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Paper Abstract and Keywords
Presentation 2012-12-10 17:15
Comparison of Worst-case Polytopes for the Simplex Method -- Klee-Minty Cubes Are Also Goldfarb Cubes --
Bernd Gaertner, Christian Helbling (ETH Zurich), Yoshiki Ota, Takeru Takahashi (Tohoku Univ.) COMP2012-51
Abstract (in Japanese) (See Japanese page) 
(in English) The $d$-dimensional Goldfarb cube is a polytope with the property that all its $2^d$ vertices appear on some shadow of it (projection onto a $2$-dimensional plane). The Goldfarb cube is the solution set of a system of $2d$ linear inequalities with at most $3$ variables per inequality. We show in this paper that the $d$-dimensional Klee-Minty cube --- constructed from inequalities with at most $2$ variables per inequality --- also has a shadow with $2^d$ vertices. In contrast, with one variable per inequality, the size of the shadow is bounded by $2d$.
Keyword (in Japanese) (See Japanese page) 
(in English) linear programming / simplex method / pivot rule / Goldfarb cube / Klee-Minty cube / / /  
Reference Info. IEICE Tech. Rep., vol. 112, no. 340, COMP2012-51, pp. 49-53, Dec. 2012.
Paper # COMP2012-51 
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)
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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 Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Comparison of Worst-case Polytopes for the Simplex Method 
Sub Title (in English) Klee-Minty Cubes Are Also Goldfarb Cubes 
Keyword(1) linear programming  
Keyword(2) simplex method  
Keyword(3) pivot rule  
Keyword(4) Goldfarb cube  
Keyword(5) Klee-Minty cube  
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1st Author's Name Bernd Gaertner  
1st Author's Affiliation ETH Zurich (ETH Zurich)
2nd Author's Name Christian Helbling  
2nd Author's Affiliation ETH Zurich (ETH Zurich)
3rd Author's Name Yoshiki Ota  
3rd Author's Affiliation Tohoku University (Tohoku Univ.)
4th Author's Name Takeru Takahashi  
4th Author's Affiliation Tohoku University (Tohoku Univ.)
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Speaker Author-3 
Date Time 2012-12-10 17:15:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2012-51 
Volume (vol) vol.112 
Number (no) no.340 
Page pp.49-53 
#Pages 5 
Date of Issue 2012-12-03 (COMP) 

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