TY - JOUR

T1 - Partitioning a graph of bounded tree-width to connected subgraphs of almost uniform size

AU - Ito, Takehiro

AU - Zhou, Xiao

AU - Nishizeki, Takao

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2006/3

Y1 - 2006/3

N2 - Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. 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 an "almost uniform" 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 fixed number p of components. All these problems are NP-complete or NP-hard, respectively, even for series-parallel graphs. In this paper we show that both the minimum partition problem and the maximum partition problem can be solved in time O(u4n) and the p-partition problem can be solved in time O(p2u4n) for any series-parallel graph with n vertices. The algorithms can be extended for partial k-trees, that is, graphs with bounded tree-width.

AB - Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. 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 an "almost uniform" 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 fixed number p of components. All these problems are NP-complete or NP-hard, respectively, even for series-parallel graphs. In this paper we show that both the minimum partition problem and the maximum partition problem can be solved in time O(u4n) and the p-partition problem can be solved in time O(p2u4n) for any series-parallel graph with n vertices. The algorithms can be extended for partial k-trees, that is, graphs with bounded tree-width.

KW - (l,u)-partition

KW - Algorithm

KW - Lower bound

KW - Maximum partition problem

KW - Minimum partition problem

KW - Partial k-tree

KW - Series-parallel graph

KW - Upper bound

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U2 - 10.1016/j.jda.2005.01.005

DO - 10.1016/j.jda.2005.01.005

M3 - Article

AN - SCOPUS:33644593096

VL - 4

SP - 142

EP - 154

JO - Journal of Discrete Algorithms

JF - Journal of Discrete Algorithms

SN - 1570-8667

IS - 1

ER -