Introduction

The (localized) topology-control technique lets each wireless device (locally) adjust its transmission range and select certain neighbors for communication while maintaining a decent global structure to support energy-efficient routing and to improve the overall network performance. A distributed method is localized if it runs in a constant number of rounds (Naor and Stockmeyer, 1993). By enabling each wireless node to shrink its transmission power (which is usually much smaller than its maximum transmission power) enough to cover its farthest selected neighbor or selecting only a portion of nodes to forward data for others, topology-control schemes can not only save energy and prolong network life but can also improve the network throughput through mitigating the MAC-level medium contention. Unlike traditional wired and cellular networks, the movement of wireless devices during communication could change the network topology to some extent. Hence, it is more challenging to design a topology-control algorithm for ad hoc wireless networks: The topology should be locally and self-adaptively maintained at a low communication cost, without affecting the whole network's performance.

Wireless networks have drawn a good deal of attention in recent years because of the potential applications in various areas. Many routing protocols have recently been proposed for wireless ad hoc networks. The simplest routing method is to flood the message, which not only wastes the rare resources of wireless nodes but also diminishes the throughput of the network.