Optimal Error-detection system for Identifying Codes
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Assume that a graph G models a detection system for a facility with a possible “intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing detectors at a subset of vertices in G to determine the location of an intruder if there is any. Many types of detection systems have been defined for different sensor capabilities; in particular, we focus on Identifying Codes, where each detector can determine whether there is an intruder within its closed neighborhood. In this research we explore a fault-tolerant variant of identifying codes applicable to real-world systems. Specifically, error-detecting identifying codes permit a false negative transmission from any single detector. We investigate minimum-sized error-detecting identifying codes in several classes of graphs, including cubic graphs and infinite grids, and show that the problem of determining said minimum size in arbitrary graphs is NP-complete.
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