Matrix completion problems are concerned with determining whether partially speciied matrices can be completed to fully speciied matrices satisfying certain prescribed properties. In this article we survey some results and provide references about these problems for the following matrix properties: positive semideenite matrices, Euclidean distance matrices, completely positive matrices, contrac...

 This paper present unequal-sized facilities layout solutions generated by a genetic search program named LADEGA (Layout Design using a Genetic Algorithm). The generalized quadratic assignment problem requiring pre-determined distance and material flow matrices as the input data and the continuous plane model employing a dynamic distance measure and a material flow matrix are discussed. Computa...

Received by the editors on November 13, 2011. Accepted for publication on July 8, 2013. Handling Editor: Bryan L. Shader. FMF and IMFM, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia, and IAM, University of Primorska, Slovenia ([email protected]). XLAB d.o.o., Pot za Brdom 100, 1125 Ljubljana, Slovenia, and FMF, University of Ljubljana, Slovenia ([email protected]...

Phylogenies are fundamental to comparative biology as they help to identify independent events on which statistical tests rely. Two groups of phylogenetic comparative methods (PCMs) can be distinguished: those that take phylogenies into account by introducing explicit models of evolution and those that only consider phylogenies as a statistical constraint and aim at partitioning trait values in...

We present an efficient algorithm to find a realization of a (full) n × n squared Euclidean distance matrix in the smallest possible dimension. Most existing algorithms work in a given dimension: most of these can be transformed to an algorithm to find the minimum dimension, but gain a logarithmic factor of n in their worstcase running time. Our algorithm performs cubically in n (and linearly w...

We present a fast converging method for distance-based phylogenetic inference, which is novel in two respects. First, it is the only method (to our knowledge) to guarantee accuracy when knowledge about the model tree, i.e bounds on the edge lengths, is not assumed. Second, our algorithm guarantees that, with high probability, no false assertions are made. The algorithm produces a maximal forest...

In this paper we prove that a vertex-centered automorphism of a tree gives a proper factor of the characteristic polynomial of its distance or adjacency matrix. We also show that the characteristic polynomial of the distance matrix of any graph always has a factor of degree equal to the number of vertex orbits of the graph. These results are applied to full k-ary trees and some other problems. ...

Finding the interacting pairs of proteins between two different protein families whose members are known to interact is an important problem in molecular biology. We developed and tested an algorithm that finds optimal matches between two families of proteins by comparing their distance matrices. A distance matrix provides a measure of the sequence similarity of proteins within a family. Since ...