Abstract
Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. One wish 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 \((l, u) \mbox{-}\)partition. We deal with three problems to find an \((l, u) \mbox{-}\)partition of a given graph. The minimum partition problem is to find an \((l, u) \mbox{-}\)partition with the minimum number of components. The maximum partition problem is defined similarly. The p-partition problem is to find an \((l, u) \mbox{-}\)partition with a fixed number p of components. All these problems are NP-complete or NP-hard 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(u 4 n) and the p-partition problem can be solved in time O(p 2 u 4 n) for any series-parallel graph of n vertices. The algorithms can be easily extended for partial k-trees, that is, graphs with bounded tree-width.
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© 2004 Springer-Verlag Berlin Heidelberg
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Ito, T., Zhou, X., Nishizeki, T. (2004). Partitioning a Weighted Graph to Connected Subgraphs of Almost Uniform Size. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_31
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DOI: https://doi.org/10.1007/978-3-540-30559-0_31
Publisher Name: Springer, Berlin, Heidelberg
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