Let $G$ be a graph of a network system with vertices, $V(G)$, representing physical locations and edges, $E(G)$, representing informational connectivity. A \emph{locating-dominating (LD)} set $S \subseteq V(G)$ is a subset of vertices representing detectors capable of sensing an "intruder" at precisely their location or somewhere in their open-neighborhood -- an LD set must be capable of locating an intruder anywhere in the graph. We explore three types of fault-tolerant LD sets: \emph{redundant LD} sets, which allow a detector to be removed, \emph{error-detecting LD} sets, which allow at most one false negative, and \emph{error-correcting LD} sets, which allow at most one error (false positive or negative). In particular, we determine lower and upper bounds for the minimum density of these three fault-tolerant locating-dominating sets in the \emph{infinite king grid}.

翻译：设$G$为一个网络系统的图，其顶点集$V(G)$表示物理位置，边集$E(G)$表示信息连通性。一个\emph{定位支配（LD）集}$S \subseteq V(G)$是顶点的子集，表示能够在其精确位置或其开邻域内感知“入侵者”的探测器——LD集必须能够定位图中任意位置的入侵者。我们研究了三种类型的容错LD集：\emph{冗余LD}集（允许移除一个探测器）、\emph{错误检测LD}集（允许至多一个假阴性）和\emph{错误纠正LD}集（允许至多一个错误，假阳性或假阴性）。特别地，我们确定了在\emph{无限国王网格}中这三种容错定位支配集的最小密度的下界和上界。