Polylogarithmic Collective Tree Exploration

Romain Cosson; Laurent Massoulié

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arXiv · 2609.26789

Polylogarithmic Collective Tree Exploration

Romain Cosson·Laurent Massoulié

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Abstract

We study asynchronous collective tree exploration, where $k$ agents with unrestricted communication start at the root of an unknown tree and discover edges online. At each step, an adversary chooses which agent moves. We give a deterministic algorithm that explores any tree with $n$ nodes and depth $D$ in at most \[ 2n+O\left(k\log^2(k)D\right) \] moves, matching known lower bounds up to a constant factor. As a direct consequence, we obtain a near-optimal competitive ratio of $O(\log^2 k)$ for synchronous collective tree exploration, where all agents move at each round. The proof relies on a multiscale power regularizer that may be of independent interest.

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BibTeX RIS

Romain Cosson, Laurent Massoulié. 2026-09-22. Polylogarithmic Collective Tree Exploration. https://arxiv.org/abs/2609.26789

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