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Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level

Authors Bernd Gärtner , Sebastian Haslebacher , Hung P. Hoang

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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • ARRIVAL
  • Rotor-Routing
  • Simple Stochastic Games

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Abstract

ARRIVAL is the problem of deciding whether a token, following a deterministic process, eventually reaches a designated destination. While the problem is known to lie in NP ∩ CoNP, whether it can be solved in polynomial time remains a major open question. In this article, we study ladders, a class of graphs that constitutes a family of worst-case instances for many existing algorithms, including the currently best known algorithm by Gärtner, Haslebacher, and Hoang (ICALP 2021). We show that ARRIVAL restricted to ladders can be solved in polynomial time, and we further extend this result to stopping binary simple stochastic games (SSG).

Cite As Get BibTex

Bernd Gärtner, Sebastian Haslebacher, and Hung P. Hoang. Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.19

Author Details

Bernd Gärtner
  • Department of Computer Science, ETH Zürich, Switzerland
Sebastian Haslebacher
  • Department of Computer Science, ETH Zürich, Switzerland
Hung P. Hoang
  • Algorithms and Complexity Group, Faculty of Informatics, TU Wien, Austria

Funding

  • Hoang, Hung P.: Austrian Science Foundation (FWF, project ESP1136425).

Acknowledgements

We are grateful to three anonymous referees for their helpful comments.

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