A black hole is a malicious node in a graph that destroys resources entering into it without leaving any trace. The problem of Black Hole Search (BHS) using mobile agents requires that at least one agent survives and terminates after locating the black hole. Recently, this problem has been studied on 1-bounded 1-interval connected dynamic graphs \cite{BHS_gen}, where there is a footprint graph, and at most one edge can disappear from the footprint in a round, provided that the graph remains connected. In this setting, the authors in \cite{BHS_gen} proposed an algorithm that solves the BHS problem when all agents start from a single node (rooted initial configuration). They also proved that at least $2δ_{BH} + 1$ agents are necessary to solve the problem when agents are initially placed arbitrarily across the nodes of the graph (scattered initial configuration), where $δ_{BH}$ denotes the degree of the black hole. In this work, we present an algorithm that solves the BHS problem using $2δ_{BH} + 17$ initially scattered agents. Our result matches asymptotically with the rooted algorithm of \cite{BHS_gen} under the same model assumptions. Further, we study the Eventual Black Hole Search (\textsc{Ebhs}) problem, in which the black hole may appear at any node and at any time during the execution of the algorithm, destroying all agents located on that node at the time of its appearance. However, the black hole cannot emerge at the home base in round~0, where the home base is the node at which all agents are initially co-located. Once the black hole appears, it remains active at that node for the rest of the execution. This problem has been studied on static rings~\cite{Bonnet25}; here we extend it to arbitrary static graphs and provide a solution using four agents. Moreover, it does not require any knowledge of global parameters or additional model assumptions.

翻译：黑洞是图中的恶意节点，会销毁进入其中的资源且不留任何痕迹。使用移动代理的黑洞搜索问题要求至少有一个代理在定位黑洞后存活并终止。最近，该问题已在1-有界1-区间连通动态图\cite{BHS_gen}上得到研究，其中存在一个足迹图，且每轮至多有一条边从足迹图中消失（需保持图的连通性）。在此设定下，\cite{BHS_gen}的作者提出了一种算法，可在所有代理从单一节点启动（根植初始配置）时解决BHS问题。他们还证明了当代理初始随机分布在图的各个节点上（分散初始配置）时，至少需要$2δ_{BH} + 1$个代理才能解决问题，其中$δ_{BH}$表示黑洞的度数。本工作中，我们提出一种使用$2δ_{BH} + 17$个初始分散代理解决BHS问题的算法。该结果在相同模型假设下与\cite{BHS_gen}的根植算法渐近匹配。此外，我们研究了最终黑洞搜索问题，其中黑洞可能在算法执行期间的任意时间出现在任意节点，并销毁其出现时位于该节点的所有代理。但黑洞不能在初始轮（第0轮）出现在主基地（即所有代理初始共置的节点）。黑洞一旦出现，将在该节点持续活跃至算法执行结束。该问题此前已在静态环结构~\cite{Bonnet25}中得到研究；本文将其扩展至任意静态图，并提出一种使用四个代理的解决方案。该方案无需全局参数知识或额外的模型假设。