Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search

Published: 28 Oct 2023, Last Modified: 09 Nov 2023MATH-AI 23 PosterEveryoneRevisionsBibTeX
Keywords: AlphaZero, tabu search, graph theory, curriculum
TL;DR: Solving extremal graph problems using AlphaZero and tabu search with curriculum
Abstract: This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdős, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum---jump-starting the search for larger graphs using good graphs found at smaller sizes---we improve the state-of-the-art lower bounds for several sizes. Lastly, we propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.
Submission Number: 21