Strong Refutation of Random Ordering CSPs

Xifan Yu

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arXiv · 2607.09410

Strong Refutation of Random Ordering CSPs

Xifan Yu

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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 $\varepsilon$-refutation algorithm for random ordering CSP with predicate $P$ when the number of clauses is above the threshold $\tilde{\Omega}\left(n^{d/2}/\varepsilon^2\right)$, where $d$ is the coordinate degree of the predicate $P$. We further give a smooth three-way tradeoff between the running time, the clause density, and the refutation strength $\varepsilon$ 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.

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Xifan Yu. 2026-07-10. Strong Refutation of Random Ordering CSPs. https://arxiv.org/abs/2607.09410

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