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Paper Abstract and Keywords
Presentation 2015-10-02 10:00
Upper and lower bounds and time complexities on the Frobenius problem obtained from analysing its additive structure
Shunichi Matsubara (Aoyama Gakuin Univ.) COMP2015-22
Abstract (in Japanese) (See Japanese page) 
(in English) In this work, we investigate upper and lower bounds for the Frobenius problem, using some existing results in additive combinatorics. Given a relatively prime finite set A of two or more positive integers, we define the Frobenius number for A as the maximum integer g(A) that cannot be represented by any nonnegative integer combination of A. The Frobenius problem is the problem that asks for finding g(A) for a given finite set A of relatively prime two or more positive integers. The Frobenius problem is known to be solved in polynomial time if we assume the cardinality of A to be fixed. However, the problem is also known to be NP-hard under Cook-reduction if we do not set the assumption. Thus, it is important to find better upper and lower bounds for the problem. In this paper, we investigate new upper and lower bounds for the Frobenius problem by applying Mann's theorem and Plunnecke's theorem, which is known for useful tools in additive combinatorics.
Keyword (in Japanese) (See Japanese page) 
(in English) Frobenius number / upper and lower bounds for the Frobenius problem / NP-hardness / computational complexity / additive combinatorics / / /  
Reference Info. IEICE Tech. Rep., vol. 115, no. 235, COMP2015-22, pp. 1-5, Oct. 2015.
Paper # COMP2015-22 
Date of Issue 2015-09-25 (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 2015-10-02 - 2015-10-02 
Place (in Japanese) (See Japanese page) 
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Paper Information
Registration To COMP 
Conference Code 2015-10-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Upper and lower bounds and time complexities on the Frobenius problem obtained from analysing its additive structure 
Sub Title (in English)  
Keyword(1) Frobenius number  
Keyword(2) upper and lower bounds for the Frobenius problem  
Keyword(3) NP-hardness  
Keyword(4) computational complexity  
Keyword(5) additive combinatorics  
1st Author's Name Shunichi Matsubara  
1st Author's Affiliation Aoyama Gakuin University (Aoyama Gakuin Univ.)
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Date Time 2015-10-02 10:00:00 
Presentation Time 30 minutes 
Registration for COMP 
Paper # COMP2015-22 
Volume (vol) vol.115 
Number (no) no.235 
Page pp.1-5 
Date of Issue 2015-09-25 (COMP) 

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