## 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 wishes 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. The first is a linear-time algorithm for the partition problem. The second is a pseudopolynomial-time algorithm for the maximum partition problem. The third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.

Original language | English |
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Pages (from-to) | 803-827 |

Number of pages | 25 |

Journal | International Journal of Foundations of Computer Science |

Volume | 16 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2005 Aug |

## Keywords

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