## 抄録

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.

本文言語 | English |
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ページ（範囲） | 803-827 |

ページ数 | 25 |

ジャーナル | International Journal of Foundations of Computer Science |

巻 | 16 |

号 | 4 |

DOI | |

出版ステータス | Published - 2005 8 1 |

## ASJC Scopus subject areas

- コンピュータ サイエンス（その他）