Time: 12:00 noon Tuesday, 16th August 2016.
Location: SIT 459
Speaker: Joachim Gudmundsson, University of Sydney
Title: Fast Algorithms for Diameter-Optimally Augmenting Trees
We consider the problem of augmenting an n-vertex graph embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present exact algorithms for the cases when (i) the input graph is a path, running in O(n log^3 n) time, and (ii) the input graph is a tree, running in O(n^2 log n) time. We also present an algorithm that computes a (1+\eps)-approximation in O(n + 1/eps^3) time, for paths in R^d, where d is a constant.