Hard and easy instances of L-tromino tilings

Akagi, Javier T., Gaona, Carlos F., Mendoza, Fabricio, Saikia, Manjil and Villagra, Marcos 2020. Hard and easy instances of L-tromino tilings. Theoretical Computer Science 815 , pp. 197-212. 10.1016/j.tcs.2020.02.025

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Abstract

We study tilings of regions in the square lattice with L-shaped trominoes. Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where it either remains NP-complete or has a polynomial time algorithm. First, we characterize the possibility of when an Aztec rectangle and an Aztec diamond has an L-tromino tiling. Then, we study tilings of arbitrary regions where only rotations of L-trominoes are available. For this particular case we show that deciding the existence of a tiling remains NP-complete; yet, if a region does not contains certain so-called “forbidden polyominoes” as sub-regions, then there exists a polynomial time algorithm for deciding a tiling.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Publisher:	Elsevier
ISSN:	0304-3975
Date of First Compliant Deposit:	25 February 2020
Date of Acceptance:	17 February 2020
Last Modified:	28 Nov 2024 23:31
URI:	https://orca.cardiff.ac.uk/id/eprint/129922

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