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| Presentation | 2009-05-26 16:15 Enumeration of Polyominoes for p4 Tiling Takashi Horiyama, Masato Samejima (Saitama Univ.)  COMP2009-17 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Polyominoes are the two dimensional shapes made by connecting n unit squares, joined along their edges. In this paper, we propose algorithms to enumerate polyominoes for p4 tiling, i.e., those covering the plane by only 90 degrees rotations around the two rotation centers. The conventional methods are basically trial and error, i.e., they repeat generating polyominoes and checking whether the shape has been already generated. Our approach is based on the reverse search, in which we design rules to generate the next. This technique has the following two characteristics: (1) No trial and error, which implies that we can reduce the computation time. (2) No need to store already enumerated polyominoes. Thus, we can also reduce the space complexity. We also implement the algorithm and enumerate all polyominoes for p4 tiling up to n = 18. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | algorithms / enumeration / tiling / rotational symmetry / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 109, no. 54, COMP2009-17, pp. 51-55, May 2009. | |
| Paper # | COMP2009-17 | |
| Date of Issue | 2009-05-19 (COMP) | |
| ISSN | Print edition: ISSN 0913-5685 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 | COMP2009-17 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2009-05-26 - 2009-05-26 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Saitama Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2009-05-COMP |
| Language | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Enumeration of Polyominoes for p4 Tiling |
| Sub Title (in English) | |
| Keyword(1) | algorithms |
| Keyword(2) | enumeration |
| Keyword(3) | tiling |
| Keyword(4) | rotational symmetry |
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| 1st Author's Name | Takashi Horiyama |
| 1st Author's Affiliation | Saitama University (Saitama Univ.) |
| 2nd Author's Name | Masato Samejima |
| 2nd Author's Affiliation | Saitama University (Saitama Univ.) |
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| Speaker | Author-1 |
| Date Time | 2009-05-26 16:15:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2009-17 |
| Volume (vol) | vol.109 |
| Number (no) | no.54 |
| Page | pp.51-55 |
| #Pages | 5 |
| Date of Issue | 2009-05-19 (COMP) |
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