Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search
Abstract
This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erd\H{o}s, 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. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.
Keywords
Cite
@article{arxiv.2311.03583,
title = {Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search},
author = {Abbas Mehrabian and Ankit Anand and Hyunjik Kim and Nicolas Sonnerat and Matej Balog and Gheorghe Comanici and Tudor Berariu and Andrew Lee and Anian Ruoss and Anna Bulanova and Daniel Toyama and Sam Blackwell and Bernardino Romera Paredes and Petar Veličković and Laurent Orseau and Joonkyung Lee and Anurag Murty Naredla and Doina Precup and Adam Zsolt Wagner},
journal= {arXiv preprint arXiv:2311.03583},
year = {2024}
}
Comments
To appear in the proceedings of IJCAI 2024. First three authors contributed equally, last two authors made equal senior contribution