A black hole is a malicious node in a graph that destroys any resource entering it without leaving a trace. In the Black Hole Search (BHS) problem with mobile agents, at least one agent must survive and terminate after locating the black hole. Recently, BHS has been studied on 1-bounded 1-interval connected dynamic graphs \cite{BHS_gen}, where a footprint graph exists and at most one edge may disappear per round while connectivity is preserved. Under this model, \cite{BHS_gen} presents an algorithm for the rooted initial configuration, where all agents start from a single node, and proves that at least $2δ_{BH}+1$ agents are necessary in the scattered initial configuration, where agents are arbitrarily placed and $δ_{BH}$ denotes the degree of the black hole. We present an algorithm that solves BHS in the scattered setting using $2δ_{BH}+17$ agents, matching asymptotically the rooted algorithm of \cite{BHS_gen} under the same assumptions. We further investigate the Eventual Black Hole Search (\textsc{Ebhs}) problem, where the black hole may appear at any node and at any time during execution, destroying all agents located there upon its emergence; however, it cannot appear at the home base in round 0, where all agents are initially co-located, and once created, it remains permanently active. While \textsc{Ebhs} has been studied on static rings \cite{Bonnet25}, we extend it to arbitrary static graphs and provide a solution using the minimum number of agents. For rings, our algorithm is optimal in both the number of agents and the running time, and it does not require knowledge of global parameters or additional model assumptions.

翻译：黑洞是图中的恶意节点，它会销毁任何进入其中的资源且不留痕迹。在移动智能体场景下的黑洞搜索问题中，至少需有一个智能体在定位黑洞后存活并终止。近期研究在1-有界1-区间连通动态图模型上探讨了该问题，该模型要求存在足迹图且每轮至多有一条边消失，同时保持图的连通性。在此模型下，已有研究针对根节点初始配置提出了算法，并证明在分散初始配置中至少需要$2δ_{BH}+1$个智能体。我们提出一种在分散配置下使用$2δ_{BH}+17$个智能体解决黑洞搜索的算法，其渐近复杂度与现有根节点配置算法相当。进一步研究了最终黑洞搜索问题，其中黑洞可在任意节点、任意执行时刻出现，并在出现时销毁该节点上的所有智能体；但黑洞不会在第0轮出现在所有智能体初始聚集的基地节点，且一旦出现将永久保持活跃。尽管该问题已在静态环结构上被研究，我们将其扩展至任意静态图，并给出了使用最小数量智能体的解决方案。对于环结构，我们的算法在智能体数量与运行时间上均达到最优，且无需全局参数知识或额外的模型假设。