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| Presentation | 2012-10-31 16:10 On classes of polytopes whose LP orientations can be characterized by the shelling property Yoshikazu Aoshima (Univ. of Tokyo), Hiroyuki Miyata, Sonoko Moriyama (Tohoku Univ.)  COMP2012-41 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Today, it is one of the most outstanding problems in combinatorial optimization to decide whether linear programs can be solved in strongly polynomial time. In particular, the question whether the simplex method with a suitable pivot rule can be a strongly polynomial time algorithm for linear programs is gathering large attention. In this context, it is important to investigate combinatorial properties of linear program digraphs, which describe all possible behaviors of the simplex method. In this paper, we consider classes of polytopes whose LP orientations can be characterized by the shelling property, a combinatorial property of linear program digraphs proposed by Avis and Moriyama (2009). We first review existing results on combinaotorial characterizations of LP orientations of polytopes in some restricted classes and then study LP orientations of $d$-polytopes with $d+2$ vertices, which were characeterized in a purely combinatorial way by Mihalisin. We prove that they can also be characterized by the shelling property. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | polytope / linear programming / shelling / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 112, no. 272, COMP2012-41, pp. 45-51, Oct. 2012. | |
| Paper # | COMP2012-41 | |
| Date of Issue | 2012-10-24 (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 | COMP2012-41 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2012-10-31 - 2012-10-31 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Tohoku University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2012-10-COMP |
| Language | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | On classes of polytopes whose LP orientations can be characterized by the shelling property |
| Sub Title (in English) | |
| Keyword(1) | polytope |
| Keyword(2) | linear programming |
| Keyword(3) | shelling |
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| 1st Author's Name | Yoshikazu Aoshima |
| 1st Author's Affiliation | University of Tokyo (Univ. of Tokyo) |
| 2nd Author's Name | Hiroyuki Miyata |
| 2nd Author's Affiliation | Tohoku University (Tohoku Univ.) |
| 3rd Author's Name | Sonoko Moriyama |
| 3rd Author's Affiliation | Tohoku University (Tohoku Univ.) |
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| Speaker | Author-2 |
| Date Time | 2012-10-31 16:10:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2012-41 |
| Volume (vol) | vol.112 |
| Number (no) | no.272 |
| Page | pp.45-51 |
| #Pages | 7 |
| Date of Issue | 2012-10-24 (COMP) |
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