Tree edge decomposition with an application to minimum ultrametric tree approximation

Chia-Mao Huang (), Bang Ye Wu () and Chang-Biau Yang ()
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Chia-Mao Huang: National Sun Yat-sen University
Bang Ye Wu: Shu-Te University, YenChau
Chang-Biau Yang: National Sun Yat-sen University

Journal of Combinatorial Optimization, 2006, vol. 12, issue 3, No 3, 217-230

Abstract: Abstract A k-decomposition of a tree is a process in which the tree is recursively partitioned into k edge-disjoint subtrees until each subtree contains only one edge. We investigated the problem how many levels it is sufficient to decompose the edges of a tree. In this paper, we show that any n-edge tree can be 2-decomposed (and 3-decomposed) within at most ⌈1.44 log n⌉ (and ⌈log n⌉ respectively) levels. Extreme trees are given to show that the bounds are asymptotically tight. Based on the result, we designed an improved approximation algorithm for the minimum ultrametric tree.

Keywords: Tree; Decomposition; Ultrametric; Approximation algorithm (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10878-006-9626-z

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