论文标题
在无限的国王网格上定位的耐故障定位套件
Fault-tolerant Locating-Dominating Sets on the Infinite King Grid
论文作者
论文摘要
令$ g $为具有顶点的网络系统的图表，$ v（g）$，代表物理位置和边缘，$ e（g）$，代表信息连接。 a \ emph {jotating-dominating（ld）} seet $ s \ subseteq v（g）$是代表能够在其位置或确切的开放式邻里的某个地方感知“入侵者”的探测器的子集 - 必须在图表中找到Intruder的任何地方。我们探索了三种类型的耐故障LD集合：\ emph {redaint LD}集，它们允许删除检测器，\ emph {错误检测LD}集，最多允许一个false负面，并且\ emph {errect-correcting correcting ld}集合允许以一个错误或负面的误差（false off false offers或false）。特别是，我们确定了\ emph {Infinite King Grid}中这三个易于断层的定位集的最小密度的下限和上限。
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}.
