Further Improvements on Approximating the Uniform Cost-Distance Steiner Tree Problem

TL;DR

This paper advances approximation algorithms for the Uniform Cost-Distance Steiner Tree Problem, reducing the approximation factor from 2.39 to 2.15, which improves solutions for signal transmission network design.

Contribution

It introduces a refined approach that further reduces the approximation factor for the problem, building on recent improvements.

Findings

Approximation factor improved to 2.15

Enhanced algorithmic approach for the problem

Better solutions for signal transmission network design

Abstract

In this paper, we consider the Uniform Cost-Distance Steiner Tree Problem in metric spaces, a generalization of the well-known Steiner tree problem. Cost-distance Steiner trees minimize the sum of the total length and the weighted path lengths from a dedicated root to the other terminals, which have a weight to penalize the path length. They are applied when the tree is intended for signal transmission, e.g. in chip design or telecommunication networks, and the signal speed through the tree has to be considered besides the total length. Constant factor approximation algorithms for the uniform cost-distance Steiner tree problem have been known since the first mentioning of the problem by Meyerson, Munagala, and Plotkin. Recently, the approximation factor was improved from 2.87 to 2.39 by Khazraei and Held. We refine their approach further and reduce the approximation factor down to 2.15.