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Finding Shortest Walks in Kuru Kuru Kururin

Authors Mickaël Laurent , Maher Mallem

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LIPIcs.FUN.2026.29.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Shortest paths
Keywords
  • Shortest path
  • Complexity

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Abstract

This paper serves as a celebration of the twenty-fifth anniversary of Kuru Kuru Kururin. Although this video game is presented as a collection of two-dimensional puzzles based on rotation, it naturally invites players to complete its levels as quickly as possible. This has led to a surprisingly rich and challenging playing field to finding foremost temporal walks. In this work, we tackle this problem both in theory and in practice. First, we introduce a model for the game and provide an in-depth complexity analysis. Most notably, we show how each gameplay mechanic independently brings a layer of NP-hardness and/or co-NP-hardness. We also provide a pseudo-polynomial time algorithm for the general problem and identify several cases which can be solved in polynomial time. Along the way, we discuss connections to the more established framework of temporal graphs, both in the point model and the interval model. Then, we propose simple and flexible algorithmic techniques to reduce state space and guide the search, offering trade-offs between precision and computation speed in practice. These techniques were implemented and tested using a full recreation of the game physics and the levels from the original game. We demonstrate the efficiency of our framework in several settings - with or without taking damage, with or without unintended game mechanics - and relate empirical struggles which we encountered in practice to our complexity analysis. Our implementation is open source and fully available online, offering a novel and amusing setting to benchmark shortest path algorithms.

Cite As Get BibTex

Mickaël Laurent and Maher Mallem. Finding Shortest Walks in Kuru Kuru Kururin. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.29

Author Details

Mickaël Laurent
  • Charles University, Prague, Czech Republic
Maher Mallem
  • Inria, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP, UMR 5668, 69342, Lyon cedex 07, France

Funding

  • Laurent, Mickaël: This work was supported by the Czech Ministry of Education, Youth and Sports under program ERC-CZ, grant agreement LL2325.

Acknowledgements

We would like to thank the organizers and reviewers of the FUN2026 conference.

Supplementary Materials

References

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