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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 communication… (More)

The initialization problem, also known as naming, consists to give a unique identifier ranging from 1 to n to a set of n indistinguishable nodes in a given network. We consider a network where n nodes (processors) are randomly deployed in a square (respectively, cube) X. We assume that the time is slotted and the network is synchronous, two nodes are able… (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 this work, we consider a large-scale geographic area populated by tiny sensors and some more powerful devices called actors, authorized to organize the sensors in their vicinity into short-lived, actor-centric sensor networks. The tiny sensors run on miniature nonrechargeable batteries, are anonymous, and are unaware of their location. The sensors differ… (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)