Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are integers such that 0∈ ∈l∈ ∈u. 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 given number p of components. All these problems are NP-hard even for series-parallel graphs, but are solvable for paths in linear time and for trees in polynomial time. In this paper, we give polynomial-time algorithms to solve the three problems for trees, which are much simpler and faster than the known algorithms. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
Ito, T., Uno, T., Zhou, X., & Nishizeki, T. (2008). Partitioning a weighted tree to subtrees of almost uniform size. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5369 LNCS, pp. 196–207). https://doi.org/10.1007/978-3-540-92182-0_20
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