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| Presentation | 2012-12-10 16:40 Enumeration of PLCP-orientations on the 4-cube Komei Fukuda, Lorenz Klaus (ETH Zurich), Hiroyuki Miyata (Tohoku Univ.)  COMP2012-50 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | The linear complementarity problem (LCP) is an important problem, which provides unified approaches to many problems such as linear programs, convex quadratic problems and bimatrix games. In general, the LCP is known to be NP-hard, but there are some positive results that implies the possibility that the LCP whose coefficient matrix is a $P$-matrix (PLCP) might be polynomial-time solvable. However, no polynomial-time algorithm for the PLCP has been found yet and the computational complexity of the PLCP remains unknown. Bard-type algorithms are ones of candidates for polynomial-time algorithms for the PLCP. In 1978, Stickney and Watson interpreted Bard-type algorithms as algorithms to find a sink of a cube graph with a certain orientation, called a PLCP-orientations, and performed the enumeration of PLCP-orientaions on the $3$-cube. In this paper, we perform the enumeration of PLCP-orientations on the $4$-cube via the realizability problem of oriented matroids. We also present some insights obtained in the computational experiments. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | the linear complementarity problem / oriented matroids / the realizability problem / unique sink orientations / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 112, no. 340, COMP2012-50, pp. 41-48, Dec. 2012. | |
| Paper # | COMP2012-50 | |
| Date of Issue | 2012-12-03 (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 | COMP2012-50 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2012-12-10 - 2012-12-10 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kyushu University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2012-12-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 PLCP-orientations on the 4-cube |
| Sub Title (in English) | |
| Keyword(1) | the linear complementarity problem |
| Keyword(2) | oriented matroids |
| Keyword(3) | the realizability problem |
| Keyword(4) | unique sink orientations |
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| 1st Author's Name | Komei Fukuda |
| 1st Author's Affiliation | Swiss Federal Institute of Technology Zurich (ETH Zurich) |
| 2nd Author's Name | Lorenz Klaus |
| 2nd Author's Affiliation | Swiss Federal Institute of Technology Zurich (ETH Zurich) |
| 3rd Author's Name | Hiroyuki Miyata |
| 3rd Author's Affiliation | Tohoku University (Tohoku Univ.) |
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| Speaker | Author-3 |
| Date Time | 2012-12-10 16:40:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2012-50 |
| Volume (vol) | vol.112 |
| Number (no) | no.340 |
| Page | pp.41-48 |
| #Pages | 8 |
| Date of Issue | 2012-12-03 (COMP) |
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