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 |
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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COMP2021-33 |
Conference Information |
Committee |
COMP |
Conference Date |
2022-03-06 - 2022-03-06 |
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(See Japanese page) |
Place (in English) |
Online |
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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 |
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Sports Scheduling Problem |
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Kirkman Schedule |
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Partial Team Swap |
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Partial Round Swap |
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Yusuke Kashiwagi |
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Seikei University (Seikei Univ) |
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Speaker |
Author-1 |
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 |
8 |
Date of Issue |
2022-02-27 (COMP) |
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