# GAT-Steiner: Rectilinear Steiner Minimal Tree Prediction Using GNNs

arXiv: https://arxiv.org/abs/2407.01440 · HTML: https://mlsanity.com/paper/2407.01440/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Graph Neural Networks in TensorFlow and Keras with Spektral](https://mlsanity.com/paper/2006.12138/) (2020)
- [NN-Steiner: A Mixed Neural-algorithmic Approach for the Rectilinear Steiner Minimum Tree Problem](https://mlsanity.com/paper/2312.10589/) (2023)

## Abstract (arXiv)

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.