Abstract
In the article we study important properties of random geometric graphs with randomly deleted edges which are natural models of wireless ad hoc networks with communication constraints. We concentrate on two problems which are most important in the context of theoretical studies on wireless ad hoc networks. The first is how to set parameters of the network (graph) to have it connected. The second is the problem of an effective message transmition i.e. the problem of construction of routing protocols in wireless networks. We provide a thorough mathematical analysis of connectivity property and a greedy routing protocol. The models we use are: an intersection of a random geometric graph with an Erdős–Rényi random graph and an intersection of a random geometric graph with a uniform random intersection graph. The obtained results are asymptotically tight up to a constant factor.KeywordsSensor NetworkWireless NetworkWireless Sensor NetworkRandom GraphTransmission RangeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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