A Note on Small Percolating Sets on Hypercubes via Generative AI
Gergely B\'erczi, Adam Zsolt Wagner
TL;DR
This paper uses a generative AI technique called PatternBoost to analyze bootstrap percolation on hypercubes, achieving a slight improvement in the upper bound for percolating subset sizes.
Contribution
Introducing PatternBoost, a generative AI method, to improve bounds in bootstrap percolation on hypercubes.
Findings
Slightly improved upper bound for percolating subsets
Demonstrated effectiveness of AI pattern recognition in combinatorial problems
Potential for AI to advance theoretical bounds in percolation theory
Abstract
We apply a generative AI pattern-recognition technique called PatternBoost to study bootstrap percolation on hypercubes. With this, we slightly improve the best existing upper bound for the size of percolating subsets of the hypercube.
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Taxonomy
TopicsAdvanced Graph Theory Research · Cellular Automata and Applications · Optimization and Search Problems