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We try to close the gap between theoretical investigations of wireless network topologies and realistic wireless environments. For point-to-point communication, we examine theoretically well-analyzed sparse graphs, i.e. the Yao-graph, the SparsY-graph, and the SymmY-graph. We present distributed algorithms that can be used to build up these graphs in time O(log n) per node without the use of any geographical positioning system. Our algorithms are based only on local knowledge and local decisions and make use of power control to establish communication links with low energy-cost. We compare these algorithms with respect to congestion, dilation, and energy. For congestion we introduce different measures that allow us to investigate the difference between real-world wireless networks and models for wireless communication at a high level of abstraction. For more realistic simulations we extend our simulation environment SAHNE. We use a realistic transmission model for directed communication that uses sector subdivision. Finally, our experimental results show that our topologies and algorithms work well in a distributed environment and we give some recommendations for the topology control based on our simulations.
Date of Conference: 22-26 April 2003