The Complexity of Constructing Evolutionary Trees Using Experiments

Gerth Stølting Brodal, Rolf Fagerberg, Christian Nørgaard Storm Pedersen, and Anna Östlin

Technical Report, BRICS-RS-01-1, BRICS, Department of Computer Science, Aarhus University, 27 pages, July 2001.

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(nlog n) had a bound of 4nlog n on the number of experiments. By an explicit adversary argument, we show an Ω(ndlogd 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. We present how to maintain separator trees with height log n+O(1) under the insertion of new nodes in amortized time O(log n). Part of our dynamic algorithm is an algorithm for computing a centroid tree in optimal time O(n).

Copyright notice

Copyright © 2001, BRICS, Department of Computer Science, Aarhus University. All rights reserved.

Online version

brics-rs-01-1.pdf (311 Kb)

BIBTEX entry

@techreport{brics-rs-01-1,
  author = "Gerth St{\o}lting Brodal and Rolf Fagerberg and Christian N{\o}rgaard Storm Pedersen and Anna \"Ostlin",
  institution = "BRICS, Department of Computer Science, Aarhus University",
  issn = "0909-0878",
  month = "July",
  number = "BRICS-RS-01-1",
  pages = "27",
  title = "The Complexity of Constructing Evolutionary Trees Using Experiments",
  year = "2001"
}