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Snake in Optimal Space and Time

Authors Philip Bille , Martín Farach-Colton , Inge Li Gørtz , Ivor van der Hoog

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LIPIcs.FUN.2024.3.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Data structure
  • Snake
  • Nokia
  • String Algorithms

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Abstract

We revisit the classic game of Snake and ask the basic data structural question: how many bits does it take to represent the state of a snake game so that it can be updated in constant time? Our main result is a data structure that uses optimal space (within constant factors). To achieve our results, we introduce several interesting data structural techniques, including a decomposition technique for the problem, a tabulation scheme for encoding small subproblems, and a dynamic memory allocation scheme.

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Philip Bille, Martín Farach-Colton, Inge Li Gørtz, and Ivor van der Hoog. Snake in Optimal Space and Time. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FUN.2024.3

Author Details

Philip Bille
  • Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark
Martín Farach-Colton
  • New York University, NY, USA
Inge Li Gørtz
  • Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark
Ivor van der Hoog
  • Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark

Funding

  • Bille, Philip: Supported by the Independent Research Fund Denmark (DFF-9131-00069B and 10.46540/3105-00302B).
  • Gørtz, Inge Li: Supported by the Independent Research Fund Denmark (DFF-9131-00069B and 10.46540/3105-00302B).
  • van der Hoog, Ivor: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 899987.

References

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