IEICE TRANSACTIONS on Fundamentals
Partitioning Trees with Supply, Demand and Edge-Capacity
Summary :
Let T be a given tree. Each vertex of T is either a supply vertex or a demand vertex, and is assigned a positive number, called the supply or demand. Each demand vertex v must be supplied an amount of “power,” equal to the demand of v, from exactly one supply vertex through edges in T. Each edge is assigned a positive number called the capacity. One wishes to partition T into subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of all demands in the subtree and the power flow through each edge is no more than capacity of the edge. The “partition problem” is a decision problem to ask whether T has such a partition. The “maximum partition problem” is an optimization version of the partition problem. In this paper, we give three algorithms for the problems. First is a linear-time algorithm for the partition problem. Second is a pseudo-polynomial-time algorithm for the maximum partition problem. Third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.6 pp.1036-1043
- Publication Date
- 2013/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E96.A.1036
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
Authors
Masaki KAWABATA
Kwansei Gakuin University
Takao NISHIZEKI
Kwansei Gakuin University
Keyword
Latest Issue
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Masaki KAWABATA, Takao NISHIZEKI, "Partitioning Trees with Supply, Demand and Edge-Capacity" in IEICE TRANSACTIONS on Fundamentals,
vol. E96-A, no. 6, pp. 1036-1043, June 2013, doi: 10.1587/transfun.E96.A.1036.
Abstract: Let T be a given tree. Each vertex of T is either a supply vertex or a demand vertex, and is assigned a positive number, called the supply or demand. Each demand vertex v must be supplied an amount of “power,” equal to the demand of v, from exactly one supply vertex through edges in T. Each edge is assigned a positive number called the capacity. One wishes to partition T into subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of all demands in the subtree and the power flow through each edge is no more than capacity of the edge. The “partition problem” is a decision problem to ask whether T has such a partition. The “maximum partition problem” is an optimization version of the partition problem. In this paper, we give three algorithms for the problems. First is a linear-time algorithm for the partition problem. Second is a pseudo-polynomial-time algorithm for the maximum partition problem. Third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.1036/_p
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@ARTICLE{e96-a_6_1036,
author={Masaki KAWABATA, Takao NISHIZEKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Partitioning Trees with Supply, Demand and Edge-Capacity},
year={2013},
volume={E96-A},
number={6},
pages={1036-1043},
abstract={Let T be a given tree. Each vertex of T is either a supply vertex or a demand vertex, and is assigned a positive number, called the supply or demand. Each demand vertex v must be supplied an amount of “power,” equal to the demand of v, from exactly one supply vertex through edges in T. Each edge is assigned a positive number called the capacity. One wishes to partition T into subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of all demands in the subtree and the power flow through each edge is no more than capacity of the edge. The “partition problem” is a decision problem to ask whether T has such a partition. The “maximum partition problem” is an optimization version of the partition problem. In this paper, we give three algorithms for the problems. First is a linear-time algorithm for the partition problem. Second is a pseudo-polynomial-time algorithm for the maximum partition problem. Third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.},
keywords={},
doi={10.1587/transfun.E96.A.1036},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - Partitioning Trees with Supply, Demand and Edge-Capacity
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1036
EP - 1043
AU - Masaki KAWABATA
AU - Takao NISHIZEKI
PY - 2013
DO - 10.1587/transfun.E96.A.1036
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2013
AB - Let T be a given tree. Each vertex of T is either a supply vertex or a demand vertex, and is assigned a positive number, called the supply or demand. Each demand vertex v must be supplied an amount of “power,” equal to the demand of v, from exactly one supply vertex through edges in T. Each edge is assigned a positive number called the capacity. One wishes to partition T into subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of all demands in the subtree and the power flow through each edge is no more than capacity of the edge. The “partition problem” is a decision problem to ask whether T has such a partition. The “maximum partition problem” is an optimization version of the partition problem. In this paper, we give three algorithms for the problems. First is a linear-time algorithm for the partition problem. Second is a pseudo-polynomial-time algorithm for the maximum partition problem. Third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.
ER -
English
