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| Presentation | 2013-06-24 15:10 On a parametic integer programming algorithm using dualization of monotone Boolean function Norie Fu (NII), Takafumi Shibuta (Kyushu Univ.)  COMP2013-23 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | The {it parametric integer programing} is the integer programming with a vector of parameters as its right-hand-side vector. Motivated by the application to compiler optimization, several algorithms are proposed by Feautrier and Verdoolaege. However, it is difficult to estimate the time complexity of their algorithms. In this paper, we introduce an algorithm using Hoc{s}ten--Thomas' algebraic algorithm for the integer linear programming. We show that the problem of computing {it standard pair decomposition}, which plays the central role in Hoc{s}ten--Thomas' algorithm, can be reduced to the {it dualization of monotone Boolean functions}. Using this, we show a new upper bound for the size of the standard pair decomposition, and show an $2^{O(n (log n + log a_{max}))}$-time algorithm for the parametric integer programming. We also show that the implementation of Hoc{s}ten--Thomas' algorithm using fast software {it SHD} for the dualization of monotone Boolean functions solves many parametric integer programs faster than {it ISL}, which is an implementation of Feautrier's algorithm by Verdoolaege. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | parametric integer programming / dualization of monotone Boolean function / toric ideal / Gr"{o}bner basis / standard pair decomposition / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 113, no. 108, COMP2013-23, pp. 23-30, June 2013. | |
| Paper # | COMP2013-23 | |
| Date of Issue | 2013-06-17 (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 | COMP2013-23 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2013-06-24 - 2013-06-24 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Nara Women's University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2013-06-COMP |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | On a parametic integer programming algorithm using dualization of monotone Boolean function |
| Sub Title (in English) | |
| Keyword(1) | parametric integer programming |
| Keyword(2) | dualization of monotone Boolean function |
| Keyword(3) | toric ideal |
| Keyword(4) | Gr"{o}bner basis |
| Keyword(5) | standard pair decomposition |
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| Keyword(8) | |
| 1st Author's Name | Norie Fu |
| 1st Author's Affiliation | National Institute of Informatics (NII) |
| 2nd Author's Name | Takafumi Shibuta |
| 2nd Author's Affiliation | Kyushu University (Kyushu Univ.) |
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| Speaker | Author-2 |
| Date Time | 2013-06-24 15:10:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2013-23 |
| Volume (vol) | vol.113 |
| Number (no) | no.108 |
| Page | pp.23-30 |
| #Pages | 8 |
| Date of Issue | 2013-06-17 (COMP) |
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