2026-08-06T08:11:18Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19140 2024-03-06T11:03:31Z ddc:004 open_access

Efficient Collaborative Tree Exploration with Breadth-First Depth-Next Cosson, Romain Massoulié, Laurent Viennot, Laurent collaborative exploration online algorithms trees adversarial game competitive analysis robot swarms 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Romain Cosson and Laurent Massoulié and Laurent Viennot 2023 Is Part Of LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DISC.2023.14 urn:nbn:de:0030-drops-191409 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.14 eng https://creativecommons.org/licenses/by/4.0/legalcode