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Research on Map Folding with Boundary Order on Simple Fold
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Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.9 pp.1116-1126
- Publication Date
- 2021/09/01
- Publicized
- 2021/03/08
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2020DMP0017
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
- Algorithms and Data Structures
Authors
Yiyang JIA
University of Tsukuba
Jun MITANI
University of Tsukuba
Ryuhei UEHARA
JAIST
Keyword
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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 -
English
