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Sensor networks, that is networks of nodes with sensing ability, and wireless communication capacity are proving very useful in fields of environment and industrial monitoring, as well as security. Since the nodes are assumed to be as cheap as possible (with the so far unattained ideal being " smart dust "), and have limited energy capacity (batteries),… (More)

In this paper we consider a cutting process for random mappings. Specifically, for 0 < m < n, we consider the initial (uniform) random mapping digraph G n on n labelled vertices, and we delete (if possible), uniformly and at random, m non-cyclic directed edges from G n. The maximal random digraph consisting of the uni-cyclic components obtained after… (More)

A random mapping T ˆ D n maps the set {1, 2, ..., n} into itself and it is constructed using a collection of exchangeable random variablesˆD 1 , ...., ˆ D n which satisfy n i=1ˆD i = n. In the random digraph, G ˆ D n , which represents the mapping T ˆ D n , the in-degree sequence for the ver-tices is given by the variablesˆD 1 , ˆ D 2 , ..., ˆ D n and, in… (More)