Local-Global Shortest Path Algorithms on Random Graphs, Enhanced with GNNs
Keywords: shortest path, random graphs, graph neural networks, Erdős-Rényi
Abstract: Graph neural networks (GNNs) using local message passing were recently shown to inherit the intrinsic limitations of local algorithms in solving combinatorial graph optimization problems such as finding shortest distances (Loukas, 2020). To address this issue, Awasthi et al. (2022) proposed architectures based on Bourgain’s (1985) seminal work on Hilbert space embeddings. These architectures enhance local message passing in GNNs with a single global computation, yielding a local-global algorithm. This paper focuses on the average-case analysis of more general local-global algorithms for finding shortest distances (of which GNN+ is a particular case). Our primary contribution is a theoretical analysis of these algorithms on Erdős-Rényi (ER) random graphs. We prove that, on random graphs, these algorithms have lower distortion of shortest distances for most pairs of nodes w.h.p. while requiring a lower embedding dimension. Inspired by Awasthi et al. (2022), and to automate local computations and improve computational efficiency in practical scenarios, we further propose a modification to these algorithms that incorporates GNNs in the local computation phase. Empirical results on ER graphs and benchmark graph datasets demonstrate the enhanced performance of the GNN-augmented algorithm over the traditional approach.
Primary Area: learning on graphs and other geometries & topologies
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 13121
Loading