Low-Stretch Spanning Trees

Diploma Thesis Minimum Stretch Spanning Trees

Spanning trees have always been of great interest in various areas of computer science. The same is true for the idea of shortest paths in a graph. Minimum Stretch Spanning Trees can be described as a combination of these two concepts. On the one hand they are spanning trees, on the other hand they have a minimum stretch which means that the distances between the nodes in the spanning tree rema...

Low - Stretch Spanning Trees

On Minimum Average Stretch Spanning Trees in Polygonal 2-Trees

A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the problem of computing a minimum average stretch spanning tree in polygonal 2-trees, a super class of 2-connected outerplanar graphs. For a polygonal 2-tree on n ve...

Independent Spanning Trees with Small Stretch

A pair of spanning trees rooted at a vertex r are independent if for every vertex v the pair of unique tree paths from v to the root r are disjoint. This paper presents the rst analysis of the path lengths involved in independent spanning trees in 2-edge-connected and 2-vertex-connected graphs. We present upper and lower bounds on the stretch factors of pairs of independent spanning trees, wher...

Lecture 1: Low-stretch trees

The main theme of the workshop is fast algorithms, particularly those that relate to fast solvers for linear systems involving the Laplacian of a graph. In my lectures, I will discuss three key technical ingredients that underlie those solvers. In this first lecture, I will discuss “low-stretch trees”. Given a graph, the goal is to find a spanning subtree such that, on average, distances in the...