Monomino-Domino Tatami Coverings

Simple item page
dc.contributor.authorErickson, Alejandro
dc.contributor.supervisorRuskey, Frank
dc.date.accessioned2013-09-03T22:22:31Z
dc.date.available2013-09-03T22:22:31Z
dc.date.copyright2013en_US
dc.date.issued2013-09-03
dc.degree.departmentDept. of Computer Scienceen_US
dc.degree.levelDoctor of Philosophy Ph.D.en_US
dc.description.abstractWe 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.description.proquestcode0984en_US
dc.description.proquestcode0405en_US
dc.description.proquestemailalejandro.erickson@gmail.comen_US
dc.description.scholarlevelGraduateen_US
dc.identifier.bibliographicCitationAlejandro 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.bibliographicCitationAlejandro 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.bibliographicCitationAlejandro 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.bibliographicCitationAlejandro 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.bibliographicCitationAlejandro Erickson. TatamiMaker: A combinatorially rich mechanical game board. In Bridges, June 2013. 8 pages. http://arxiv.org/abs/1301.5969.en_US
dc.identifier.urihttp://hdl.handle.net/1828/4902
dc.languageEnglisheng
dc.language.isoenen_US
dc.rights.tempAvailable to the World Wide Weben_US
dc.subjectcombinatoricsen_US
dc.subjectcstheoryen_US
dc.subjectmath.COen_US
dc.subjectcs.CCen_US
dc.subjectcomputer science theoryen_US
dc.subjectmathematicsen_US
dc.subjecttilingen_US
dc.subjectcoveringen_US
dc.subjecttatami restrictionen_US
dc.subjectmonominoen_US
dc.subjectdominoen_US
dc.subjectenumerationen_US
dc.subjectcombinatorial algorithmsen_US
dc.subjectcombinatorial generationen_US
dc.subjectcomputational complexityen_US
dc.titleMonomino-Domino Tatami Coveringsen_US
dc.typeThesisen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Erickson_Alejandro_PhD_2013.pdf
Size:
9.81 MB
Format:
Adobe Portable Document Format
Description:
revised version with contents in TOC and EPIGRAPH titled.
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.74 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

ETD (Electronic Theses and Dissertations)
Theses (Computer Science)
 
University of Victoria Libraries

We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.