The Steiner k-eccentricity on trees

Statistical Alignment via k-Restricted Steiner Trees

When relating a set of sequences by a phylogeny, we are essentially constructing a Steiner tree connecting the sequences in the space of all finite sequences. Finding an optimal Steiner tree is in most formulations hard, so population genetics and phylogenetics have often used spanning trees as an approximation for computational expediency. In this assessment you will be asked to investigate an...

Approximating Buy-at-Bulk k-Steiner trees

In the buy-at-bulk k-Steiner tree (or rent-or-buy k-Steiner tree) problem we are given a graph G(V,E) with a set of terminals T ⊆ V including a particular vertex s called the root, and an integer k ≤ |T |. There are two cost functions on the edges of G, a buy cost b : E −→ R+ and a rent cost r : E −→ R+. The goal is to find a subtree H of G rooted at s with at least k terminals so that the cost ∑

Eccentricity approximating trees

Using the characteristic property of chordal graphs that they are the intersection graphs of subtrees of a tree, Erich Prisner showed that every chordal graph admits an eccentricity 2approximating spanning tree. That is, every chordal graph G has a spanning tree T such that eccT (v) − eccG(v) ≤ 2 for every vertex v, where eccG(v) (eccT (v)) is the eccentricity of a vertex v in G (in T , respect...

Steiner Trees and Steiner Forests

FORKS: Finding Orderings Robustly using K-means and Steiner trees

Recent advances in single cell RNA-seq technologies have provided researchers with unprecedented details of transcriptomic variation across individual cells.However, it has not been straightforward to infer differentiation trajectories from such data, due to the parameter-sensitivity of existing methods. Here, we present Finding Orderings Robustly using k-means and Steiner trees (FORKS), an alg...