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77 Shades of Grey

Authors Quentin Bramas , Stéphane Devismes , Anaïs Durand , Pascal Lafourcade , Anissa Lamani

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LIPIcs.FUN.2026.10.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Mobile robots
  • grid exploration
  • perpetual exploration

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Abstract

Bruce Wayne contacted us to help him develop a new surveillance technology for dark environments such as caves, using a swarm of Unmanned Aerial Vehicles (UAVs), called Batdroids. A Batdroid has no chirality, limited visibility, and a perfect clock to synchronize with the others. A Batdroid can produce 77 shades of grey in dark mode and four colors in light mode.
In this paper, we propose two algorithms using three Batdroids to perpetually explore a finite 3D grid modeling a cave. The first algorithm operates in darkness, uses 77 shades of grey, and requires visibility range one. The second operates in light, uses four colors and visibility range two. We also prove that three is the optimal number of Batdroids required to solve Bruce Wayne’s challenge.

Cite As Get BibTex

Quentin Bramas, Stéphane Devismes, Anaïs Durand, Pascal Lafourcade, and Anissa Lamani. 77 Shades of Grey. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.10

Author Details

Quentin Bramas
  • University of Strasbourg, ICUBE, CNRS, France
Stéphane Devismes
  • Université de Picardie Jules Verne, MIS UR 4290, Amiens, France
Anaïs Durand
  • Université Clermont Auvergne, CNRS UMR 6158, LIMOS, Clermont-Ferrand, France
Pascal Lafourcade
  • Université Clermont Auvergne, CNRS UMR 6158, LIMOS, Clermont-Ferrand, France
Anissa Lamani
  • University of Strasbourg, ICUBE, CNRS, France

Funding

This study was partially supported by the French anr projects SkyData (ANR-22-CE25-0008) and PRIVA-SIQ (ANR-23-CE39-0008).

References

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