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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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
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