发表机构
National Technical University of Athens; Archimedes, Athena Research Center（雅典国立技术大学; 阿基米德，雅典娜研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究引入k次访问覆盖，证明其为强NP完全，还给出特殊情形的算法，且发现其密度阈值无界，是覆盖场景首个强NP难结果。
AI 中文摘要
在永久调度理论中，风车覆盖问题询问，给定n个频率f_i，是否存在无限调度，使得每f_i个连续条目里包含至多一个i∈[n]的出现。该问题模拟n个智能体轮流执行一项作业，再次工作前有一个恢复周期。从某种意义上说，风车覆盖是风车打包（又称风车调度）的对偶问题，风车打包同样要求每f_i个连续条目里至少包含一个i的出现。这两个问题的复杂度都是一个重大开放问题：已知两者都属于PSPACE，但仍未知是否为PSPACE难。最近，Kanellopoulos等人（SODA 2026）引入了仅要求i∈[n]出现k次的有限版本风车打包，并证明其是强NP完全的。本研究中，我们引入k次访问覆盖，即风车覆盖的类似有限版本，证明即使k=2时该问题仍是强NP完全的。作为推论，我们得到频率可变的风车覆盖的一般化问题是强NP难的。据我们所知，这是覆盖场景下首个强NP难结果。我们补充这些结果，针对具有两个不同频率的2次访问覆盖给出线性时间算法，当不同频率数量为常数时给出随机多项式时间算法。最后，我们研究k次访问覆盖的密度阈值，证明不存在非平凡的密度界，这与有限打包版本形成对比。
英文摘要
In perpetual scheduling theory, the Pinwheel Covering problem asks, given $n$ frequencies $f_i$, whether there exists an infinite schedule such that every $f_i$ consecutive entries contain at most one occurrence of $i\in [n]$. This models $n$ agents taking turns at executing a job, with a recovery period before working again. Pinwheel Covering is, in a sense, the dual of Pinwheel Packing (also known as Pinwheel Scheduling), which similarly asks for at least one occurrence of $i$ in every $f_i$ consecutive entries. The complexity of both problems is a major open question: both are known to be in PSPACE, but PSPACE-hardness remains unknown. Recently, a finite version of Pinwheel Packing requiring only $k$ occurrences of $i\in [n]$ was introduced by [Kanellopoulos et al., SODA 2026] and proven to be strongly NP-complete. In this work we introduce $k$-Visits Covering, the analogous finite version of Pinwheel Covering, establishing strong NP-completeness even for $k=2$. As a corollary, we obtain that a generalization of Pinwheel Covering with varying frequencies is strongly NP-hard. To the best of our knowledge, this is the first strong NP-hardness result in the covering setting. We complement these results with a linear-time algorithm for $2$-Visits Covering with two distinct frequencies and a randomized polynomial-time algorithm when the number of distinct frequencies is constant. Lastly, we study the density thresholds of $k$-Visits Covering and prove that no non-trivial density bounds exist, contrasting the finite packing version.
