Abstract
A covering with dominoes of a rectilinear region is called tatami if no four dominoes meet at any point. We describe a reduction from planar 3SAT to Domino Tatami Covering. As a consequence it is therefore NP-complete to decide whether there is a perfect matching of a graph that meets every 4-cycle, even if the graph is restricted to be an induced subgraph of the grid-graph. The gadgets used in the reduction were discovered with the help of a SAT-solver.
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References
Biedl, T.: The complexity of domino tiling. In: Proceedings of the 17th Canadian Conference on Computational Geometry (CCCG), pp. 187–190 (2005)
Churchley, R., Huang, J., Zhu, X.: Complexity of cycle transverse matching problems. In: Iliopoulos, C.S., Smyth, W.F. (eds.) IWOCA 2011. LNCS, vol. 7056, pp. 135–143. Springer, Heidelberg (2011)
Eén, N., Sörensson, N.: An extensible sat-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Erickson, A., Ruskey, F.: Enumerating maximal tatami mat coverings of square grids with v vertical dominoes. Submitted to a Journal (2013), http://arxiv.org/abs/1304.0070
Erickson, A., Ruskey, F., Schurch, M., Woodcock, J.: Monomer-dimer tatami tilings of rectangular regions. The Electronic Journal of Combinatorics 18(1) #P109, 24 pages (2011)
Erickson, A., Schurch, M.: Monomer-dimer tatami tilings of square regions. Journal of Discrete Algorithms 16, 258–269 (2012)
Knuth, D.E.: The Art of Computer Programming: Combinatorial Algorithms, Part 1, 1st edn., vol. 4A. Addison-Wesley Professional (January 2011)
Lewis, H.R.: Complexity of solvable cases of the decision problem for the predicate calculus. In: 19th Annual Symposium on Foundations of Computer Science, pp. 35–47 (October 1978)
Lichtenstein, D.: Planar formulae and their uses. SIAM Journal on Computing 11(2), 329–343 (1982)
Rosenstiehl, P., Tarjan, R.E.: Rectilinear planar layouts and bipolar orientations of planar graphs. Discrete & Computational Geometry 1(1), 343–353 (1986)
Ruepp, O., Holzer, M.: The computational complexity of the Kakuro puzzle, revisited. In: Boldi, P. (ed.) FUN 2010. LNCS, vol. 6099, pp. 319–330. Springer, Heidelberg (2010)
Ruskey, F., Woodcock, J.: Counting fixed-height tatami tilings. The Electronic Journal of Combinatorics 16(1) #R126, 20 pages (2009)
Worman, C., Watson, M.D.: Tiling layouts with dominoes. In: Proceedings of the 16th Canadian Conference on Computational Geometry (CCCG), pp. 86–90 (2004)
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Erickson, A., Ruskey, F. (2013). Domino Tatami Covering Is NP-Complete. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_13
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DOI: https://doi.org/10.1007/978-3-642-45278-9_13
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