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| Presentation | 2019-12-13 17:25 The Analysis of Anti-slide Kento Kimura, Kazuyuki Amano, Tetsuya Araki (Gunma Univ.)  COMP2019-43 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Let $n$ be a positive integer. Given an $ntimes ntimes n$ box and a number of pieces of some specified shape, we consider how to pack the pieces such that none of the pieces in the box can slide in any direction. The objective of the problem is to find a packing with a minimum number of pieces. The problem is called the ``anti-slide'' puzzle. Kimura and Amano (Combinatorial Games and puzzles 14th) conjectured that the minimum number of pieces contained in such packing is one of $Theta(n^3)$, $Theta(n^2)$ or $Theta(n)$, depending on the shape of the pieces. In this paper, we analyze the anti-slide puzzle for three shapes in the second group. For each of these three shapes, we give the general structure of an anti-slide packing consisting of $O(n^2)$ pieces. In addition, we reveal that, for a 2-dimensional $ntimes n$ box and the T-shape pieces, the size of an optimal packing is quite different depending on $n$ modulo $3$. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | anti-slide / lower bound / IP solver / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 119, no. 340, COMP2019-43, pp. 101-107, Dec. 2019. | |
| Paper # | COMP2019-43 | |
| Date of Issue | 2019-12-06 (COMP) | |
| ISSN | Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | COMP2019-43 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2019-12-13 - 2019-12-13 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Ikaho Seminar House, Gunma University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2019-12-COMP |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | The Analysis of Anti-slide |
| Sub Title (in English) | |
| Keyword(1) | anti-slide |
| Keyword(2) | lower bound |
| Keyword(3) | IP solver |
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| 1st Author's Name | Kento Kimura |
| 1st Author's Affiliation | Gunma University (Gunma Univ.) |
| 2nd Author's Name | Kazuyuki Amano |
| 2nd Author's Affiliation | Gunma University (Gunma Univ.) |
| 3rd Author's Name | Tetsuya Araki |
| 3rd Author's Affiliation | Gunma University (Gunma Univ.) |
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| Speaker | Author-1 |
| Date Time | 2019-12-13 17:25:00 |
| Presentation Time | 25 minutes |
| Registration for | COMP |
| Paper # | COMP2019-43 |
| Volume (vol) | vol.119 |
| Number (no) | no.340 |
| Page | pp.101-107 |
| #Pages | 7 |
| Date of Issue | 2019-12-06 (COMP) |
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