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The Complexity of Constructing Evolutionary Trees Using Experiments

  • Gerth Stølting Brodal
  • Rolf Fagerberg
  • Christian N.S. Pedersen
  • Anna Östlin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)

Abstract

We present tight upper and lower bounds for the problem of constructing evolutionary trees in the experiment model. We describe an algorithm which constructs an evolutionary tree of n species in time O(nd logd n) using at most nd/2⌉(log2⌈d/2⌉-1 n+O(1)) experiments for d > 2, and at most n(log n+O(1)) experiments for d = 2, where d is the degree of the tree. This improves the previous best upper bound by a factor θ(log d). For d = 2 the previously best algorithm with running time O(n log n) had a bound of 4n log n on the number of experiments. By an explicit adversary argument, we show an Ω(nd logd n) lower bound, matching our upper bounds and improving the previous best lower bound by a factor θ(logd n). Central to our algorithm is the construction and maintenance of separator trees of small height, which may be of independent interest.

Keywords

Common Ancestor Internal Node Evolutionary Tree Insertion Point Construction Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Rolf Fagerberg
    • 1
  • Christian N.S. Pedersen
    • 1
  • Anna Östlin
    • 2
  1. 1.BRICS, Department of Computer ScienceUniversity of AarhusÅrhus CDenmark
  2. 2.Department of Computer ScienceLund UniversityLundSweden

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