This paper addresses the basic question of how well can a tree approximate distances of a metric space or a graph. Given a graph, the problem of constructing a spanning tree in a ...
We introduce a new notion of embedding, called minimum-relaxation ordinal embedding, parallel to the standard notion of minimum-distortion (metric) embedding. In an ordinal embedd...
Noga Alon, Mihai Badoiu, Erik D. Demaine, Martin F...
We introduce a hierarchical partitioning scheme of the Euclidean plane, called circular partitions. Such a partition consists of a hierarchy of convex polygons, each having small ...
Abstract. We consider the problem of fitting an n × n distance matrix M by a tree metric T. We give a factor O(min{n1/p , (k log n)1/p }) approximation algorithm for finding the...
We propose the use of scatter search with path relinking for the inference of phylogenetic trees. Solutions are here represented as trees whose leaves span the set of species unde...