Scheduling in wireless networks with oblivious power assignments

In this thesis we analyze scheduling in wireless networks under the physical model. In particular, we ask the following question. Given n communication requests as pairs of nodes from a metric space, how fast can we schedule all of them? We have to assign a schedule slot and a transmission power to each request and need to ensure that during each schedule step the interference at the addressed receivers is not too high. The interference is modeled in terms of the Signal to Interference Plus Noise Ratio (SINR) that compares the received signal strength with the sum of all other simultaneously sent signals plus ambient noise. We strive to minimize the schedule length. We investigate scheduling using oblivious power assignments where each request uses a transmission power depending only on the path loss between sender and receiver. The most famous examples of such power assignments are the uniform assignment, where each sender uses the same transmission power, and the linear assignment that uses transmission powers linear in the path loss between the two nodes. We first present a measure of interference that allows us to lower bound the schedule length when using linear or optimal power assignment. Based on this measure of interference we devise distributed scheduling algorithms for the linear power assignment reaching the minimal schedule length up to small factors. Second, we study the limitations of oblivious power assignments by proving lower bounds for scheduling algorithms using these power assignments. In particular, when only considering the number of nodes in the lower bound, oblivious power assignments cannot yield an approximation ratio asymptotically better than the worst possible performance guarantee. When modifying the problem to bidirectional communication these lower bounds only hold for some oblivious power assignments, e. g., for uniform and linear power assignment. This motivated us to deeply investigate the