中文

Strong Refutation of Random Ordering CSPs

数据结构与算法 2026-07-10 v1 计算复杂性

摘要

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 ε\varepsilon-refutation algorithm for random ordering CSP with predicate PP when the number of clauses is above the threshold Ω~(nd/2/ε2)\tilde{\Omega}\left(n^{d/2}/\varepsilon^2\right), where dd is the coordinate degree of the predicate PP. We further give a smooth three-way tradeoff between the running time, the clause density, and the refutation strength ε\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.

引用

@article{arxiv.2607.09410,
  title  = {Strong Refutation of Random Ordering CSPs},
  author = {Xifan Yu},
  journal= {arXiv preprint arXiv:2607.09410},
  year   = {2026}
}

备注

52 pages