### Abstract

Assume that a tree T has a number n_{s} 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 n_{s} 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 |
---|---|

Title of host publication | Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings |

Pages | 612-623 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2002 Dec 1 |

Event | 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 - Vancouver, BC, Canada Duration: 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) |
---|---|

Volume | 2518 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 |
---|---|

Country | Canada |

City | Vancouver, BC |

Period | 02/11/21 → 02/11/23 |

### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Partitioning trees of supply and demand'. Together they form a unique fingerprint.

## Cite this

*Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings*(pp. 612-623). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2518 LNCS). https://doi.org/10.1007/3-540-36136-7_53