# Solving graph compression via optimal transport

arXiv: https://arxiv.org/abs/1905.12158 · HTML: https://mlsanity.com/paper/1905.12158/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

## Built on by (most cited first, 8 of 8)

- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [Hierarchical Multi-Marginal Optimal Transport for Network Alignment](https://mlsanity.com/paper/2310.04470/) (2023)
- [Quantized Gromov-Wasserstein](https://mlsanity.com/paper/2104.02013/) (2021)
- [Partition and Code: learning how to compress graphs](https://mlsanity.com/paper/2107.01952/) (2021)
- [A Primer on Temporal Graph Learning](https://mlsanity.com/paper/2401.03988/) (2024)
- [Promise and Limitations of Supervised Optimal Transport-Based Graph Summarization via Information Theoretic Measures](https://mlsanity.com/paper/2305.07138/) (2023)
- [Latent Random Steps as Relaxations of Max-Cut, Min-Cut, and More](https://mlsanity.com/paper/2308.06448/) (2023)

## Abstract (arXiv)

We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for either directed or undirected graphs, and its dual characterization is cast in terms of distributions over the nodes. The compression pertains to the support of node distributions and makes the problem challenging to solve directly. To this end, we introduce Boolean relaxations and specify conditions under which these relaxations are exact. The relaxations admit algorithms with provably fast convergence. Moreover, we provide an exact O(d log d) algorithm for the subproblem of projecting a d-dimensional vector to transformed simplex constraints. Our method outperforms state-of-the-art compression methods on graph classification.