Strong Refutation of Random Ordering CSPs
Data Structures and Algorithms
2026-07-10 v1 Computational Complexity
Abstract
In this work, we initiate the study of strongly refuting the satisfiability of random ordering constraint satisfaction problems. We show that there is a polynomial-time -refutation algorithm for random ordering CSP with predicate when the number of clauses is above the threshold , where is the coordinate degree of the predicate . We further give a smooth three-way tradeoff between the running time, the clause density, and the refutation strength using the Kikuchi method. Finally, we complement our algorithmic results with a computational lower bound based on the class of low coordinate degree algorithms, providing evidence that the established three-way tradeoff is near optimal.
Cite
@article{arxiv.2607.09410,
title = {Strong Refutation of Random Ordering CSPs},
author = {Xifan Yu},
journal= {arXiv preprint arXiv:2607.09410},
year = {2026}
}
Comments
52 pages