Constantinos Tsirogiannis

Efficient computation of popular phylogenetic tree measures

Given a phylogenetic tree

Exact and approximate computations of watersheds on triangulated terrains

\mathcal{T}

New Algorithms for Computing Phylogenetic Biodiversity

of n nodes, and a sample R of its tips (leaf nodes) a very common problem in ecological and evolutionary research is to evaluate a distance measure for the elements in R. Two of the most common measures of this kind are the Mean Pairwise Distance (

Computing the skewness of the phylogenetic mean pairwise distance in linear time.

\ensuremath{\mathrm{MPD}}

Flow on noisy terrains: an experimental evaluation

) and the Phylogenetic Diversity (

MIRU-VNTR genotype diversity and indications of homoplasy in M. avium strains isolated from humans and slaughter pigs in Latvia

\ensuremath{\mathrm{PD}}

Species introductions and the phylogenetic and functional structure of California's grasses

). In many applications, it is often necessary to compute the expectation and standard deviation of one of these measures over all subsets of tips of

Computing the Skewness of the Phylogenetic Mean Pairwise Distance in Linear Time

\mathcal{T}

Fast generation of multiple resolution instances of raster data sets

that have a certain size. Unfortunately, existing methods to calculate the expectation and deviation of these measures are inexact and inefficient. We present analytical expressions that lead to efficient algorithms for computing the expectation and the standard deviation of the MPD and the PD. More specifically, our main contributions are: 1 We present efficient algorithms for computing the expectation and the standard deviation of the MPD exactly, in Θ(n) time. 2 We provide a Θ(n) time algorithm for computing approximately the expectation of the PD and a O(n2) time algorithm for computing approximately the standard deviation of the PD. We also describe the major computational obstacles that hinder the exact calculation of these concepts. We also describe O(n) time algorithms for evaluating the MPD and PD given a single sample of tips. Having implemented all the presented algorithms, we assess their efficiency experimentally using as a point of reference a standard software package for processing phylogenetic trees.

Computing the Expected Value and Variance of Geometric Measures

The natural way of modeling water flow on a triangulated terrain is to make the fundamental assumption that water follows the direction of steepest descent (dsd). However, computing watersheds and other flow-related structures according to the dsd model in an exact manner is difficult: the dsd model implies that water does not necessarily follow terrain edges, which makes designing exact algorithms difficult and causes robustness problems when implementing them. As a result, existing software implementations for computing watersheds are inexact: they either assume a simplified flow model or they perform computations using inexact arithmetic, which leads to inexact and sometimes inconsistent results. We perform a detailed study of various issues concerning the exact or approximate computation of watersheds according to the dsd model. Our main contributions are the following. • We provide the first implementation that computes watersheds on triangulated terrains following strictly the dsd model and using exact arithmetic, and we experimentally investigate its computational cost. Our experiments show that the algorithm cannot handle large data sets effectively, due to the bit-sizes needed in the exact computations and the computation of an intermediate structure called the strip map. • Using our exact algorithm as a point of reference, we evaluate the quality of several existing heuristics for computing watersheds. We also investigate hybrid methods, which use heuristics in a first phase of the algorithm and exact computation in a second phase. The hybrid methods are almost as fast as the heuristics, but give significantly more accurate results. • We describe and theoretically analyze a new exact algorithm for computing watersheds, which avoids the computation of the strip map.