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Replacing Cops with Zombies

Authors Fengyi Liu , Avery Miller

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LIPIcs.FUN.2026.30.pdf
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  • 12 pages

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Pursuit-Evasion Games
  • Grid Graphs
  • Cop Number
  • Zombie Number
  • Throttling Number

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Abstract

In the Cops and Robbers game, two players take turns to move their pieces in a given graph, and the goal of the Cop player is to have any of their pieces capture the piece controlled by the Robber player. In the Zombies and Survivors variant, the Zombie player is trying to catch the piece controlled by the Survivor player, but the pursuers are more restricted: the zombie pieces must always move, and must do so toward the survivor along a shortest path. Essentially, the zombies move in a 'brainless' way, which severely limits the design of algorithmic strategies. In a practical setting where the pursuers are robots or drones, the zombie strategies can be carried out by simpler/cheaper devices. This motivates the question: when can cops be replaced by zombies? In contrast to previous work that highlights graph classes where cops are significantly more useful when trying to catch the evader, we examine some situations where the simpler restricted movements imposed on zombies can be sufficient.

Cite As Get BibTex

Fengyi Liu and Avery Miller. Replacing Cops with Zombies. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 30:1-30:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.30

Author Details

Fengyi Liu
  • Department of Computer Science, University of Manitoba, Winnipeg, Canada
Avery Miller
  • Department of Computer Science, University of Manitoba, Winnipeg, Canada

Funding

  • Miller, Avery: Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Discovery Grant RGPIN-2024-06411.

References

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