1 /*******************************************************************************
2 * SAT4J: a SATisfiability library for Java Copyright (C) 2004, 2012 Artois University and CNRS
3 *
4 * All rights reserved. This program and the accompanying materials
5 * are made available under the terms of the Eclipse Public License v1.0
6 * which accompanies this distribution, and is available at
7 * http://www.eclipse.org/legal/epl-v10.html
8 *
9 * Alternatively, the contents of this file may be used under the terms of
10 * either the GNU Lesser General Public License Version 2.1 or later (the
11 * "LGPL"), in which case the provisions of the LGPL are applicable instead
12 * of those above. If you wish to allow use of your version of this file only
13 * under the terms of the LGPL, and not to allow others to use your version of
14 * this file under the terms of the EPL, indicate your decision by deleting
15 * the provisions above and replace them with the notice and other provisions
16 * required by the LGPL. If you do not delete the provisions above, a recipient
17 * may use your version of this file under the terms of the EPL or the LGPL.
18 *
19 * Based on the original MiniSat specification from:
20 *
21 * An extensible SAT solver. Niklas Een and Niklas Sorensson. Proceedings of the
22 * Sixth International Conference on Theory and Applications of Satisfiability
23 * Testing, LNCS 2919, pp 502-518, 2003.
24 *
25 * See www.minisat.se for the original solver in C++.
26 *
27 * Contributors:
28 * CRIL - initial API and implementation
29 *******************************************************************************/
30
31 package org.sat4j.tools.encoding;
32
33 import org.sat4j.core.ConstrGroup;
34 import org.sat4j.core.VecInt;
35 import org.sat4j.specs.ContradictionException;
36 import org.sat4j.specs.IConstr;
37 import org.sat4j.specs.ISolver;
38 import org.sat4j.specs.IVecInt;
39
40 /**
41 * Commander encoding for "at most one" and "at most k" cases.
42 *
43 * The case "at most one" is introduced in W. Klieber and G. Kwon
44 * "Efficient CNF encoding for selecting 1 from N objects" in Fourth Workshop on
45 * Constraints in Formal Verification, 2007.
46 *
47 * The generalization to the "at most k" case is described in A. M. Frisch and P
48 * . A. Giannaros, "SAT Encodings of the At-Most-k Constraint", in International
49 * Workshop on Modelling and Reformulating Constraint Satisfaction Problems,
50 * 2010
51 *
52 * @author sroussel
53 * @since 2.3.1
54 */
55 public class Commander extends EncodingStrategyAdapter {
56
57 /**
58 *
59 */
60 private static final long serialVersionUID = 1L;
61
62 /**
63 * In this encoding, variables are partitioned in groups. Kwon and Klieber
64 * claim that the fewest clauses are produced when the size of the groups is
65 * 3, thus leading to 3.5 clauses and introducing n/2 variables.
66 */
67 @Override
68 public IConstr addAtMostOne(ISolver solver, IVecInt literals)
69 throws ContradictionException {
70
71 return addAtMostOne(solver, literals, 3);
72 }
73
74 private IConstr addAtMostOne(ISolver solver, IVecInt literals, int groupSize)
75 throws ContradictionException {
76
77 ConstrGroup constrGroup = new ConstrGroup(false);
78
79 IVecInt clause = new VecInt();
80 IVecInt clause1 = new VecInt();
81
82 final int n = literals.size();
83
84 int nbGroup = (int) Math.ceil((double) literals.size()
85 / (double) groupSize);
86
87 if (nbGroup == 1) {
88 for (int i = 0; i < literals.size() - 1; i++) {
89 for (int j = i + 1; j < literals.size(); j++) {
90 clause.push(-literals.get(i));
91 clause.push(-literals.get(j));
92 constrGroup.add(solver.addClause(clause));
93 clause.clear();
94 }
95 }
96 return constrGroup;
97 }
98
99 int[] c = new int[nbGroup];
100
101 for (int i = 0; i < nbGroup; i++) {
102 c[i] = solver.nextFreeVarId(true);
103 }
104
105 int nbVarLastGroup = n - (nbGroup - 1) * groupSize;
106
107 // Encoding <=1 for each group of groupLitterals
108 for (int i = 0; i < nbGroup; i++) {
109 int size = 0;
110 if (i == nbGroup - 1) {
111 size = nbVarLastGroup;
112 } else {
113 size = groupSize;
114 }
115 // Encoding <=1 for each group of groupLitterals
116 for (int j = 0; j < size - 1; j++) {
117 for (int k = j + 1; k < size; k++) {
118 clause.push(-literals.get(i * groupSize + j));
119 clause.push(-literals.get(i * groupSize + k));
120 constrGroup.add(solver.addClause(clause));
121 clause.clear();
122 }
123 }
124
125 // If a commander variable is true then some variable in its
126 // corresponding group must be true (clause1)
127 // If a commander variable is false then no variable in its group
128 // can be true (clause)
129 clause1.push(-c[i]);
130 for (int j = 0; j < size; j++) {
131 clause1.push(literals.get(i * groupSize + j));
132 clause.push(c[i]);
133 clause.push(-literals.get(i * groupSize + j));
134 constrGroup.add(solver.addClause(clause));
135 clause.clear();
136 }
137 constrGroup.add(solver.addClause(clause1));
138 clause1.clear();
139 }
140
141 // encode <=1 on commander variables
142
143 constrGroup.add(addAtMostOne(solver, new VecInt(c), groupSize));
144 return constrGroup;
145 }
146
147 @Override
148 public IConstr addAtMost(ISolver solver, IVecInt literals, int degree)
149 throws ContradictionException {
150 return super.addAtMost(solver, literals, degree);
151 }
152
153 @Override
154 public IConstr addExactlyOne(ISolver solver, IVecInt literals)
155 throws ContradictionException {
156 ConstrGroup group = new ConstrGroup();
157
158 group.add(addAtLeastOne(solver, literals));
159 group.add(addAtMostOne(solver, literals));
160
161 return group;
162 }
163
164 @Override
165 public IConstr addExactly(ISolver solver, IVecInt literals, int degree)
166 throws ContradictionException {
167 ConstrGroup group = new ConstrGroup();
168
169 group.add(addAtLeast(solver, literals, degree));
170 group.add(addAtMost(solver, literals, degree));
171
172 return group;
173 }
174
175 }