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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
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Conference Information
Committee COMP  
Conference Date 2008-10-10 - 2008-10-10 
Place (in Japanese) (See Japanese page) 
Place (in English) Tohoku Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
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)  
Keyword(1) algorithm  
Keyword(2) graph partition problem  
Keyword(3) lower bound  
Keyword(4) tree  
Keyword(5) uniform partition  
Keyword(6) upper bound  
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Keyword(8)  
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.)
4th Author's Name Takao Nishizeki  
4th Author's Affiliation Tohoku University (Tohoku Univ.)
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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
Date of Issue 2008-10-03 (COMP) 


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