A polynomial-time approximation scheme for Euclidean Steiner forest

TL;DR

This paper presents a randomized polynomial-time approximation scheme for the Euclidean Steiner forest problem, achieving near-optimal solutions efficiently for fixed approximation parameters.

Contribution

It introduces a novel approximation scheme that guarantees a (1 + eps)-approximate solution in randomized polynomial time for Euclidean Steiner forest.

Findings

Achieves a (1 + eps)-approximation for Euclidean Steiner forest.

Runs in O(n polylog n) time, efficient for large instances.

Provides theoretical guarantees for approximation quality.

Abstract

We give a randomized O(n polylog n)-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed eps > 0 and given n terminals in the plane with connection requests between some pairs of terminals, our scheme finds a (1 + eps)-approximation to the minimum-length forest that connects every requested pair of terminals.