Paper Abstract and Keywords |
Presentation |
2020-10-23 14:30
Mathematical Characterization and Computational Complexity of Anti-Slide Puzzles Ko Minamisawa, Ryuhei Uehara (JAIST), Masao Hara (Tokai Univ.) COMP2020-13 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
For a given set of pieces, an anti-slide puzzle asks us to arrange the pieces so that none of the pieces can slide. In this paper, we investigate the anti-slide puzzle in 2D. We first give mathematical characterizations of anti-slide puzzles and show the relationship between the previous work. Using the mathematical characterization, we give a polynomial-time algorithm for determining if a given arrangement of pieces is anti-slide or not. Next, the decision problem whether a given set of pieces can be arranged to be anti-slide or not is strongly $NP$-complete even if every piece is $x$-monotone. On the other hand, we prove that a set of pieces cannot be arranged to be anti-slide if all pieces are convex. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Anti-slide puzzle / interlocking / strongly $NP$-completeness / strongly connected / $x$-monotone / convexity / / |
Reference Info. |
IEICE Tech. Rep., vol. 120, no. 209, COMP2020-13, pp. 10-17, Oct. 2020. |
Paper # |
COMP2020-13 |
Date of Issue |
2020-10-16 (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) |
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COMP2020-13 |
Conference Information |
Committee |
COMP |
Conference Date |
2020-10-23 - 2020-10-23 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Osaka Univ. |
Topics (in Japanese) |
(See Japanese page) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2020-10-COMP |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Mathematical Characterization and Computational Complexity of Anti-Slide Puzzles |
Sub Title (in English) |
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Keyword(1) |
Anti-slide puzzle |
Keyword(2) |
interlocking |
Keyword(3) |
strongly $NP$-completeness |
Keyword(4) |
strongly connected |
Keyword(5) |
$x$-monotone |
Keyword(6) |
convexity |
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1st Author's Name |
Ko Minamisawa |
1st Author's Affiliation |
Japan Advanced Institute of Science and Technology (JAIST) |
2nd Author's Name |
Ryuhei Uehara |
2nd Author's Affiliation |
Japan Advanced Institute of Science and Technology (JAIST) |
3rd Author's Name |
Masao Hara |
3rd Author's Affiliation |
Tokai University (Tokai Univ.) |
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Speaker |
Author-1 |
Date Time |
2020-10-23 14:30:00 |
Presentation Time |
35 minutes |
Registration for |
COMP |
Paper # |
COMP2020-13 |
Volume (vol) |
vol.120 |
Number (no) |
no.209 |
Page |
pp.10-17 |
#Pages |
8 |
Date of Issue |
2020-10-16 (COMP) |
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