Boosting Rectilinear Steiner Minimum Tree Algorithms with Augmented Bounding Volume Hierarchy

TL;DR

This work tackles the Rectilinear Steiner Minimum Tree problem by introducing a Bounding Volume Hierarchy (BVH)–based boosting framework that augments existing solvers and extends the Pareto front of speed-quality trade-offs. The core idea is a partition-and-merge strategy with an augmented BVH that maintains segment-level neighbor information, achieving an overall $O(N \log N)$ construction time. Empirically, augmented GeoSteiner attains substantially faster runtimes while maintaining high accuracy, REST gains substantial accuracy improvements, and FLUTE remains fast with tradeoffs in overhead. The approach demonstrates practical potential for large-scale RSMT computations by enabling robust, parallelizable solving across solver classes.

Abstract

The rectilinear Steiner minimum tree (RSMT) problem computes the shortest network connecting a given set of points using only horizontal and vertical lines, possibly adding extra points (Steiner points) to minimize the total length. RSMT solvers seek to balance speed and accuracy. In this work, we design a framework to boost existing RSMT solvers, extending the Pareto front. Combined with GeoSteiner, our algorithm reaches 5.16\% length error on nets with 1000 pins. The average time needed is 0.46 seconds. This provides an effective way to solve large-scale RSMT problems with small-scale solvers.

Figures (6)

• Figure 1: Partitioned Graph
• Figure 2: Segment
• Figure 3: Constructing BVH
• Figure 4: Steps
• Figure 5: Results