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Paper Abstract and Keywords
Presentation 2006-10-17 10:25
Approximability of Partitioning Graphs with Supply and Demand
Takehiro Ito (Tohoku Univ.), Erik D.Demaine (MIT), Xiao Zhou, Takao Nishizeki (Tohoku Univ.)
Abstract (in Japanese) (See Japanese page) 
(in English) Suppose that each vertex of a graph $G$ is either a supply vertex or a demand vertex and is assigned a positive real number, called the supply or the demand. Each demand vertex can receive ``power'' from at most one supply vertex through edges in $G$. One thus wishes to partition $G$ into connected components so that each component $C$ either has no supply vertex or has exactly one supply vertex whose supply is at least the sum of demands in $C$, and wishes to maximize the fulfillment, that is, the sum of demands in all components with supply vertices. This maximization problem is known to be NP-hard even for trees having exactly one supply vertex and strongly NP-hard for general graphs. In this paper, we focus on the approximability of the problem. We first show that the problem is MAXSNP-hard and hence there is no polynomial-time approximation scheme (PTAS) for general graphs unless ${\rm P}={\rm NP}$. We then present a fully polynomial-time approximation scheme (FPTAS) for series-parallel graphs having exactly one supply vertex. The FPTAS can be easily extended for partial $k$-trees, that is, graphs with bounded treewidth.
Keyword (in Japanese) (See Japanese page) 
(in English) approximation algorithm / demand / FPTAS / maximum partition problem / MAXSNP-hard / partial $k$-tree / series-parallel graph / supply  
Reference Info. IEICE Tech. Rep., vol. 106, no. 289, COMP2006-33, pp. 17-23, Oct. 2006.
Paper # COMP2006-33 
Date of Issue 2006-10-10 (COMP) 
ISSN Print edition: ISSN 0913-5685
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Conference Information
Committee COMP  
Conference Date 2006-10-17 - 2006-10-17 
Place (in Japanese) (See Japanese page) 
Place (in English) Tohoku University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2006-10-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Approximability of Partitioning Graphs with Supply and Demand 
Sub Title (in English)  
Keyword(1) approximation algorithm  
Keyword(2) demand  
Keyword(3) FPTAS  
Keyword(4) maximum partition problem  
Keyword(5) MAXSNP-hard  
Keyword(6) partial $k$-tree  
Keyword(7) series-parallel graph  
Keyword(8) supply  
1st Author's Name Takehiro Ito  
1st Author's Affiliation Tohoku University (Tohoku Univ.)
2nd Author's Name Erik D.Demaine  
2nd Author's Affiliation Massachusetts Institute of Technology (MIT)
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 2006-10-17 10:25:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2006-33 
Volume (vol) vol.106 
Number (no) no.289 
Page pp.17-23 
#Pages
Date of Issue 2006-10-10 (COMP) 


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