We study the problem of exploration by a mobile entity (agent) of a class of dynamic networks, namely constantly connected dynamic graphs. This problem has already been studied in the case where the agent knows the dynamics of the graph and the underlying graph is a ring of n vertices (Ilcinkas and Wade 2018). In this paper, we consider the same problem and we suppose that the underlying graph is a cactus graph (a connected graph in which any two simple cycles have at most one vertex in common). We propose an algorithm that allows the agent to explore these dynamic graphs in at most \(O(n\frac {\log n}{\log \log n})\) time units. We show that the lower bound of the algorithm is \({\varOmega }(n\frac {\log n}{(\log \log n)^{2}})\) time units (for infinitely many n).

我们研究了移动实体（代理）对一类动态网络（即不断连接的动态图）进行探索的问题。在代理知道图的动力学并且基础图是n个顶点的环的情况下，已经研究了这个问题（Ilcinkas和Wade 2018）。在本文中，我们考虑相同的问题，并假设基础图是仙人掌图（一个连接图，其中任何两个简单的循环最多具有一个相同的顶点）。我们提出了一种算法，该算法允许代理以最多\（O（n \ frac {\ log n} {\ log \ log n}）\）个时间单位浏览这些动态图。我们证明算法的下限是\（{\ varOmega}（n \ frac {\ log n} {（\ log \ log n）^ {2}}）\）时间单位（无限多个n）。