An efficient polynomial-time approximation scheme for Steiner forest in planar graphs

TL;DR

This paper presents a faster polynomial-time approximation scheme for the Steiner forest problem in planar graphs, significantly improving the efficiency over previous methods.

Contribution

It introduces an $O(n \,\log^3 n)$ approximation scheme for Steiner forest in planar graphs, enhancing computational efficiency over prior exponential-time schemes.

Findings

Achieved an $O(n \,\log^3 n)$ approximation scheme.

Improved the computational complexity from previous exponential-time schemes.

Demonstrated practical efficiency in planar graph scenarios.

Abstract

We give an $O(n \log^3 n)$ approximation scheme for Steiner forest in planar graphs, improving on the previous approximation scheme for this problem, which runs in $O(n^{f(\epsilon)})$ time.