Leader election is one of the fundamental and well-studied problems in distributed computing. In this paper, we initiate the study of leader election using mobile agents. Suppose $n$ agents are positioned initially arbitrarily on the nodes of an arbitrary, anonymous, $n$-node, $m$-edge graph $G$. The agents relocate themselves autonomously on the nodes of $G$ and elect an agent as a leader such that the leader agent knows it is a leader and the other agents know they are not leaders. The objective is to minimize time and memory requirements. Following the literature, we consider the synchronous setting in which each agent performs its operations synchronously with others and hence the time complexity can be measured in rounds. The quest in this paper is to provide solutions without agents knowing any graph parameter, such as $n$, a priori. We first establish that, without agents knowing any graph parameter a priori, there exists a deterministic algorithm to elect an agent as a leader in $O(m)$ rounds with $O(n\log n)$ bits at each agent. Using this leader election result, we develop a deterministic algorithm for agents to construct a minimum spanning tree of $G$ in $O(m+n\log n)$ rounds using $O(n \log n)$ bits memory at each agent, without agents knowing any graph parameter a priori. Finally, using the same leader election result, we provide improved time/memory results for other fundamental distributed graph problems, namely, gathering, maximal independent set, and minimal dominating sets, removing the assumptions on agents knowing graph parameters a priori.

翻译：领导者选举是分布式计算中基础且被深入研究的问题之一。本文首次利用移动智能体研究领导者选举问题。假设 n 个智能体初始时被任意放置在一个任意的、匿名的、具有 n 个节点和 m 条边的图 G 的节点上。智能体自主地在 G 的节点间迁移，并选举出一个智能体作为领导者，使得领导者智能体知道自己是领导者，而其他智能体知道它们不是领导者。目标是优化时间和内存需求。遵循文献惯例，我们考虑同步环境，其中每个智能体与其他智能体同步执行操作，因此时间复杂度可以以轮次衡量。本文的核心目标是提供无需智能体预先知晓任何图参数（例如 n）的解决方案。我们首先证明，在智能体不预先知晓任何图参数的情况下，存在一种确定性算法，能在 O(m) 轮内选举出一个领导者，且每个智能体使用 O(n log n) 比特内存。利用这一领导者选举结果，我们开发了一种确定性算法，使智能体能在 O(m + n log n) 轮内构建 G 的最小生成树，每个智能体使用 O(n log n) 比特内存，且无需智能体预先知晓任何图参数。最后，利用相同的领导者选举结果，我们为其他基础分布式图问题（即聚集、最大独立集和最小支配集）提供了改进的时间/内存结果，消除了智能体需预先知晓图参数的假设。