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 ui, 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 li and at most ui 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