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The Complexity of Symmetry-Breaking Formulas

The Complexity of Symmetry-Breaking Formulas Symmetry-breaking formulas for a constraint-satisfaction problem are satisfied by exactly one member (e.g., the lexicographic leader) from each set of “symmetrical points” in the search space. Thus, the incorporation of such formulas can accelerate the search for a solution without sacrificing satisfiability. We study the computational complexity of generating lex-leader formulas. We show, even for abelian symmetry groups, that the number of essential clauses in the “natural” lex-leader formula could be exponential. Furthermore, we show the intractability (NP-hardness) of finding any expression of lex-leadership without reordering the variables, even for elementary abelian groups with orbits of size 3. Nevertheless, using techniques of computational group theory, we describe a reordering relative to which we construct small lex-leader formulas for abelian groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

The Complexity of Symmetry-Breaking Formulas

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References (27)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Kluwer Academic Publishers
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1023/B:AMAI.0000018578.92398.10
Publisher site
See Article on Publisher Site

Abstract

Symmetry-breaking formulas for a constraint-satisfaction problem are satisfied by exactly one member (e.g., the lexicographic leader) from each set of “symmetrical points” in the search space. Thus, the incorporation of such formulas can accelerate the search for a solution without sacrificing satisfiability. We study the computational complexity of generating lex-leader formulas. We show, even for abelian symmetry groups, that the number of essential clauses in the “natural” lex-leader formula could be exponential. Furthermore, we show the intractability (NP-hardness) of finding any expression of lex-leadership without reordering the variables, even for elementary abelian groups with orbits of size 3. Nevertheless, using techniques of computational group theory, we describe a reordering relative to which we construct small lex-leader formulas for abelian groups.

Journal

Annals of Mathematics and Artificial Intelligence – Springer Journals

Published: Oct 5, 2004

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