Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces
We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the problem is strongly NP-complete even if the pieces are all polyominos. On the positive side, we show that the problem can be solved in polynomial time if the number of pieces is a fixed constant.
- 3.Fox-Epstein, E., Uehara, R.: The convex configurations of “Sei Shonagon Chie no Ita" and other dissection puzzles. In: 26th Canadian Conference on Computational Geometry (CCCG), pp. 386–389 (2014)Google Scholar
- 4.Iwase, N.: Symmetrix. In: 24th International Puzzle Party (IPP 24), p. 54. IPP24 Committee (2005, unpublished)Google Scholar
- 5.Slocum, J.: The Tangram Book: The Story of the Chinese Puzzle with over Puzzle to Solve. Sterling Publishing, New York (2000)Google Scholar
- 7.Yamamoto, H.: Personal communication (2014)Google Scholar