Polylogarithmic Collective Tree Exploration

2026-09-22

AI Summary

研究了k个代理异步探索未知树的问题，提出了一种确定性算法，在最多2n+O(k log^2(k)D)步内完成探索，达到了接近最优的竞争比。

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.

Problem

• asynchronous
• collective tree exploration
• agents
• unrestricted communication
• unknown tree

Innovation

• deterministic algorithm
• asynchronous collective tree exploration
• multiscale power regularizer
• near-optimal competitive ratio