Fast domino tileability
Igor Pak, Adam Sheffer, Martin Tassy
TL;DR
This paper improves the efficiency of determining domino tileability by reducing the time complexity from nearly linear in the area to nearly linear in the perimeter, enhancing computational performance in Discrete Geometry.
Contribution
It advances Thurston's height function method to achieve nearly linear time complexity based on the perimeter of regions.
Findings
Enhanced algorithm for domino tileability with nearly linear perimeter time complexity
Significant improvement over previous area-based methods
Potential applications in computational geometry and tiling problems
Abstract
Domino tileability is a classical problem in Discrete Geometry, famously solved by Thurston for simply connected regions in nearly linear time in the area. In this paper, we improve upon Thurston's height function approach to a nearly linear time in the perimeter.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Computational Geometry and Mesh Generation