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Collective Tree Exploration via Potential Function Method

Authors Romain Cosson , Laurent Massoulié

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LIPIcs.ITCS.2024.35.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • collective exploration
  • online algorithms
  • evolving tree
  • competitive analysis

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Abstract

We study the problem of collective tree exploration (CTE) in which a team of k agents is tasked to traverse all the edges of an unknown tree as fast as possible, assuming complete communication between the agents [FGKP06]. In this paper, we present an algorithm performing collective tree exploration in 2n/k+𝒪(kD) rounds, where n is the number of nodes in the tree, and D is the tree depth. This leads to a competitive ratio of 𝒪(√k), the first polynomial improvement over the 𝒪(k) ratio of depth-first search. Our analysis holds for an asynchronous generalization of collective tree exploration. It relies on a game with robots at the leaves of a continuously growing tree extending the "tree-mining game" of [C23] and resembling the "evolving tree game" of [BCR22]. Another surprising consequence of our results is the existence of algorithms {𝒜_k}_{k ∈ ℕ} for layered tree traversal (LTT) with cost at most 2L/k+𝒪(kD), where L is the sum of all edge lengths. For the case of layered trees of width w and unit edge lengths, our guarantee is thus in 𝒪(√wD).

Cite As Get BibTex

Romain Cosson and Laurent Massoulié. Collective Tree Exploration via Potential Function Method. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 35:1-35:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITCS.2024.35

Author Details

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

Funding

This work was supported by PRAIRIE ANR-19-P3IA-0001.

Acknowledgements

The authors thank Laurent Viennot for stimulating discussions, the Argo team at Inria, as well as the anonymous reviewers for their suggestions.

References

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