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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)

- Josep Díaz, Alexis C. Kaporis, Graeme Kemkes, Lefteris M. Kirousis, Xavier Pérez, Nicholas C. Wormald
- Journal of Graph Theory
- 2009

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)

- Josep Díaz, Xavier Pérez, Maria J. Serna, Nicholas C. Wormald
- SIAM J. Discrete Math.
- 2008

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)

- Josep Díaz, Dieter Mitsche, Xavier Pérez
- SIAM J. Discrete Math.
- 2007

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 show that uniformly random 5-regular graphs of n ver-tices are 3-colorable with probability that is positive independently of n.

- Xavier Carreras Pérez, Llúıs Màrquez Villodre
- 2005

This thesis takes a machine learning approach to the general problem of recognizing phrases in a sentence. This general problem instantiates in many dis-ambiguation tasks of Natural Language Processing, such as Shallow Syntactic Parsing, Clause Identification, Named Entity Extraction or Semantic Role Labeling. In all of them, a sentence has to be segmented… (More)

- Josep Díaz, Dieter Mitsche, Xavier Pérez
- ArXiv
- 2008

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

- Josep Díaz, Xavier Pérez, Maria J. Serna, Nicholas C. Wormald
- STACS
- 2005

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)

- Josep Díaz, Dieter Mitsche, Xavier Pérez
- ArXiv
- 2007

In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static random geometric graphs. We provide precise asymptotic results for the expected length of the connectivity and disconnectivity periods of the network. We… (More)

- Rachana Khanduri, S. S. Rattan, +18 authors Alex Kesselman
- 2013

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)