RamseyRL: A Framework for Intelligent Ramsey Number Counterexample Searching

TL;DR

RamseyRL introduces a reinforcement learning framework utilizing deep neural networks and graph vectorization to efficiently explore counterexamples for Ramsey numbers, improving search speed and effectiveness.

Contribution

The paper presents a novel RL-based framework with graph vectorization and neural heuristics for Ramsey counterexample search, optimizing runtime and exploration capabilities.

Findings

Enhanced search efficiency over prior methods

Effective neural network heuristics for graph evaluation

Open-source code and tools provided

Abstract

The Ramsey number is the minimum number of nodes, $n = R(s, t)$, such that all undirected simple graphs of order $n$, contain a clique of order $s$, or an independent set of order $t$. This paper explores the application of a best first search algorithm and reinforcement learning (RL) techniques to find counterexamples to specific Ramsey numbers. We incrementally improve over prior search methods such as random search by introducing a graph vectorization and deep neural network (DNN)-based heuristic, which gauge the likelihood of a graph being a counterexample. The paper also proposes algorithmic optimizations to confine a polynomial search runtime. This paper does not aim to present new counterexamples but rather introduces and evaluates a framework supporting Ramsey counterexample exploration using other heuristics. Code and methods are made available through a PyPI package and GitHub repository.