In the graph exploration problem, a team of mobile computational entities, called agents, arbitrarily positioned at some nodes of a graph, must cooperate so that each node is eventually visited by at least one agent. In the literature, the main focus has been on graphs that are static ; that is, the topology is either invariant in time or subject to localized changes. The few studies on exploration of dynamic graphs have been almost all limited to the centralized case (i.e., assuming complete a priori knowledge of the changes and the times of their occurrence). We investigate the decentralized exploration of dynamic graphs (i.e., when the agents are unaware of the location and timing of the changes) focusing, in this paper, on dynamic systems whose underlying graph is a ring . We first consider the fully-synchronous systems traditionally assumed in the literature; i.e., all agents are active at each time step. We then introduce the notion of semi-synchronous systems, where only a subset of agents might be active at each time step (the choice of the subset is made by an adversary); this model is common in the context of mobile agents in continuous spaces but has never been studied before for agents moving in graphs. Our main focus is on the impact that the level of synchrony as well as other factors such as anonymity, knowledge of the size of the ring, and chirality (i.e., common orientation) have on the solvability of the problem, focusing on the minimum number of agents necessary. We draw an extensive map of feasibility, and of complexity in terms of minimum number of agent movements. All our sufficiency proofs are constructive, and almost all our solution protocols are asymptotically optimal.

中文翻译：

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动态环的分布式探索

在图探索问题中，一组称为代理的移动计算实体，任意定位在图的某些节点上，必须合作，以便每个节点最终至少被一个代理访问。在文献中，主要关注的是静态图；也就是说，拓扑要么随时间不变，要么受局部变化的影响。对动态图探索的少数研究几乎都局限于集中案例（即，假设对变化及其发生的时间有完整的先验知识）。在本文中，我们研究了动态图的分散探索（即当代理不知道变化的位置和时间时），重点放在其底层图是环的动态系统上。我们首先考虑文献中传统上假设的全同步系统；即，所有代理在每个时间步都处于活动状态。然后我们引入了半同步系统的概念，其中每个时间步只有一部分代理可能处于活动状态（子集的选择由对手做出）；该模型在连续空间中的移动代理的上下文中很常见，但之前从未研究过在图中移动的代理。我们主要关注同步水平以及其他因素（例如匿名性、环大小的知识和手性（即共同方向））对问题可解性的影响，重点关注最小数需要的代理。我们绘制了一个广泛的可行性地图，以及在代理移动的最少数量方面的复杂性。