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Folding an m×n square grid pattern along the edges of a grid is called map folding. We consider a decision problem in terms of whether a partial overlapping order of the squares aligning on the boundary of an m×n map is valid in a particular fold model called simple fold. This is a variation of the decision problem of valid total orders of the map in a simple fold model. We provide a linear-time algorithm to solve this problem, by defining an equivalence relation and computing the folding sequence sequentially, either uniquely or representatively.
Yiyang JIA
University of Tsukuba
Jun MITANI
University of Tsukuba
Ryuhei UEHARA
JAIST
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Yiyang JIA, Jun MITANI, Ryuhei UEHARA, "Research on Map Folding with Boundary Order on Simple Fold" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 9, pp. 1116-1126, September 2021, doi: 10.1587/transfun.2020DMP0017.
Abstract: Folding an m×n square grid pattern along the edges of a grid is called map folding. We consider a decision problem in terms of whether a partial overlapping order of the squares aligning on the boundary of an m×n map is valid in a particular fold model called simple fold. This is a variation of the decision problem of valid total orders of the map in a simple fold model. We provide a linear-time algorithm to solve this problem, by defining an equivalence relation and computing the folding sequence sequentially, either uniquely or representatively.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020DMP0017/_p
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@ARTICLE{e104-a_9_1116,
author={Yiyang JIA, Jun MITANI, Ryuhei UEHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Research on Map Folding with Boundary Order on Simple Fold},
year={2021},
volume={E104-A},
number={9},
pages={1116-1126},
abstract={Folding an m×n square grid pattern along the edges of a grid is called map folding. We consider a decision problem in terms of whether a partial overlapping order of the squares aligning on the boundary of an m×n map is valid in a particular fold model called simple fold. This is a variation of the decision problem of valid total orders of the map in a simple fold model. We provide a linear-time algorithm to solve this problem, by defining an equivalence relation and computing the folding sequence sequentially, either uniquely or representatively.},
keywords={},
doi={10.1587/transfun.2020DMP0017},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - Research on Map Folding with Boundary Order on Simple Fold
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1116
EP - 1126
AU - Yiyang JIA
AU - Jun MITANI
AU - Ryuhei UEHARA
PY - 2021
DO - 10.1587/transfun.2020DMP0017
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2021
AB - Folding an m×n square grid pattern along the edges of a grid is called map folding. We consider a decision problem in terms of whether a partial overlapping order of the squares aligning on the boundary of an m×n map is valid in a particular fold model called simple fold. This is a variation of the decision problem of valid total orders of the map in a simple fold model. We provide a linear-time algorithm to solve this problem, by defining an equivalence relation and computing the folding sequence sequentially, either uniquely or representatively.
ER -