Fault-tolerant relay node placement in wireless sensor networks: formulation and approximation

A two-tiered network model has been proposed for prolonging lifetime and improving scalability in wireless sensor networks (Gupta, G. and Younis, M., Proc. IEEE WCNC'03, p.1579-84, 2003; Proc. IEEE ICC'03, p.1848-52, 2003). This two-tiered network is a cluster-based network. Relay nodes are placed in the playing field to act as cluster heads and to form a connected topology for data transmission in the higher tier. They are able to fuse data packets from sensor nodes in their clusters and send them to sinks through wireless multi-hop paths. However, this model is not fault-tolerant as the network may be disconnected if a relay node fails. We formulate and study a fault-tolerant relay node placement problem in wireless sensor networks. In this problem, we want to place a minimum number of relay nodes in the playing field of a sensor network such that (1) each sensor node can communicate with at least two relay nodes and (2) the relay node network is 2-connected. We present a polynomial time approximation algorithm for this problem and prove the worst-case performance given by our algorithm is bounded within O(D log n) times of the size of an optimal solution, where n is the number of sensor nodes in the network, D is the (2, 1) diameter of the network formed by a sufficient set of possible positions for relay nodes.