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Tree edge decomposition with an application to minimum ultrametric tree approximation

Author

Listed:
  • Chia-Mao Huang

    (National Sun Yat-sen University)

  • Bang Ye Wu

    (Shu-Te University, YenChau)

  • Chang-Biau Yang

    (National Sun Yat-sen University)

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.

Suggested Citation

  • Chia-Mao Huang & Bang Ye Wu & Chang-Biau Yang, 2006. "Tree edge decomposition with an application to minimum ultrametric tree approximation," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 217-230, November.
    • Handle: RePEc:spr:jcomop:v:12:y:2006:i:3:d:10.1007_s10878-006-9626-z
    DOI: 10.1007/s10878-006-9626-z
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    References listed on IDEAS

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    1. Bang Ye Wu & Kun-Mao Chao & Chuan Yi Tang, 1999. "Approximation and Exact Algorithms for Constructing Minimum Ultrametric Trees from Distance Matrices," Journal of Combinatorial Optimization, Springer, vol. 3(2), pages 199-211, July.
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