Abstract
This paper deals with the (in)approximability of Edge Matching Puzzles. The interest in EdgeMatching Puzzles has been raised in the last few years with the release of the Eternity II TM puzzle, with a $2 million prize for the first submitted correct solution. It is known [1] it is NP-hard to obtain an exact solution to Edge Matching Puzzles. We extend on that result by showing an approximation-preserving reduction from Max-3DM-B and thus proving that Edge Matching Puzzles do not admit polynomial-time approximation schemes unless P=NP. We then show that the problem is APX-complete, and study the difficulty of finding an approximate solution for several other optimisation variants of the problem.
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References
Demaine, E.D., Demaine, M.L.: Jigsaw Puzzles, Edge Matching, and Polyonymo Packing: Connections and Complexity. Graphs and Combinatorics 23, 195–208 (2007)
Berger, R.: The Undecidability of the Domino Problem. Memoirs of the American Mathematical Society 66 (1966)
Garey, M.R., Johnson, D.S., Papadimitriou, C.H.: Computers and Intractability: A Guide to the Theory of NP-completeness, p. 257. W.H. Freeman & Co., New York (1979)
Savelsberg, M.P.W., van Emde Boas, P.: BOUNDED TILING, an Alternative to SATISFIABILITY? In: Proceedings 2nd Frege Conference, vol. 20, pp. 354–363. Akademie Verlag, Schwerin (1984)
Chlebus, B.S.: Domino-Tiling Games. Journal of Computer and System Sciences 32, 374–392 (1986)
Benoist, T., Bourreau, E.: Fast Global Filtering for Eternity II. Constraint Programming Letters 3, 36–49 (2008)
Ansótegui, C., Béjar, R., Fernández, C., Mateau, C.: Edge Matching Puzzles as Hard SAT/CSP Benchmarks. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 560–565. Springer, Heidelberg (2008)
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation: Combinatorial Optimization Problems and their Approximability Properties. Springer, Heidelberg (1999)
Papadimitriou, C.H., Yannakakis, M.: Optimization, Approximation, and Complexity Classes. Journal of Computer and System Sciences 43, 425–440 (1991)
Kann, V.: Maximum Bounded 3-Dimensional Matching is MAX SNP-Complete. Information Processing Letters 37, 27–35 (1991)
Chlebìk, M., Chlebìkovà, J.: Approximation Hardness for Small Occurrence Instances of NP-hard Problems. In: Petreschi, R., Persiano, G., Silvestri, R. (eds.) CIAC 2003. LNCS, vol. 2653. Springer, Heidelberg (2003); (also ECCC Report) (2002)
Chlebìk, M., Chlebìkovà, J.: Inapproximability Results for Bounded Variants of Optimization Problems. In: Proocedings of FCT 2003: the 14th International Symposium on Fundamentals of Computation Theory (2003)
Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
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Antoniadis, A., Lingas, A. (2010). Approximability of Edge Matching Puzzles. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_13
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DOI: https://doi.org/10.1007/978-3-642-11266-9_13
Publisher Name: Springer, Berlin, Heidelberg
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