Dijkstra meets Steiner: a fast exact goal-oriented Steiner tree algorithm

TL;DR

This paper introduces a new exact algorithm for the Steiner tree problem that significantly improves practical performance and can solve larger instances than previous methods, especially in VLSI design and high-dimensional rectilinear cases.

Contribution

The paper presents a novel goal-oriented Steiner tree algorithm that enhances classical dynamic programming with pruning and future costs, achieving better practical results.

Findings

Outperforms previous algorithms on large VLSI instances

Solves larger high-dimensional rectilinear Steiner trees

Matches best known worst-case runtime with improved practical efficiency

Abstract

We present a new exact algorithm for the Steiner tree problem in edge-weighted graphs. Our algorithm improves the classical dynamic programming approach by Dreyfus and Wagner. We achieve a significantly better practical performance via pruning and future costs, a generalization of a well-known concept to speed up shortest path computations. Our algorithm matches the best known worst-case run time and has a fast, often superior, practical performance: on some large instances originating from VLSI design, previous best run times are improved upon by orders of magnitudes. We are also able to solve larger instances of the $d$-dimensional rectilinear Steiner tree problem for $d \in \{3, 4, 5\}$, whose Hanan grids contain up to several millions of edges.