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Paper Abstract and Keywords
Presentation 2013-12-21 11:00
Sublinear-time cake-cutting algorithms
Takahiro Ueda (Kyoto Univ.), Hiro Ito (Univ. of Electro-Comm.) COMP2013-51
Abstract (in Japanese) (See Japanese page) 
(in English) In this research, we show sub-linear time algorithms for the cake-cutting problem. The cake-cutting problem is a problem of dividing a cake into pieces and handing them down to players who have different measures of the value of the cake, and then they must be “satisfied”. Though the definition of “satisfaction” are various, e.g. simple-fair, envy-free and so on, we talk about simple-fair division, i. e., each player must have 1/n value in his/her piece of cake in his/her own value function. It is known that the query complexity for the cake-cutting problem is Θ(n log n) for both deterministic and random algorithms. But no o(n)-time algorithm have been knows for dividing a piece only for the first player. We construct a framework to solve the cake-cutting problem in sublinear-time, and show algorithms in this framework. In particular, algorithms with ϵn-victims for dividing a cake for r = o(n) players in O(r/ϵ) times. And then the first r players who are assigned a piece of cake must be satisfied. Furthermore, we extend this algorithm to general f(n)-victims.
Keyword (in Japanese) (See Japanese page) 
(in English) Cake Cutting Problem / simple-fair devision / sub-linear time algorithms / victims / / / /  
Reference Info. IEICE Tech. Rep., vol. 113, no. 371, COMP2013-51, pp. 73-79, Dec. 2013.
Paper # COMP2013-51 
Date of Issue 2013-12-13 (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 COMP2013-51

Conference Information
Committee COMP  
Conference Date 2013-12-20 - 2013-12-21 
Place (in Japanese) (See Japanese page) 
Place (in English) Okinawa Industry Support Center 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2013-12-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Sublinear-time cake-cutting algorithms 
Sub Title (in English)  
Keyword(1) Cake Cutting Problem  
Keyword(2) simple-fair devision  
Keyword(3) sub-linear time algorithms  
Keyword(4) victims  
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1st Author's Name Takahiro Ueda  
1st Author's Affiliation Kyoto Univerisity (Kyoto Univ.)
2nd Author's Name Hiro Ito  
2nd Author's Affiliation The Univeristy of Electro-Communications (Univ. of Electro-Comm.)
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Speaker Author-1 
Date Time 2013-12-21 11:00:00 
Presentation Time 25 minutes 
Registration for COMP 
Paper # COMP2013-51 
Volume (vol) vol.113 
Number (no) no.371 
Page pp.73-79 
#Pages 7 
Date of Issue 2013-12-13 (COMP) 

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