Monomino-Domino Tatami Coverings

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dc.contributor.author Erickson, Alejandro
dc.date.accessioned 2013-09-03T22:22:31Z
dc.date.available 2013-09-03T22:22:31Z
dc.date.copyright 2013 en_US
dc.date.issued 2013-09-03
dc.identifier.uri http://hdl.handle.net/1828/4902
dc.description.abstract We present several new results on the combinatorial properties of a locally restricted version of monomino-domino coverings of rectilinear regions. These are monomino-domino tatami coverings, and the restriction is that no four tiles may meet at any point. The global structure that the tatami restriction induces has numerous implications, and provides a powerful tool for solving enumeration problems on tatami coverings. Among these we address the enumeration of coverings of rectangles, with various parameters, and we develop algorithms for exhaustive generation of coverings, in constant amortised time per covering. We also con- sider computational complexity on two fronts; firstly, the structure shows that the space required to store a covering of the rectangle is linear in its longest dimension, and secondly, it is NP-complete to decide whether an arbitrary polyomino can be tatami-covered only with dominoes. en_US
dc.language English eng
dc.language.iso en en_US
dc.subject combinatorics en_US
dc.subject cstheory en_US
dc.subject math.CO en_US
dc.subject cs.CC en_US
dc.subject computer science theory en_US
dc.subject mathematics en_US
dc.subject tiling en_US
dc.subject covering en_US
dc.subject tatami restriction en_US
dc.subject monomino en_US
dc.subject domino en_US
dc.subject enumeration en_US
dc.subject combinatorial algorithms en_US
dc.subject combinatorial generation en_US
dc.subject computational complexity en_US
dc.title Monomino-Domino Tatami Coverings en_US
dc.type Thesis en_US
dc.contributor.supervisor Ruskey, Frank
dc.degree.department Dept. of Computer Science en_US
dc.degree.level Doctor of Philosophy Ph.D. en_US
dc.rights.temp Available to the World Wide Web en_US
dc.identifier.bibliographicCitation Alejandro Erickson and Mark Schurch. Monomer-dimer tatami tilings of square regions. Journal of Discrete Algorithms, 16(0):258–269, October 2012. en_US
dc.identifier.bibliographicCitation Alejandro Erickson and Mark Schurch. Enumerating tatami mat arrange- ments of square grids. In International Workshop on Combinatorial Algorithms (IWOCA), volume 7056 of LNCS, pages 223–235. Springer Berlin / Heidel- berg, January 2011. en_US
dc.identifier.bibliographicCitation Alejandro Erickson, Frank Ruskey, Mark Schurch, and Jennifer Woodcock. Monomer-dimer tatami tilings of rectangular regions. The Electronic Journal of Combinatorics, 18(1):24, 2011. en_US
dc.identifier.bibliographicCitation Alejandro Erickson and Frank Ruskey. Domino Tatami Covering is NP- complete. In The International Workshop on Combinatorial Algorithms (IWOCA), July 2013. 10 pages, to appear in Lecture Notes in Computer Science (LNCS). http://arxiv.org/abs/1305.6669. en_US
dc.identifier.bibliographicCitation Alejandro Erickson. TatamiMaker: A combinatorially rich mechanical game board. In Bridges, June 2013. 8 pages. http://arxiv.org/abs/1301.5969. en_US
dc.description.scholarlevel Graduate en_US
dc.description.proquestcode 0984 en_US
dc.description.proquestcode 0405 en_US

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