Introduction

Hundreds of protocols (Bose et al., 2001; Chlamtac and Farago, 1999; Das et al., 2000; Johnson and Maltz, 1996; Ko and Vaidya, 1997; X.-Y. Li et al., 2002a; Maltz et al., 1999; Perkins, 1997a; Ramanathan and Steenstrup, 1996; Royer and Toh, 1999; Stojmenovic and Lin, 2001; Y. Wang and Li, 2002b; Zaruba et al., 2001) that take into account the unique characteristics of wireless ad hoc networks have been developed. Among them, energy efficiency, routing, and MAC layer protocols have attracted the most attention. One of the remaining fundamental and critical issues is to have fault-tolerant network deployment without sacrificing the spectrum-reusing property. In other words, the network should support multiple disjoint paths connecting every pair of nodes. Obviously, we can increase the transmission range of all nodes to increase the fault tolerance of the network. However, increasing the transmission range will cause more signal interference (thus reducing the throughput) and increase the power consumption of every node. Because power is a scarce resource in wireless networks, it is important to save the power consumption without losing the network connectivity. The universal minimum power used by all wireless nodes such that the induced network topology is connected is called the critical power.