Efficient Collaborative Tree Exploration with Breadth-First Depth-Next

Authors Romain Cosson , Laurent Massoulié , Laurent Viennot

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Romain Cosson
  • Inria, Paris, France
Laurent Massoulié
  • Inria, Paris, France
Laurent Viennot
  • Inria, Paris, France


The authors thank the anonymous reviewers for their useful remarks and the entire Argo team at Inria for enlightening discussions. RC thanks Pierre Fraigniaud for precious advice and Maxime Cartan for his implementation of a Python demo (available at https://github.com/Romcos/BFDN). A brief announcement appeared in PODC' 23 [Romain Cosson et al., 2023] and some extensions are available on arXiv [Cosson et al., 2023].

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Romain Cosson, Laurent Massoulié, and Laurent Viennot. Efficient Collaborative Tree Exploration with Breadth-First Depth-Next. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We study the problem of collaborative tree exploration introduced by Fraigniaud, Gasieniec, Kowalski, and Pelc [Pierre Fraigniaud et al., 2006] where a team of k agents is tasked to collectively go through all the edges of an unknown tree as fast as possible and return to the root. Denoting by n the total number of nodes and by D the tree depth, the 𝒪(n/log(k)+D) algorithm of [Pierre Fraigniaud et al., 2006] achieves a 𝒪(k/log(k)) competitive ratio with respect to the cost of offline exploration which is at least max{{2n/k,2D}}. Brass, Cabrera-Mora, Gasparri, and Xiao [Peter Brass et al., 2011] study an alternative performance criterion, the competitive overhead with respect to the cost of offline exploration, with their 2n/k+𝒪((D+k)^k) guarantee. In this paper, we introduce "Breadth-First Depth-Next" (BFDN), a novel and simple algorithm that performs collaborative tree exploration in 2n/k+𝒪(D²log(k)) rounds, thus outperforming [Peter Brass et al., 2011] for all values of (n,D,k) and being order-optimal for trees of depth D = o(√n). Our analysis relies on a two-player game reflecting a problem of online resource allocation that could be of independent interest. We extend the guarantees of BFDN to: scenarios with limited memory and communication, adversarial setups where robots can be blocked, and exploration of classes of non-tree graphs. Finally, we provide a recursive version of BFDN with a runtime of 𝒪_𝓁(n/k^{1/𝓁}+log(k) D^{1+1/𝓁}) for parameter 𝓁 ≥ 1, thereby improving performance for trees with large depth.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Distributed algorithms
  • Mathematics of computing → Graph algorithms
  • collaborative exploration
  • online algorithms
  • trees
  • adversarial game
  • competitive analysis
  • robot swarms


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