Treasure Hunt with Volatile Pheromones

Authors Evangelos Bampas , Joffroy Beauquier, Janna Burman, William Guy--Obé

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Author Details

Evangelos Bampas
  • Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, 91400 Orsay, France
Joffroy Beauquier
  • Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, 91400 Orsay, France
Janna Burman
  • Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, 91400 Orsay, France
William Guy--Obé
  • Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, 91400 Orsay, France


We thank the DISC 2023 anonymous reviewers for their careful reading and comments.

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Evangelos Bampas, Joffroy Beauquier, Janna Burman, and William Guy--Obé. Treasure Hunt with Volatile Pheromones. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


In the treasure hunt problem, a team of mobile agents need to locate a single treasure that is hidden in their environment. We consider the problem in the discrete setting of an oriented infinite rectangular grid, where agents are modeled as synchronous identical deterministic time-limited finite-state automata, originating at a rate of one agent per round from the origin. Agents perish τ rounds after their creation, where τ ≥ 1 is a parameter of the model. An algorithm solves the treasure hunt problem if every grid position at distance τ or less from the origin is visited by at least one agent. Agents may communicate only by leaving indistinguishable traces (pheromone) on the nodes of the grid, which can be sensed by agents in adjacent nodes and thus modify their behavior. The novelty of our approach is that, in contrast to existing literature that uses permanent pheromone markers, we assume that pheromone traces evaporate over μ rounds from the moment they were placed on a node, where μ ≥ 1 is another parameter of the model. We look for uniform algorithms that solve the problem without knowledge of the parameter values, and we investigate the implications of this very weak communication mechanism to the treasure hunt problem. We show that, if pheromone persists for at least two rounds (μ ≥ 2), then there exists a treasure hunt algorithm for all values of agent lifetime. We also develop a more sophisticated algorithm that works for all values of μ, hence also for the fastest possible pheromone evaporation of μ = 1, but only if agent lifetime is at least 16.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Design and analysis of algorithms
  • Mobile Agents
  • Exploration
  • Search
  • Treasure Hunt
  • Pheromone
  • Evaporation


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