Streaming cache placement problems: complexity and algorithms
International Journal of Computational Science and Engineering
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Optimization problems occur in diverse areas of telecommunications. Some problems have become classical examples of application for techniques in operations research, such as the theory of network flows. Other opportunities for applications in telecommunications arise frequently, given the dynamic nature of the field. Every new technique presents different challenges that can be answered using appropriate optimization techniques. In this dissertation, problems occurring in telecommunications are discussed, with emphasis for applications in the Internet. First, a study of problems occurring in multicast routing is presented. Here, the objective is to allow the deployment of multicast services with minimum cost. A description of the problem is provided, and variations that occur frequently in some of these applications are discussed. Complexity results are presented for multicast problems, showing that it is NP-hard to approximate these problems effectively. Despite this, we also describe algorithms that give some guarantee of approximation. A second problem in multicast networks studied in this dissertation is the multicast routing problem. Its objective is to find a minimum cost route linking source to destinations, with additional quality of service constraints. A heuristic based on a Steiner tree algorithm is proposed, and used to construct solutions for the routing problem. This construction heuristic is also used as the basis to develop a restarting method, based on the greedy randomized adaptive search procedure (GRASP). The last part of the dissertation is concerned with problems in wireless networks. Such networks have numerous applications due to its highly dynamic nature. Algorithms to compute near optimal solutions for the minimum backbone problem are proposed, which perform in practice much better than other methods. A distributed version of the algorithm is also provided.