Error-correcting 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 (the minimum number of) detectors at a subset of vertices in G to automatically determine if there is an intruder, and if so, its precise location. In this research we explore a fault-tolerant variant of identifying codes, known as error-correcting identifying codes, which permit one false positive or negative and are applicable to real-world systems. We present the proof of NP-completeness of the problem of determining said minimum size in arbitrary graphs, and determine bounds on the parameter in cubic graphs.
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