Wooden Geometric Puzzles: Design and Hardness Proofs
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting theoretical questions. This leads to the search for instances of partition that use only integers and are uniquely solvable. We show that instances of polynomial size exist with this property. This result also holds for partition into k subsets with the same sum: We construct instances of n integers with subset sum O(n k + 1), for fixed k.
KeywordsPartition Problem Hamiltonian Circuit Unique Partition Hardness Proof Solvable Instance
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- 1.Cubism For Fun website, http://cff.helm.lu/
- 2.Culberson, J.: SOKOBAN is PSPACE-complete. In: Proceedings in Informatics 4 (Int. Conf. FUN with Algorithms 1998), pp. 65–76 (1999)Google Scholar
- 3.Demaine, E.D.: Playing games with algorithms: Algorithmic combinatorial game theory. In: Proc. of Math. Found. of Comp. Sci. pp. 18–32 (2001)Google Scholar
- 5.Demaine, E.D., Hohenberger, S., Liben-Nowell, D.: Tetris is hard, even to approximate. Technical Report MIT-LCS-TR-865, MIT (2002)Google Scholar
- 6.Flake, G.W., Baum, E.B.: Rush Hour is PSPACE-complete, or why you should generously tip parking lot attendants (Manuscript)(2001)Google Scholar
- 11.van Kreveld, M.: Some tetraform puzzles. Cubism For Fun 68, 12–15 (2005)Google Scholar
- 12.van Kreveld, M.: Gate puzzles. Cubism For Fun 71, 28–30 (2006)Google Scholar