Optimal Partial Tiling of Manhattan Polyominoes

TL;DR

This paper presents a linear-time algorithm for optimally tiling Manhattan polyominoes with dominoes, addressing a specific case of the broader open problem of partial tiling algorithms.

Contribution

It introduces a novel linear-time algorithm for domino tiling of Manhattan polyominoes, leveraging graph optimization techniques.

Findings

Algorithm runs in linear time relative to the number of columns.

Provides an optimal tiling solution for Manhattan polyominoes.

Utilizes graph optimization methods from traditional problems.

Abstract

Finding an efficient optimal partial tiling algorithm is still an open problem. We have worked on a special case, the tiling of Manhattan polyominoes with dominoes, for which we give an algorithm linear in the number of columns. Some techniques are borrowed from traditional graph optimisation problems.