The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
Models of Computation: Exploring the Power of Computing
Models of Computation: Exploring the Power of Computing
Backtrack Searching in the Presence of Symmetry
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Excluding Symmetries in Constraint-Based Search
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Modern Computer Algebra
Exploiting symmetry in lifted CSPs
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Breaking symmetries in all different problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Improving combinatorial optimization: extended abstract
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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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.