# Partitioning trees of supply and demand

Takehiro Ito, Xiao Zhou, Takao Nishizeki

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Citations (Scopus)

## Abstract

Assume that a tree T has a number ns of "supply vertices" and all the other vertices are "demand vertices." Each supply vertex is assigned a positive number called a supply, while each demand vertex is assigned a positive number called a demand. One wish to partition T into exactly ns subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of demands of all demand vertices in the subtree. 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.

Original language English Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings 612-623 12 https://doi.org/10.1007/3-540-36136-7_53 Published - 2002 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 - Vancouver, BC, CanadaDuration: 2002 Nov 21 → 2002 Nov 23

### Publication series

Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2518 LNCS 0302-9743 1611-3349

### Conference

Conference 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 Canada Vancouver, BC 02/11/21 → 02/11/23

## Keywords

• Algorithm
• Approximation
• Demand
• FPTAS
• Maximum partition problem
• Partition problem
• Supply
• Tree

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