Generating Tatami Coverings Efficiently release_nasjavnwpzev5odhu7hrp7ah3i

by Alejandro Erickson, Frank Ruskey

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2014  

Abstract

We present two algorithms to list certain classes of monomino-domino coverings which conform to the tatami restriction; no four tiles meet. Our methods exploit structural features of tatami coverings in order to create the lists in O(1) time per covering. This is faster than known methods for generating certain classes of matchings in bipartite graphs. We discuss tatami coverings of n× n grids with n monominoes and v vertical dominoes, as well as tatami coverings of a two-way infinitely-wide strip of constant height, subject to the constraint that they have a finite number of non-trivial structural "features". These two classes are representative of two differing structural characterisations of tatami coverings which may be adapted to count other classes of tatami coverings or locally restricted matchings, such as tatami coverings of rectangles.
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Date   2014-03-19
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Language   en ?
arXiv  1403.4776v1
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