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Paper Abstract and Keywords
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
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.
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
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)
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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  
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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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 
Date of Issue 2013-06-17 (COMP) 

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