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AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
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Information Processing Letters
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Graphs and Combinatorics
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CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Bounding the Phase Transition on Edge Matching Puzzles
ISMVL '09 Proceedings of the 2009 39th International Symposium on Multiple-Valued Logic
How Hard is a Commercial Puzzle: the Eternity II Challenge
Proceedings of the 2008 conference on Artificial Intelligence Research and Development: Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence
MINION: A Fast, Scalable, Constraint Solver
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Modeling choices in quasigroup completion: SAT vs. CSP
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Further investigations into regular XORSAT
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Exact phase transitions in random constraint satisfaction problems
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Hiding satisfying assignments: two are better than one
Journal of Artificial Intelligence Research
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IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
The symmetric alldiff constraint
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Generating highly balanced sudoku problems as hard problems
Journal of Heuristics
Watched literals for constraint propagation in minion
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Effective preprocessing in SAT through variable and clause elimination
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Edge matching puzzles have been amongst us for a long time now and traditionally they have been considered, both, a children's game and an interesting mathematical divertimento. Their main characteristics have already been studied, and their worst-case complexity has been properly classified as a NP-complete problem. It is in recent times, specially after being used as the problem behind a money-prized contest, with a prize of 2US$ million for the first solver, that edge matching puzzles have attracted mainstream attention from wider audiences, including, of course, computer science people working on solving hard problems. We consider these competitions as an interesting opportunity to showcase SAT/CSP solving techniques when confronted to a real world problem to a broad audience, a part of the intrinsic, i.e. monetary, interest of such a contest. This article studies the NP-complete problem known as edge matching puzzle using SAT and CSP approaches for solving it. We will focus on providing, first and foremost, a theoretical framework, including a generalized definition of the problem. We will design and show algorithms for easy and fast problem instances generation, generators with easily tunable hardness. Afterwards we will provide with SAT and CSP models for the problems and we will study problem complexity, both typical case and worst-case complexity. We will also provide some specially crafted heuristics that result in a boost in solving time and study which is the effect of such heuristics.