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

Takehiro Ito; Kazuya Goto; Xiao Zhou; Takao Nishizeki

doi:10.1093/ietisy/e90-d.2.449

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

Takehiro Ito, Kazuya Goto, Xiao Zhou, Takao Nishizeki

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-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 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
Pages (from-to)	449-456
Number of pages	8
Journal	IEICE Transactions on Information and Systems
Volume	E90-D
Issue number	2
DOIs	https://doi.org/10.1093/ietisy/e90-d.2.449
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

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10.1093/ietisy/e90-d.2.449

Cite this

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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.",

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AU - Ito, Takehiro

AU - Goto, Kazuya

AU - Zhou, Xiao

AU - Nishizeki, Takao

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N2 - 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.

AB - 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.

KW - Algorithm

KW - Choice partition

KW - Lower bound

KW - Maximum partition problem

KW - Minimum partition problem

KW - Multi-weighted graph

KW - Partial k-tree

KW - Series-parallel graph

KW - Uniform partition

KW - Upper bound

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

Abstract

Keywords

ASJC Scopus subject areas

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