Asynchronous Collective Tree Exploration: a Distributed Algorithm, and a new Lower Bound

2025-07-21

AI Summary

This paper studies the distributed collective exploration of an unknown tree by $k$ asynchronous mobile agents starting from the root, where agents communicate indirectly via node-attached whiteboards and aim to minimize total edge traversals. Under a highly adversarial setting—where agent speeds are fully controlled by an adversary, no global information is available, and agents possess only local perception—we present the first deterministic algorithm that is both distributed and asynchronous. Our theoretical contributions are threefold: (1) We design two algorithms with rigorous guarantees: one completes exploration in $2n + O(k^2 2^k D)$ steps; the other achieves a competitive ratio of $Oig((k/log k)(n + kD)ig)$. (2) We establish the first lower bound $Omega(log^2 k)$ on the competitive ratio for asynchronous collective exploration, revealing its inherent difficulty. (3) By integrating cooperative traversal, conflict avoidance, and combinatorial competitive analysis, our approach attains asymptotic optimality in expectation.

Technology Category

• Multiagent Systems: Adversarial Agents
• Search and Optimization: Adversarial Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We study the problem of collective tree exploration in which a team of $k$ mobile agents must collectively visit all nodes of an unknown tree in as few moves as possible. The agents all start from the root and discover adjacent edges as they progress in the tree. Communication is distributed in the sense that agents share information by reading and writing on whiteboards located at all nodes. Movements are asynchronous, in the sense that the speeds of all agents are controlled by an adversary at all times. All previous competitive guarantees for collective tree exploration are either distributed but synchronous, or asynchronous but centralized. In contrast, we present a distributed asynchronous algorithm that explores any tree of $n$ nodes and depth $D$ in at most $2n+O(k^2 2^kD)$ moves, i.e., with a regret that is linear in $D$, and a variant algorithm with a guarantee in $O(k/log k)(n+kD)$, i.e., with a competitive ratio in $O(k/log k)$. We note that our regret guarantee is asymptotically optimal (i.e., $1$-competitive) from the perspective of average-case complexity. We then present a new general lower bound on the competitive ratio of asynchronous collective tree exploration, in $Ω(log^2 k)$. This lower bound applies to both the distributed and centralized settings, and improves upon the previous lower bound in $Ω(log k)$.

Problem

• Distributed asynchronous collective tree exploration algorithm
• Optimal regret linear in tree depth D
• New lower bound on competitive ratio

Innovation

• Distributed asynchronous algorithm for tree exploration
• Linear regret guarantee in tree depth
• Optimal competitive ratio in average-case