Journal of Computer and System Sciences
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity
Graphs and Combinatorics
Edge Matching Puzzles as Hard SAT/CSP Benchmarks
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Approximation hardness for small occurrence instances of NP-hard problems
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
Edge-matching problems with rotations
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
A Guide-and-Observe Hyper-Heuristic Approach to the Eternity II Puzzle
Journal of Mathematical Modelling and Algorithms
A Guide-and-Observe Hyper-Heuristic Approach to the Eternity II Puzzle
Journal of Mathematical Modelling and Algorithms
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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.