Finding Almost Tight Witness Trees

TL;DR

This paper improves approximation algorithms for the Witness Tree problem, which is key to better solutions for Steiner Tree and Node-Tree Augmentation problems, by identifying nearly optimal witness trees.

Contribution

It introduces a refined approach to selecting witness trees, leading to enhanced approximation guarantees for specific network design problems.

Findings

Improved approximation ratios for Node-Tree Augmentation.

Enhanced Steiner Tree solutions in special graph classes.

Demonstrated the effectiveness of better witness tree choices.

Abstract

This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in the analysis of the best approximation algorithms for two fundamental network design problems: Steiner Tree and Node-Tree Augmentation. We will show how a wiser choice of witness trees leads to an improved approximation for Node-Tree Augmentation, and for Steiner Tree in special classes of graphs.