How Hard is a Commercial Puzzle: the Eternity II Challenge

  • Authors:

  • Carlos Ansótegui;Ramon Béjar;Cèsar Fernández;Carles Mateu

  • Affiliations:

  • {carlos, ramon, cesar, carlesm}@diei.udl.cat, Dept. of Computer Science, Universitat de Lleida, SPAIN;{carlos, ramon, cesar, carlesm}@diei.udl.cat, Dept. of Computer Science, Universitat de Lleida, SPAIN;{carlos, ramon, cesar, carlesm}@diei.udl.cat, Dept. of Computer Science, Universitat de Lleida, SPAIN;{carlos, ramon, cesar, carlesm}@diei.udl.cat, Dept. of Computer Science, Universitat de Lleida, SPAIN

  • Venue:
  • Proceedings of the 2008 conference on Artificial Intelligence Research and Development: Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence
  • Year:
  • 2008

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Abstract

Recently, edge matching puzzles, an NP-complete problem, have received, thanks to money-prized contests, considerable attention from wide audiences. We consider these competitions not only a challenge for SAT/CSP solving techniques but also as an opportunity to showcase the advances in the SAT/CSP community to a general audience. This paper studies the NP-complete problem of edge matching puzzles focusing on providing generation models of problem instances of variable hardness and on its resolution through the application of SAT and CSP techniques. From the generation side, we also identify the phase transition phenomena for each model. As solving methods, we employ both; SAT solvers through the translation to a SAT formula, and two ad-hoc CSP solvers we have developed, with different levels of consistency, employing several generic and specialized heuristics. Finally, we conducted an extensive experimental investigation to identify the hardest generation models and the best performing solving techniques.