TY - GEN

T1 - Partitioning a weighted tree to subtrees of almost uniform size

AU - Ito, Takehiro

AU - Uno, Takeaki

AU - Zhou, Xiao

AU - Nishizeki, Takao

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-540-92182-0_20

DO - 10.1007/978-3-540-92182-0_20

M3 - Conference contribution

AN - SCOPUS:58549083812

SN - 3540921818

SN - 9783540921813

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 196

EP - 207

BT - Algorithms and Computation - 19th International Symposium, ISAAC 2008, Proceedings

T2 - 19th International Symposium on Algorithms and Computation, ISAAC 2008

Y2 - 15 December 2008 through 17 December 2008

ER -