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Paper Abstract and Keywords
Presentation 2019-12-13 17:25
The Analysis of Anti-slide
Kento Kimura, Kazuyuki Amano, Tetsuya Araki (Gunma Univ.) COMP2019-43
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 $3$.
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 Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
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)
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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  
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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Date Time 2019-12-13 17:25:00 
Presentation Time 25 
Registration for COMP 
Paper # IEICE-COMP2019-43 
Volume (vol) IEICE-119 
Number (no) no.340 
Page pp.101-107 
#Pages IEICE-7 
Date of Issue IEICE-COMP-2019-12-06 

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