多对数级集体树探索

中文摘要 AI 辅助

我们研究异步集体树探索问题，其中$k$个具有无限制通信的智能体从一棵未知树的根节点出发，在线发现边。每一步中，对手选择哪个智能体移动。我们给出一个确定性算法，该算法以最多\\[ 2n+O\left(k\log^2(k)D\right) \\] 步移动探索任何具有$n$个节点和深度$D$的树，与已知下界匹配至常数因子。作为直接结果，我们为同步集体树探索（即每轮所有智能体都移动）获得了$O(\log^2 k)$的近似最优竞争比。证明依赖于一个可能具有独立意义的多尺度幂正则化器。

英文摘要

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.

发表机构

• New York University（纽约大学）
• Inria, Paris（法国国家信息与自动化研究所，巴黎）

机构由 AI 辅助整理，请以论文原文为准。