Domino Tatami Covering is NP-complete
Alejandro Erickson, Frank Ruskey
TL;DR
This paper proves that determining a domino tatami covering of a rectilinear region is NP-complete by reducing from planar 3SAT, highlighting the computational complexity of such geometric covering problems.
Contribution
It introduces a novel NP-completeness proof for domino tatami coverings using SAT-solver generated gadgets, linking geometric covering to computational complexity.
Findings
Deciding domino tatami coverings is NP-complete.
Reduction from planar 3SAT establishes complexity.
Gadgets were discovered with SAT-solver assistance.
Abstract
A covering with dominoes of a rectilinear region is called \emph{tatami} if no four dominoes meet at any point. We describe a reduction from planar 3SAT to Domino Tatami Covering. As a consequence it is NP-complete to decide whether there is a perfect matching of a graph that meets every 4-cycle, even if the graph is restricted to be an induced subgraph of the grid-graph. The gadgets used in the reduction were discovered with the help of a SAT-solver.
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Taxonomy
TopicsFormal Methods in Verification · Advanced Graph Theory Research · Model-Driven Software Engineering Techniques