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| Presentation | 2018-03-05 14:50 A recognition algorithm for simple-triangle graphs Asahi Takaoka (Kanagawa Univ.)  COMP2017-50 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a longstanding open problem, which was recently settled. This paper provides a new recognition algorithm for simple-triangle graphs to improve the time bound from $O(n^2 overline{m})$ to $O(nm)$, where $n$, $m$, and $overline{m}$ are the number of vertices, edges, and non-edges of the graph, respectively. The algorithm uses the vertex ordering characterization in our previous paper that a graph is a simple-triangle graph if and only if there is a linear ordering of the vertices containing both an alternating orientation of the graph and a transitive orientation of the complement of the graph. We also show, as a byproduct, that an alternating orientation can be obtained in $O(nm)$ time for cocomparability graphs, and it is NP-complete to decide whether a cocomparability graph has an orientation that is alternating and acyclic. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Alternately orientable graphs / Cocomparability graphs / Intersection graphs / PI graphs / Recognition algorithm / Simple-triangle graphs / Vertex ordering characterization / | |
| Reference Info. | IEICE Tech. Rep., vol. 117, no. 474, COMP2017-50, pp. 27-34, March 2018. | |
| Paper # | COMP2017-50 | |
| Date of Issue | 2018-02-26 (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 | COMP2017-50 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2018-03-05 - 2018-03-05 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Osaka Prefecture Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2018-03-COMP |
| Language | English |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A recognition algorithm for simple-triangle graphs |
| Sub Title (in English) | |
| Keyword(1) | Alternately orientable graphs |
| Keyword(2) | Cocomparability graphs |
| Keyword(3) | Intersection graphs |
| Keyword(4) | PI graphs |
| Keyword(5) | Recognition algorithm |
| Keyword(6) | Simple-triangle graphs |
| Keyword(7) | Vertex ordering characterization |
| Keyword(8) | |
| 1st Author's Name | Asahi Takaoka |
| 1st Author's Affiliation | Kanagawa University (Kanagawa Univ.) |
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| Speaker | Author-1 |
| Date Time | 2018-03-05 14:50:00 |
| Presentation Time | 25 minutes |
| Registration for | COMP |
| Paper # | COMP2017-50 |
| Volume (vol) | vol.117 |
| Number (no) | no.474 |
| Page | pp.27-34 |
| #Pages | 8 |
| Date of Issue | 2018-02-26 (COMP) |
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