Notes on the 33-point Erdős--Szekeres Problem
Published:Dec 30, 2025 08:10
•1 min read
•ArXiv
Analysis
This paper addresses the open problem of determining ES(7) in the Erdős--Szekeres problem, a classic problem in computational geometry. It's significant because it tackles a specific, unsolved case of a well-known conjecture. The use of SAT encoding and constraint satisfaction techniques is a common approach for tackling combinatorial problems, and the paper's contribution lies in its specific encoding and the insights gained from its application to this particular problem. The reported runtime variability and heavy-tailed behavior highlight the computational challenges and potential areas for improvement in the encoding.
Key Takeaways
- •Applies SAT encoding to the 33-point Erdős--Szekeres problem.
- •Uses triple-orientation variables and a 4-set convexity criterion.
- •Reports UNSAT certificates for anchored subfamilies.
- •Highlights runtime variability and heavy-tailed behavior, indicating computational challenges.
Reference
“The framework yields UNSAT certificates for a collection of anchored subfamilies. We also report pronounced runtime variability across configurations, including heavy-tailed behavior that currently dominates the computational effort and motivates further encoding refinements.”