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A Robust Model for Finding Optimal Evolutionary Trees
, 1993
"... Constructing evolutionary trees for species sets is a fundamental problem in computational biology. One of the standard models assumes the ability to compute distances between every pair of species and seeks to find an edgeweighted tree T in which the distance d T ij in the tree between the leaves ..."
Abstract

Cited by 78 (14 self)
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Constructing evolutionary trees for species sets is a fundamental problem in computational biology. One of the standard models assumes the ability to compute distances between every pair of species and seeks to find an edgeweighted tree T in which the distance d T ij in the tree between the leaves of T corresponding to the species i and j exactly equals the observed distance, d ij . When such a tree exists, this is expressed in the biological literature by saying that the distance function or matrix is additive, and trees can be constructed from additive distance matrices in O(n 2 ) time. Real distance data is hardly ever additive, and we therefore need ways of modeling the problem of finding the bestfit tree as an optimization problem. In this paper we present several natural and realistic ways of modeling the inaccuracies in the distance data. In one model we assume that we have upper and lower bounds for the distances between pairs of species and try to find an additive distanc...
Verification and Sensitivity Analysis Of Minimum Spanning Trees In Linear Time
 SIAM J. Comput
, 1992
"... . Koml'os has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree. The total computational work required by his method is much larger than linear, however. We describe a lineartime algorithm for verif ..."
Abstract

Cited by 54 (2 self)
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. Koml'os has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree. The total computational work required by his method is much larger than linear, however. We describe a lineartime algorithm for verifying a minimum spanning tree. Our algorithm combines the result of Koml'os with a preprocessing and table lookup method for small subproblems and with a previously known almostlineartime algorithm. Additionally, we present an optimal deterministic algorithm and a lineartime randomized algorithm for sensitivity analysis of minimum spanning trees. 1. Introduction. Suppose we wish to solve some problem for which we know in advance the size of the input data, using an algorithm from some welldefined class of algorithms. For example, consider sorting n numbers, when n is fixed in advance, using a binary comparison tree. Given a sufficient amount of preprocessing time and storage space, we ca...