Seminar: Vera Traub (ETH Zürich)

The Weighted Tree Augmentation Problem (WTAP) is one of the most basic connectivity augmentation problems. It asks how to increase the edge-connectivity of a given graph from 1 to 2 in the cheapest possible way by adding some additional edges from a given set. In the first part of this talk we present the first algorithm that improves on the longstanding approximation ratio of 2 for WTAP.

In the second part of the talk we show how this algorithm can be used to obtain the first better-than-2 approximation algorithm for the Forest Augmentation Problem. In this problem we want to choose a minimum number of edges, among a given set of options, that we can add to a graph G to make it 2-edge connected. In contrast to the Tree Augmentation Problem, we do not require the given graph G to be connected.

This talk is based on joint works with Fabrizio Grandoni, Afrouz Jabal Ameli, and Rico Zenklusen.