pair of distinct rows.
* <br/>
* A BIBD is therefore specified by its parameters (v,b,r,k,lambda)."
* <br/>
*
* @author Charles Prud'homme
* @since 02/08/11
*/
public class BIBD extends AbstractProblem {
@Option(name = "-v", usage = "matrix first dimension.", required = false)
private int v = 7;
@Option(name = "-k", usage = "ones per column.", required = false)
private int k = 3;
@Option(name = "-p", usage = "scalar product.", required = false)
private int l = 20;
@Option(name = "-b", usage = "matrix second dimension.", required = false)
private int b = -1;
@Option(name = "-r", usage = "ones per row.", required = false)
private int r = -1;
BoolVar[][] vars, _vars;
@Override
public void createSolver() {
solver = new Solver("BIBD");
}
@Override
public void buildModel() {
if (b == -1) {
b = (v * (v - 1) * l) / (k * (k - 1));
}
if (r == -1) {
r = (l * (v - 1)) / (k - 1);
}
vars = new BoolVar[v][b];
_vars = new BoolVar[b][v];
for (int i = 0; i < v; i++) {
for (int j = 0; j < b; j++) {
vars[i][j] = VariableFactory.bool("V(" + i + "," + j + ")", solver);
_vars[j][i] = vars[i][j];
}
}
// r ones per row
IntVar R = VariableFactory.fixed(r, solver);
for (int i = 0; i < v; i++) {
solver.post(IntConstraintFactory.sum(vars[i], R));
}
// k ones per column
IntVar K = VariableFactory.fixed(k, solver);
for (int j = 0; j < b; j++) {
solver.post(IntConstraintFactory.sum(_vars[j], K));
}
// Exactly l ones in scalar product between two different rows
IntVar L = VariableFactory.fixed(l, solver);
for (int i1 = 0; i1 < v; i1++) {
for (int i2 = i1 + 1; i2 < v; i2++) {
BoolVar[] score = VariableFactory.boolArray(String.format("row(%d,%d)", i1, i2), b, solver);
for (int j = 0; j < b; j++) {
solver.post(IntConstraintFactory.times(_vars[j][i1], _vars[j][i2], score[j]));
}
solver.post(IntConstraintFactory.sum(score, L));
}
}
// Symmetry breaking
BoolVar[][] rev = new BoolVar[v][];
for (int i = 0; i < v; i++) {
rev[i] = vars[v - 1 - i];
}
solver.post(IntConstraintFactory.lex_chain_less_eq(rev));
BoolVar[][] _rev = new BoolVar[b][];
for (int i = 0; i < b; i++) {
_rev[i] = _vars[b - 1 - i];
}
solver.post(IntConstraintFactory.lex_chain_less_eq(_rev));
}
@Override
public void configureSearch() {
solver.set(IntStrategyFactory.lexico_LB(ArrayUtils.flatten(vars)));
}
@Override
public void solve() {
solver.findSolution();
}
@Override
public void prettyOut() {
LoggerFactory.getLogger("bench").info("BIBD({},{},{},{},{})", new Object[]{v, b, r, k, l});
StringBuilder st = new StringBuilder();
if (solver.isFeasible() == ESat.TRUE) {
for (int i = 0; i < v; i++) {
st.append("\t");
for (int j = 0; j < b; j++) {
st.append(_vars[j][i].getValue()).append(" ");
}
st.append("\n");
}
} else {
st.append("\tINFEASIBLE");
}
LoggerFactory.getLogger("bench").info(st.toString());
}
public static void main(String[] args) {
new BIBD().execute(args);
}
}