Percolation of Lipschitz Surface and Tight Bounds on the Spread of Information Among Mobile Agents

Authors Peter Gracar, Alexandre Stauffer

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Author Details

Peter Gracar
  • Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Köln, Germany
Alexandre Stauffer
  • Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdom

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Peter Gracar and Alexandre Stauffer. Percolation of Lipschitz Surface and Tight Bounds on the Spread of Information Among Mobile Agents. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We consider the problem of spread of information among mobile agents on the torus. The agents are initially distributed as a Poisson point process on the torus, and move as independent simple random walks. Two agents can share information whenever they are at the same vertex of the torus. We study the so-called flooding time: the amount of time it takes for information to be known by all agents. We establish a tight upper bound on the flooding time, and introduce a technique which we believe can be applicable to analyze other processes involving mobile agents.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probability and statistics
  • Lipschitz surface
  • spread of information
  • flooding time
  • moving agents


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