Breaking Row and Column Symmetries in Matrix Models
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Backtracking Algorithms and Search Heuristics to Generate Test Suites for Combinatorial Testing
COMPSAC '06 Proceedings of the 30th Annual International Computer Software and Applications Conference - Volume 01
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Combinatorial testing: learnings from our experience
ACM SIGSOFT Software Engineering Notes
Symmetry Breaking using Value Precedence
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
SEM: a system for enumerating models
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
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Orthogonal arrays are very important combinatorial objects which can be used in software testing and other areas. Mathematical methods for constructing such arrays have been studied extensively in the past decades. In contrast, computer search techniques, in particular exhaustive search methods, are rarely used to solve the problem. In this paper, we present an algorithm which finds orthogonal arrays of given sizes or shows their non-existence. The algorithm is essentially a backtrack search procedure, but enhanced with some novel symmetry breaking (isomorphism elimination) techniques. The orthogonal array is generated column by column, and the constraints are checked by an efficient SAT solver or pseudo-Boolean constraint solver. We have implemented a tool called BOAS (Backtrack-style OA Searcher) using MiniSat and PBS. Experimental results show that our tool can find many orthogonal arrays quickly, especially those with strength higher than 2.