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Hardness, Tractability and Density Thresholds of Finite Pinwheel Scheduling Variants

Authors Sotiris Kanellopoulos , Giorgos Mitropoulos , Christos Pergaminelis , Thanos Tolias

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LIPIcs.ICALP.2026.122.pdf
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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Pinwheel Scheduling
  • Perpetual Scheduling
  • NP-Completeness
  • Parameterized Complexity

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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., 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 √2-1/2≈ 0.9142 lower bound for the density threshold of 2-Visits and prove that the density threshold of k-Visits approaches 5/6≈ 0.8333 for k → ∞.

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Sotiris Kanellopoulos, Giorgos Mitropoulos, Christos Pergaminelis, and Thanos Tolias. Hardness, Tractability and Density Thresholds of Finite Pinwheel Scheduling Variants. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 122:1-122:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.122

Author Details

Sotiris Kanellopoulos
  • National Technical University of Athens, Greece
  • Archimedes, Athena Research Center, Greece
Giorgos Mitropoulos
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
Christos Pergaminelis
  • National Technical University of Athens, Greece
  • Archimedes, Athena Research Center, Greece
Thanos Tolias
  • National Technical University of Athens, Greece
  • Archimedes, Athena Research Center, Greece

Funding

This work has been partially supported by project MIS 5154714 of the National Recovery and Resilience Plan Greece 2.0 funded by the European Union under the NextGenerationEU Program.

Acknowledgements

We are grateful to our professors Aris Pagourtzis and Dimitris Fotakis, as well as our colleague Panos Paskalis, for valuable discussions and insights regarding Pinwheel Scheduling, k-Visits and Exact Matching. We are also grateful to professor Euripides Markou, who suggested the k-Visits problem as a research topic.

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