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We give simple, deterministic, distributed algorithms for computing maximal matchings, maximal independent sets and colourings. We show that edge colourings with at most $2\Delta-1$ colours, and maximal matchings can be computed within ${\cal O}(\log^* n + \Delta)$ deterministic rounds, where $\Delta$ is the maximum degree of the network. We also show how(More)
We consider the two problems of finding the maximum number of node disjoint triangles and edge disjoint triangles in an undirected graph. We show that the first (respectively second) problem is polynomially solvable if the maximum degree of the input graph is at most 3 (respectively 4), whereas it is APX-hard for general graphs and NP-hard for planar graphs(More)
SNP haplotyping problems have been the subject of extensive research in the last few years, and are one of the hottest areas of Computational Biology today. In this paper we report on our work of the last two years, whose preliminary results were presented at the European Symposium on Algorithms (Proceedings of the Annual European Symposium on Algorithms(More)
We consider a dynamic problem introduced by B. Hartnell in 1995 [4]. Let (G, r) be a connected rooted graph (where r ∈ V (G)). At time 0, a fire breaks out at r. At each subsequent time interval, the firefighter defends some vertex which is not on fire, and then the fire spreads to all undefended neighbours of each burning (i.e., on fire) vertex. Once(More)
Broadcast is an efficient and scalable way of transmitting data to an unlimited number of clients that are listening to a channel. Cyclically broadcasting data over the channel is a basic scheduling technique, which is known as flat scheduling. When multiple channels are available, a data allocation technique is needed to assign data to channels.(More)
In this paper, we define a new problem that has not been addressed in the past: the trade-off between energy efficiency and throughput for multicast services in 802.16e or similar mobile networks. In such networks, the mobile host can reduce its energy consumption by entering the sleep mode when it is not supposed to receive or transmit information. For(More)