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Abstract:The k-Visits problem is a recently introduced finite version of Pinwheel Scheduling [Kanellopoulos et al., SODA 2026]. Given the deadlines of n tasks, the problem asks whether there exists a schedule of length kn executing each task exactly k times, with no deadline expiring between consecutive visits (executions) of each task.
In this work we prove that 2-Visits is strongly NP-complete even when the maximum multiplicity of the input is equal to 2, settling an open question from [Kanellopoulos et al., SODA 2026] and contrasting the tractability of 2-Visits for simple sets. On the other hand, we prove that 2-Visits is in RP when the number of distinct deadlines is constant, thus making progress on another open question regarding the parameterization of 2-Visits by the number of numbers. We then generalize all existing positive results for 2-Visits to a version of the problem where some tasks must be visited once and some other tasks twice, while providing evidence that some of these results are unlikely to transfer to 3-Visits.
Lastly, we establish bounds for the density thresholds of k-Visits, analogous to the $(5/6)$-threshold of Pinwheel Scheduling [Kawamura, STOC 2024]; in particular, we show a $\sqrt{2}-1/2\approx 0.9142$ lower bound for the density threshold of 2-Visits and prove that the density threshold of k-Visits approaches $5/6\approx 0.8333$ for $k \to \infty$.

Submission history

From: Sotiris Kanellopoulos [view email]
[v1] Fri, 17 Apr 2026 13:00:32 UTC (934 KB)
[v2] Mon, 20 Apr 2026 20:42:41 UTC (935 KB)
[v3] Mon, 27 Apr 2026 15:46:38 UTC (935 KB)
[v4] Sat, 4 Jul 2026 10:21:53 UTC (935 KB)