Abstract
Analysis of Algorithms We consider questions concerning the tileability of orthogonal polygons with colored dominoes. A colored domino is a rotatable 2 × 1 rectangle that is partitioned into two unit squares, which are called faces, each of which is assigned a color. In a colored domino tiling of an orthogonal polygon P, a set of dominoes completely covers P such that no dominoes overlap and so that adjacent faces have the same color. We demonstrated that for simple layout polygons that can be tiled with colored dominoes, two colors are always sufficient. We also show that for tileable non-simple layout polygons, four colors are always sufficient and sometimes necessary. We describe an O(n) time algorithm for computing a colored domino tiling of a simple orthogonal polygon, if such a tiling exists, where n is the number of dominoes used in the tiling. We also show that deciding whether or not a non-simple orthogonal polygon can be tiled with colored dominoes is NP-complete.
Highlights
We study a computational tiling problem where the tiles model the commonly used domino game piece
Colored dominoes are similar to Wang tiles [1; 13; 9; 20; 4], which are unit squares with colored sides
In the colored domino tiling problems studied in [21] and [5], a multiset of dominoes is provided, and in tilings the multiplicity of the dominoes cannot exceed those in the multiset
Summary
We study a computational tiling problem where the tiles model the commonly used domino game piece. Chris Worman and Boting Yang is described for computing colored domino tilings of so-called “paths” or “cycles” This algorithm runs in time linear in the number of dominoes used in the tiling. The authors of [21] consider a colored domino tiling problem where some dominoes have already been positioned on the polygon, and we are asked to decide if the tiling can be completed. It is shown that PARTIAL DOMINO TILING is NP-complete, and remains so even for so-called “paths” or “cycles”. We describe an O(n) time algorithm for computing a colored domino tiling of a simple orthogonal polygon, where n is the number of dominoes used in the tiling. We show that deciding whether or not a non-simple orthogonal polygon can be tiled with colored dominoes is NP-complete
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call