## Abstract

Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l andu are given integers such that 0 ≤ l≤ u. One wishes to partition G into connected components by deleting edges from G so that the total weight of each component is at least l and at most u. Such a partition is called an (l,u)-partition. We deal with three problems to find an (l,u)-partition of a given graph: the minimum partition problem is to find an (l,u)-partition with the minimum number of components; the maximum partition problem is defined analogously; and the p-partition problem is to find an (l,u)-partition with a given number p of components. All these problems are NP-hard even for series-parallel graphs, but are solvable in linear time for paths. In this paper, we present the first polynomial-time algorithm to solve the three problems for arbitrary trees.

Original language | English |
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Pages (from-to) | 823-841 |

Number of pages | 19 |

Journal | Algorithmica |

Volume | 62 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2012 Apr 1 |

## Keywords

- Algorithm
- Dynamic programming
- Fast Fourier transform
- Graph partition
- Polynomial-time
- Subtree
- Tree

## ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics