Reply to: Modern graph neural networks do worse than classical greedy algorithms in solving combinatorial optimization problems like maximum independent set

TL;DR

This paper defends the effectiveness of modern graph neural networks over classical greedy algorithms in solving combinatorial optimization problems, emphasizing their scalability and broader applicability beyond specific cases like maximum independent set.

Contribution

The authors provide a comprehensive rebuttal to criticism, showcasing improved numerical results, runtime scaling, and discussing the broader potential of graph neural networks in combinatorial optimization.

Findings

GNNs outperform greedy algorithms in scalability.

Random graph benchmarks are not universally representative.

GNNs show potential for solving complex combinatorial problems.

Abstract

We provide a comprehensive reply to the comment written by Chiara Angelini and Federico Ricci-Tersenghi [arXiv:2206.13211] and argue that the comment singles out one particular non-representative example problem, entirely focusing on the maximum independent set (MIS) on sparse graphs, for which greedy algorithms are expected to perform well. Conversely, we highlight the broader algorithmic development underlying our original work, and (within our original framework) provide additional numerical results showing sizable improvements over our original results, thereby refuting the comment's performance statements. We also provide results showing run-time scaling superior to the results provided by Angelini and Ricci-Tersenghi. Furthermore, we show that the proposed set of random d-regular graphs does not provide a universal set of benchmark instances, nor do greedy heuristics provide a universal algorithmic baseline. Finally, we argue that the internal (parallel) anatomy of graph neural networks is very different from the (sequential) nature of greedy algorithms and emphasize that graph neural networks have demonstrated their potential for superior scalability compared to existing heuristics such as parallel tempering. We conclude by discussing the conceptual novelty of our work and outline some potential extensions.