A Topology Control Algorithm with Good Spanner Properties for Wireless Sensor Networks

The main design challenge for wireless sensor network solutions is energy efficiency to prolong the network operable lifetime. Since most energy is spent for radio communications, an effective approach for energy conservation is scheduling sleep intervals for extraneous nodes, while the remaining nodes stay active to provide continuous service. Assuming node position information is unavailable we propose an algorithm to construct a sparse spanner network topology for these networks. It uses two-hop neighborhood information to select a subset of nodes to be active among all nodes in the neighborhood. Each node in the network selects its own set of active neighbors from among its one-hop neighbors. This set is determined such that it covers all two-hop neighbors. Our proposed algorithm is proved to achieve several desirable properties on both Euclidean and general weighted graphs: (1) the resulting graph is symmetric and connected; (2) the resulting graph also exhibits good spanner properties for both distance/energy and hops; (3) it is constructed locally in a fully distributed fashion; (4) we prove that on the average-case unit disk graphs, the resulting topology features the bounded degree property; (5) finally, the computation cost of our algorithm is at most O(n^3 ), and the communication cost is bounded by O(n^2 ).