Partitioning a multi-weighted graph to connected subgraphs of almost uniform size

Takehiro Ito, Kazuya Goto, Xiao Zhou, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)449-456
Number of pages8
JournalIEICE Transactions on Information and Systems
VolumeE90-D
Issue number2
DOIs
Publication statusPublished - 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

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