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Paper Abstract and Keywords
Presentation 2022-03-06 10:50
On properties of Kirkman schedules applied the partial team swap
Yusuke Kashiwagi (Seikei Univ) COMP2021-33
Abstract (in Japanese) (See Japanese page) 
(in English) In this study, we show some properties of Kirkman schedules in applying the partial team swap. Kirkman schedule is the most representative single-round schedule in sports scheduling problems. The partial team swap (PTS) and the partial round swap (PRS) are representative neighborhood search methods in local search for sports scheduling problem. Let $n$ be the number of teams, $k$ be some team other than $n$, and $p$ be a prime number. Also, let $P_{i,j}= [n] verb|| { i,j }=bigcup_{x=1}^{X_{i,j}}{P_{i,j}^{x}}$, where $P_{i,j}^{x}$ is the set of vertices split by Partial Team Swap, and $X_{i,j}$ is the number of splits when $i,j$ are exchange points. We showed the property that a Kirkman schedule satisfying (1) $n-1 neq p$ or (2) $n-1=p and P^{x}_{k,n}subsetneq P_{k,n}$ can not be a Kirkman schedule when applied the partial team swap. The above property has already been shown in cite{riffle}, but the proofs of (1) and (2) were done using different lemmas, so we simplified the proofs and gave a unified proof using only one lemma for the two conditions. As a supplement, assuming that $n-1=p$, in the proposition that if $n-1$ is a Mersenne prime, then $P^{x}_{i,j}subsetneq [n]verb|| { i,j }$, the sufficient condition is satisfied but it is not necessary. We also showed that applying Partial Round Swap a Kirkman schedule can not be a Kirkman schedule isormorphic to the original one.
Keyword (in Japanese) (See Japanese page) 
(in English) Sports Scheduling Problem / Kirkman Schedule / Partial Team Swap / Partial Round Swap / / / /  
Reference Info. IEICE Tech. Rep., vol. 121, no. 407, COMP2021-33, pp. 16-23, March 2022.
Paper # COMP2021-33 
Date of Issue 2022-02-27 (COMP) 
ISSN Online edition: ISSN 2432-6380
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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 2022-03-06 - 2022-03-06 
Place (in Japanese) (See Japanese page) 
Place (in English) Online 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2022-03-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) On properties of Kirkman schedules applied the partial team swap 
Sub Title (in English)  
Keyword(1) Sports Scheduling Problem  
Keyword(2) Kirkman Schedule  
Keyword(3) Partial Team Swap  
Keyword(4) Partial Round Swap  
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1st Author's Name Yusuke Kashiwagi  
1st Author's Affiliation Seikei University (Seikei Univ)
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Date Time 2022-03-06 10:50:00 
Presentation Time 30 minutes 
Registration for COMP 
Paper # COMP2021-33 
Volume (vol) vol.121 
Number (no) no.407 
Page pp.16-23 
#Pages
Date of Issue 2022-02-27 (COMP) 


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