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 |
Download PDF |
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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) |
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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) |
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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 |
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Tohoku University (Tohoku Univ.) |
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Speaker |
Author-1 |
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 |
7 |
Date of Issue |
2006-10-10 (COMP) |
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