Fault-tolerant relay node placement in wireless sensor networks

The paper addresses the relay node placement problem in two-tiered wireless sensor networks. Given a set of sensor nodes in an Euclidean plane, our objective is to place minimum number of relay nodes to forward data packets from sensor nodes to the sink, such that: 1) the network is connected, 2) the network is 2-connected. For case one, we propose a (6 + epsilon)-approximation algorithm for any epsilon > 0 with polynomial running time when epsilon is fixed. For case two, we propose two approximation algorithms with (24 + epsilon) and (6/T + 12 + epsilon), respectively, where T is the ratio of the number of relay nodes placed in case one to the number of sensors.