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In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the… (More)

Denote by an ℓ-component a connected b-uniform hypergraph with k edges and k(b − 1) − ℓ vertices. We prove that the expected number of creations of ℓ-component during a random hypergraph process tends to 1 as ℓ and b tend to ∞ with the total number of vertices n such that ℓ = o 3 n b. Under the same conditions, we also show that the expected number of… (More)

Address autoconfiguration is an important mechanism required to set the IP address of a node automatically in a wireless network. The address autoconfiguration, also known as initialization or naming, consists to give a unique identifier ranging from 1 to n for a set of n indistinguishable nodes. We consider a wireless network where n nodes (processors) are… (More)

We study the sizes of connected components according to their excesses during a random graph process built with n vertices. The considered model is the continuous one defined in [16]. An ℓ-component is a connected component with ℓ edges more than vertices. ℓ is also called the excess of such component. As our main result, we show that when ℓ and n ℓ are… (More)

In the minimum sum edge coloring problem, we aim to assign natural numbers to edges of a graph, so that adjacent edges receive different numbers, and the sum of the numbers assigned to the edges is minimum. The chromatic edge strength of a graph is the minimum number of colors required in a minimum sum edge coloring of this graph. We study the case of… (More)

Radio networks (RN) are distributed systems (ad hoc networks) consisting in n ≥ 2 radio stations. Assuming the number n unknown, two distinct models of RN without collision detection (no-CD) are addressed: the model with weak no-CD RN and the one with strong no-CD RN. We design and analyze two distributed leader election protocols, each one running in each… (More)