Codes identifying sets of vertices in random networks

In this paper we deal with codes identifying sets of vertices in random networks; that is, (1, ≤ 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 (1, ≤ 1)-identifying codes are of special interest. For random graphs we use the model G(n, p), in which each one of the `n 2 ´ possible edges exists with probability p. We give upper and lower bounds on the minimum cardinality of a (1, ≤ ℓ)-identifying code in a random graph, as well as threshold functions for the property of admitting such a code. We ∗2000 Mathematics Subject Classification 94C12, 05C80, 94B60 †Research partially supported by NSF grant CCR-0200945 ‡Corresponding author. Research partially supported by NSA grant H98230-05-1-0257

• Type: Journal
• Year: 2007
• Where: DM
• Authors: Alan M. Frieze, Ryan Martin, Julien Moncel, Miklós Ruszinkó, Clifford D. Smyth
• Keywords: DM 2007, Faulty Processors, Random, Random Networks