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

Authors:
Takehiro Ito;Kazuya Goto;Xiao Zhou;Takao Nishizeki
Affiliations:
Graduate School of Information Sciences, Tohoku University, Sendai, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Venue:
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Year:
2006

Citing 5
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Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees

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Easy problems for tree-decomposable graphs

Journal of Algorithms
Most uniform path partitioning and its use in image processing

Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Linear-time computability of combinatorial problems on series-parallel graphs

Journal of the ACM (JACM)
Operating systems

Operating systems

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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 li 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. Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width.