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The NP-completeness of Redundant Open-Locating-Dominating Set (2201.05252v1)
Published 14 Jan 2022 in cs.DM, cs.IT, and math.IT
Abstract: For a graph G, a dominating set D is a subset of vertices in G where each of the vertices in G is in D or adjacent to some vertex in D. An open-locating-dominating (OLD) set models a system with sensors to detect an intruder in a facility or a faulty component in a network of processors. The goal is to detect and pinpoint an intruder's exact location in a system with a minimum number of sensors. In this paper, we focus on a variant of an OLD set called a redundant OLD set and present a proof for the NP-completeness of the problem of a redundant OLD set.