Xavier Pérez

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Effort is supported by the functionality of the current 802.11 standard in such a way that legacy IEEE 802.11 terminals behave as Best Effort terminals in the DIME architecture. While the performance of the Assured Forwarding extension has been thoroughly evaluated by the authors elsewhere [1], this paper concentrates on the overall architecture and the(More)
It was only recently shown by Shi and Wormald, using the differential equation method to analyse an appropriate algorithm, that a random 5-regular graph asymptoti-cally almost surely has chromatic number at most 4. Here, we show that the chromatic number of a random 5-regular graph is asymptotically almost surely equal to 3, provided a certain four-variable(More)
We present a model of the establishment and maintenance of communication between mobile agents. We assume that the agents move through a fixed environment modeled by a motion graph and are able to communicate if they are within distance at most d of each other. As the agents move randomly, we analyze the evolution in time of the connectivity between a set(More)
We show for an arbitrary ℓp norm that the property that a random geometric graph G(n, r) contains a Hamiltonian cycle exhibits a sharp threshold at r = r(n) = log n αp n , where αp is the area of the unit disk in the ℓp norm. The proof is constructive and yields a linear time algorithm for finding a Hamiltonian cycle of G(n, r) a.a.s., provided r = r(n) ≥(More)
We present a mathematical model to analyse the establishment and maintenance of communication between mobile agents. We assume that the agents move through a fixed environment modelled by a motion graph, and are able to communicate if they are at distance at most d. As the agents move randomly, we analyse the evolution in time of the connectivity between a(More)
Now days, in practical application scenario, with increasing demand of wireless LANs, higher data rates are required. Wireless Local Area Network (WLAN) is based on IEEE 802. 11 standard and is also popular by the name as Wireless Fidelity (Wi-Fi). The task groups within the 802. 11 working group introduced few extensions to the original specifications. The(More)
The world of data communication has undergone many changes over the last few years. Probably the most important one is the convergence of voice, video and data communication under the roof of the Internet Protocol (IP) suite. Originally, IP was designed to support elastic services, i.e. data applications like file transfer, electronic mail and remote(More)