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In this paper, we address the problem of determining an optimal topology for Bluetooth wireless personal area networks (BT-WPAN). In BT-WPAN, multiple communication channels are available, thanks to the use of a frequency hopping technique. The way network nodes are grouped to share the same channel, and which nodes are selected to bridge traffic from a channel to another, has a significant impact on the capacity and the throughput of the system, as well as the nodes' battery lifetime. The determination of an optimal topology is thus extremely important; nevertheless, to the best of our knowledge, this problem is tackled here for the first time. Our optimization approach is based on a model derived from constraints that are specific to the BT-WPAN technology, but the level of abstraction of the model is such that it can be related to the more general field of ad hoc networking. By using a min-max formulation, we find the optimal topology that provides full network connectivity, fulfills the traffic requirements and the constraints posed by the system specification, and minimizes the traffic load of the most congested node in the network, or equivalently its energy consumption. Results show that a topology optimized for some traffic requirements is also remarkably robust to changes in the traffic pattern. Due to the problem complexity, the optimal solution is attained in a centralized manner. Although this implies severe limitations, a centralized solution can be applied whenever a network coordinator is elected, and provides a useful term of comparison for any distributed heuristics

The IP (Internet Protocol) Network Design Problem can be shortly stated as follows. Given a set of nodes and a set of traffic demands, we want to determine the minimum cost capacity installation such that all the traffic is routed. Capacity is provided by means of links of a given capacity and traffic must be loaded on the network according to the OSPF-ECM (Open Shortest Path FirstEqual Commodity Multiflow) protocol, with additional constraints on the maximum number of hops. The problem is strongly NP-Hard, and the literature proposes local search-based heuristics that do not take into account max-hop constraints, or assume a simplified OSPF routing. The core in a local search approach is the network loading algorithm for the evaluation of the neighbor solutions costs. It presents critical aspects concerning both computational efficiency and memory requirements. Starting from a tabu search prototype, we show how these aspects deeply impact on the design of a local search procedure, even at the logical level. We present several properties of the related network loading problem, that allow to overcome the critical issues and lead to an efficient solution evaluation.

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