Paper Abstract and Keywords |
Presentation |
2008-10-10 14:30
Partitioning a Weighted Tree to Subtrees of Almost Uniform Size Takehiro Ito (Tohoku Univ.), Takeaki Uno (NII), Xiao Zhou, Takao Nishizeki (Tohoku Univ.) COMP2008-41 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
Assume that each vertex of a graph $G$ is assigned a nonnegative integer weight and that $l$ and $u$ are integers such that $0 \le l \le u$. One wishes to partition $G$ into connected components by deleting edges from $G$ so that the total weight of each component is at least $l$ and at most $u$. Such an ``almost uniform'' partition is called an $(l,u)$-partition. We deal with three problems to find an $(l,u)$-partition of a given graph: the minimum partition problem is to find an $(l,u)$-partition with the minimum number of components; the maximum partition problem is defined analogously; and the $p$-partition problem is to find an $(l,u)$-partition with a given number $p$ of components. All these problems are NP-hard even for series-parallel graphs, but are solvable for paths in linear time and for trees in polynomial time. In this paper, we give polynomial-time algorithms to solve the three problems for trees, which are much simpler and faster than the known algorithms. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
algorithm / graph partition problem / lower bound / tree / uniform partition / upper bound / / |
Reference Info. |
IEICE Tech. Rep., vol. 108, no. 237, COMP2008-41, pp. 55-61, Oct. 2008. |
Paper # |
COMP2008-41 |
Date of Issue |
2008-10-03 (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) |
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COMP2008-41 |
Conference Information |
Committee |
COMP |
Conference Date |
2008-10-10 - 2008-10-10 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Tohoku Univ. |
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(See Japanese page) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2008-10-COMP |
Language |
English (Japanese title is available) |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Partitioning a Weighted Tree to Subtrees of Almost Uniform Size |
Sub Title (in English) |
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Keyword(1) |
algorithm |
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graph partition problem |
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lower bound |
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tree |
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uniform partition |
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upper bound |
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1st Author's Name |
Takehiro Ito |
1st Author's Affiliation |
Tohoku University (Tohoku Univ.) |
2nd Author's Name |
Takeaki Uno |
2nd Author's Affiliation |
National Institute of Informatics (NII) |
3rd Author's Name |
Xiao Zhou |
3rd Author's Affiliation |
Tohoku University (Tohoku Univ.) |
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Takao Nishizeki |
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Tohoku University (Tohoku Univ.) |
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Speaker |
Author-1 |
Date Time |
2008-10-10 14:30:00 |
Presentation Time |
30 minutes |
Registration for |
COMP |
Paper # |
COMP2008-41 |
Volume (vol) |
vol.108 |
Number (no) |
no.237 |
Page |
pp.55-61 |
#Pages |
7 |
Date of Issue |
2008-10-03 (COMP) |
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