Power efficient and sparse spanner for wireless ad hoc networks

Due to the limited resources available in the wireless ad hoc networking nodes, the scalability is crucial for network operations. One effective approach is to maintain only a sparse spanner of a linear number of links while still preseving the power-efficient route for any pair of nodes. For any spanner G, its power stretch factor is defined as the maximum ratio of the minimum power needed to support any link in this spanner to the least necessary. In this paper, we first consider several well-known proximity graphs including the relative neighborhood graph, Gabriel graph and Yao graph. These graphs are sparse and can be constructed locally in an efficient way. We show that the power stretch factor of the Gabriel graph is always one, and the power stretch factor of the Yao graph is bounded by a constant while the power stretch factor of the relative neighborhood graph could be as large as the network size minus one. Notice that all of these graphs do not have constant degrees. We further propose another sparse spanner that has both constant degree and constant power stretch factor. An efficient local algorithm is presented for the construction of this spanner.