## Abstract

Assume that each vertex of a graph G is assigned a constant number q of nonnegative integer weights, and that q pairs of nonnegative integers l _{i} and u_{i}, 1 ≤ i ≤ q, are given. One wishes to partition G into connected components by deleting edges from G so that the total i-th weights of all vertices in each component is at least l_{i} and at most u_{i} for each index i, 1 ≤ i ≤ q. The problem of finding such a "uniform" partition is NP-hard for series-parallel graphs, and is strongly NP-hard for general graphs even for q = 1. In this paper we show that the problem and many variants can be solved in pseudo-polynomial time for series-parallel graphs and partial k-trees, that is, graphs with bounded tree-width.

Original language | English |
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Pages (from-to) | 449-456 |

Number of pages | 8 |

Journal | IEICE Transactions on Information and Systems |

Volume | E90-D |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 Feb |

## Keywords

- Algorithm
- Choice partition
- Lower bound
- Maximum partition problem
- Minimum partition problem
- Multi-weighted graph
- Partial k-tree
- Series-parallel graph
- Uniform partition
- Upper bound

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence