GAT-Steiner: Rectilinear Steiner Minimal Tree Prediction Using GNNs

TL;DR

GAT-Steiner employs graph neural networks to accurately predict Steiner points in the NP-hard RSMT problem, significantly reducing computation time while maintaining near-optimal wire lengths in VLSI design.

Contribution

This paper introduces GAT-Steiner, a novel GNN-based model that predicts Steiner points with high accuracy, enabling faster and more efficient RSMT solutions in VLSI placement.

Findings

Predicts 99.846% of nets in ISPD19 benchmark with minimal wire length increase.

Achieves 99.942% accuracy on random benchmarks with slight wire length overhead.

Parallelizable on GPUs, offering practical speedups for VLSI routing.

Abstract

The Rectilinear Steiner Minimum Tree (RSMT) problem is a fundamental problem in VLSI placement and routing and is known to be NP-hard. Traditional RSMT algorithms spend a significant amount of time on finding Steiner points to reduce the total wire length or use heuristics to approximate producing sub-optimal results. We show that Graph Neural Networks (GNNs) can be used to predict optimal Steiner points in RSMTs with high accuracy and can be parallelized on GPUs. In this paper, we propose GAT-Steiner, a graph attention network model that correctly predicts 99.846% of the nets in the ISPD19 benchmark with an average increase in wire length of only 0.480% on suboptimal wire length nets. On randomly generated benchmarks, GAT-Steiner correctly predicts 99.942% with an average increase in wire length of only 0.420% on suboptimal wire length nets.