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Paper Abstract and Keywords
Presentation 2010-01-25 15:00
An Almost Optimal Algorithm for Winkler's Sorting Pairs in Bins
Hiro Ito, Junichi Teruyama, Yuichi Yoshida (Kyoto Univ.) COMP2009-45
Abstract (in Japanese) (See Japanese page) 
(in English) We investigate the following sorting puzzle:
We are given $n$ bins with two balls in each bin.
Balls in the $i$th bin are numbered $n-i+1$.
We can swap two balls from adjacent bins.
How many number of swaps are needed in order to sort balls, i.e., move every ball to the bin with the same number.
For this puzzle the best known solution requires almost $\frac{4}{5}n^2$ swaps.
In this paper, we show an algorithm which solves this puzzle using less than $\frac{2n^2}{3}$ swaps.
Since it is known that the lower bound of the number of swaps is $\lceil \binom{2n}{2}/3 \rceil = \lceil \frac{2n^2}{3}-\frac{n}{3} \rceil$, our result is almost tight.
Furthermore, we show that for $n=2^k+1\:(k\geq 0)$ the algorithm is optimal.
Keyword (in Japanese) (See Japanese page) 
(in English) sorting / mathematical puzzle / / / / / /  
Reference Info. IEICE Tech. Rep., vol. 109, no. 391, COMP2009-45, pp. 45-49, Jan. 2010.
Paper # COMP2009-45 
Date of Issue 2010-01-18 (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 COMP2009-45

Conference Information
Committee COMP  
Conference Date 2010-01-25 - 2010-01-25 
Place (in Japanese) (See Japanese page) 
Place (in English) Nishijin Plaza, Kyushu University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2010-01-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) An Almost Optimal Algorithm for Winkler's Sorting Pairs in Bins 
Sub Title (in English)  
Keyword(1) sorting  
Keyword(2) mathematical puzzle  
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1st Author's Name Hiro Ito  
1st Author's Affiliation Kyoto University (Kyoto Univ.)
2nd Author's Name Junichi Teruyama  
2nd Author's Affiliation Kyoto University (Kyoto Univ.)
3rd Author's Name Yuichi Yoshida  
3rd Author's Affiliation Kyoto University (Kyoto Univ.)
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Speaker Author-2 
Date Time 2010-01-25 15:00:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2009-45 
Volume (vol) vol.109 
Number (no) no.391 
Page pp.45-49 
#Pages 5 
Date of Issue 2010-01-18 (COMP) 

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