Identifying codes in random networks

In this paper we deal with codes identifying sets of vertices in random graphs, that is l-identifying codes. These codes enable us to detect sets of faulty processors in a multiprocessor system, assuming that the maximum number of faulty processors is bounded by a fixed constant l. The l-identifying codes or simply identifying codes are of special interest. For random graphs we use the model G(n,p), in which each one of the (₂ ⁿ) possible edges exists with probability p. We give upper and lower bounds on the minimum cardinality of an l-identifying code in a random graph, as well as threshold functions for the property of admitting such a code. We derive existence results from probabilistic constructions. A connection between identifying codes and superimposed codes is also established