Mobile agents (agents) are objects which can migrate autonomously in a distributed system and execute actions at visited nodes. One of the most fundamental problems of agents is exploration, which requires that each node should be visited by at least one agent. For a long time, researchers focus on exploration of static networks while exploration of dynamic networks has been studied recently. In this paper, we consider exploration of a dynamic torus under some constraints on the dynamics (or topology changes). An $n\times m$ torus ($3\le n\le m$) is considered as a collection of n row rings and m column rings. The constraint on the dynamics is that each ring should be 1-interval connected, which allows at most one link to be missing at any time in each ring. For the $n\times m$ dynamic torus, we propose exploration algorithms with and without the link presence detection. With the link presence detection, an agent can detect which incident links are missing (if some link is missing) before determining its next move. On the other hand, without the link presence detection, an agent has to determine its next move without knowing which incident links are missing, which makes the agent stay on the same node when it tries to move through a missing link. The main contribution of this paper is to clarify the necessary and sufficient number of agents to explore an $n\times m$ dynamic torus with and without the link presence detection. Specifically, it is proven that, without the link presence detection, $n+1$ agents are necessary and sufficient to explore the $n\times m$ dynamic torus. It also proven that, with the link presence detection, $\lceil n/2\rceil +1$ agents are necessary and sufficient when $n\ne 4$ and, $\lceil n/2\rceil +2$ (i.e., four) agents are necessary and sufficient when $n=4$ to explore the $n\times m$ dynamic torus. With respect to the time complexity, we propose asymptotically time-optimal algorithms with and without the link presence detection.

移动代理（代理）是可以在分布式系统中自主迁移并在访问的节点上执行操作的对象。代理最基本的问题之一是探索，它要求每个节点至少应由一个代理访问。长期以来，研究人员一直专注于静态网络的探索，而最近对动态网络的探索进行了研究。在本文中，我们考虑在动力学（或拓扑变化）的某些约束下探索动态环面。一个$ñ\times 米$ 圆环（$3\le ñ\le 米$）被视为n个行环和m个列环的集合。动力学方面的限制是每个环应以1间隔连接，这样每个环中的任何时间最多都不会丢失一个链接。为了$ñ\times 米$动态环面，我们提出了有无链路存在检测的探索算法。使用链接存在检测，代理可以在确定下一步移动之前检测到哪些事件链接丢失（如果某些链接丢失）。另一方面，在没有链路存在检测的情况下，代理必须确定其下一步行动，而又不知道丢失了哪些事件链接，这使得代理在尝试通过丢失的链路移动时会停留在同一节点上。本文的主要贡献在于阐明必要和足够数量的代理商以探索$ñ\times 米$带有和不带有链接存在检测的动态环面。具体来说，事实证明，如果没有链路存在检测，$ñ+\mathrm{1个}$ 代理商对于探索 $ñ\times 米$动态环面。还证明了通过链路存在检测，$\lceil ñ/2\rceil +\mathrm{1个}$ 代理商在必要时是足够的 $ñ\ne 4$ 和， $\lceil ñ/2\rceil +2$ （即四个）代理在必要时是足够的 $ñ=4$ 探索 $ñ\times 米$动态环面。关于时间复杂度，我们提出了有和没有链路存在检测的渐近时间最优算法。