Tree reconstruction from partial orders
- Arizona Univ., Tucson, AZ (United States)
- Sandia National Labs., Albuquerque, NM (United States)
The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species, which determine either a linear ordering of the three pairwise distances (called Total Order Model or TOM experiments) or only the pair(s) of minimum distance apart (called Partial Order Model or POM experiments). The POM and TOM experimental model is inspired by the model proposed by Kannan, Lawler, and Warnow for constructing trees from experiments which determine the rooted topology for any triple of species. We examine issues of construction of trees and consistency of TOM and POM experiments, where the trees may either be weighted or unweighted. Using these experiments to construct unweighted trees without nodes of degree two is motivated by a similar problem studied by Winkler, called the Discrete Metric Realization problem, which he showed to be strongly NP-hard. We have the following results: Determining consistency of a set of TOM or POM experiments is NP-Complete whether the tree is weighted or constrained to be unweighted and without degree two nodes. We can construct unweighted trees without degree two nodes from TOM experiments in optimal O(n[sup 3]) time and from POM experiments in O(n[sup 4]) time.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE; National Science Foundation (NSF); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 6518517
- Report Number(s):
- SAND-93-0689C; CONF-930884-1; CONF-930770-1; ON: DE93009841; CNN: CCR 91-08969; IRI 89-02813
- Resource Relation:
- Conference: Workshop on algorithms and data structures; International congress on automata and language processing, Montreal (Canada); Lund (Sweden), 11-13 Aug 1993; Jul 1993
- Country of Publication:
- United States
- Language:
- English
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