2021
DOI: 10.48550/arxiv.2110.05184
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Solving Rep-tile by Computers: Performance of Solvers and Analyses of Solutions

Abstract: A rep-tile is a polygon that can be dissected into smaller copies (of the same size) of the original polygon. A polyomino is a polygon that is formed by joining one or more unit squares edge to edge. These two notions were first introduced and investigated by Solomon W. Golomb in the 1950s and popularized by Martin Gardner in the 1960s. Since then, dozens of studies have been made in communities of recreational mathematics and puzzles. In this study, we first focus on the specific rep-tiles that have been inve… Show more

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Cited by 3 publications
(12 citation statements)
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“…They compared a well-known puzzle solver, a few algorithms based on dancing links, an MIP solver, and a SAT-based solver with respect to solving the packing puzzles. In [11], the authors concluded that the SAT-based solver is significantly faster than the other methods. The common shape puzzle has similar properties to the rep-tile problem.…”
Section: Improved Solutions For Common Multiple Shapesmentioning
confidence: 99%
“…They compared a well-known puzzle solver, a few algorithms based on dancing links, an MIP solver, and a SAT-based solver with respect to solving the packing puzzles. In [11], the authors concluded that the SAT-based solver is significantly faster than the other methods. The common shape puzzle has similar properties to the rep-tile problem.…”
Section: Improved Solutions For Common Multiple Shapesmentioning
confidence: 99%
“…Based on these facts, there are some researches which aim at solving NP-complete problems in practical time for certain n. We here briefly introduce three approaches to solve instances of NP-complete problems efficiently in practice. Further details can be found in [7].…”
Section: Solvers For Np-complete Problemsmentioning
confidence: 99%
“…Recently, the authors of [7] focused on these three polyominoes of size 6, and tried to resolve them completely for small k. The results of the computation can be found in Table 2. By the results, we can conclude that the smallest numbers of dissections of these three polyominoes of size 6 are 11 2 ¼ 121, 6 2 ¼ 36, and 8 2 ¼ 64, respectively.…”
Section: Case Analysis: Rep-tilementioning
confidence: 99%
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