On the complexity of distance-based evolutionary tree reconstruction

  • Authors:
  • Valerie King;Li Zhang;Yunhong Zhou

  • Affiliations:
  • University of Victoria, Victoria, BC, Canada;Hewlett-Packard Labs, Palo Alto, CA;Hewlett-Packard Labs, Palo Alto, CA

  • Venue:
  • SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2003

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We give the first tight lower bounds on the complexity of reconstructing k-ary evolutionary trees from additive distance data. We also consider the problem under DNA-based distance estimation assumptions, where the accuracy of distance data depends on the length of the sequence and the distance. We give the first o(n2) algorithm to reconstruct trees in this context, and prove a trade-off between the length of the DNA sequences and the number of distance queries needed to reconstruct the tree. We introduce new computational models for understanding this problem, which simplify the development of algorithms. We prove lower bounds in these models which apply to the type of techniques currently in use.