Experimental analysis of adjustable sectorized topologies for static ad hoc networks

Abstract

We consider static wireless networks where the area around each device is subdivided into a fixed number of equal sectors or cones. Each node has one transmitter per sector and can adjust its transmitting power to send out data in each sector separately. In general, it is assumed that the sectors of the nodes underly a fixed orientation or that they are oriented as a result of the movement of nodes. We assume an extended model and allow each node to adjust the orientation of its senders not in dependence from any other conditions. We introduce new optimization tasks and present algorithms which improve the stretch factors of known sectorized topologies only by adjusting the orientation of some sectors of the nodes. Further, we present experimental results on random vertex sets to investigate the characteristics of these topologies under the extended model with regard to energy consumption, given by the so-called power spanner property, and to congestion, given by the (weak) spanner property. We take also interferences into account and measure the degree of the nodes and other statistical data.In addition, we present new algorithms to calculate exactly the power stretch factor and the weak stretch factor of a graph G=(V,E) in time O(|V|2 log |V| + |V||E|). Hence, we can determine these factors for sparse graphs, considered in this work, in time O(|V|2 log |V|. Applying this yields a lower bound for an optimal orientation of all senders, e.g., with regard to energy consumption, that can be computed in polynomial time. We use this bound to analyze the simulation results.Our extensive experimental evaluation of three sectorized topologies on random vertex sets under different sector alignments show that we can improve the known stretch factors and that the considered topologies perform well on normal vertex sets where the nodes are placed uniformly at random.