Localized topology control for heterogeneous wireless ad-hoc networks

We study topology control in heterogeneous wireless ad hoc networks, where mobile hosts may have different maximum transmission powers and two nodes are connected if they are within the maximum transmission range of each other. We present several strategies so that all wireless nodes self-maintain sparse and power efficient topologies in heterogeneous network environments with low communication cost. The first structure is sparse and can be used for broadcasting. The second structure keeps the minimum power consumption path, and the third structure is a length and power spanner with a bounded degree. Both the second and third structures are power efficient and can be used for unicast. Here a structure is power efficient if the total power consumption of the least cost path connecting any two nodes in it is no more than a small constant factor of that in the original heterogeneous communication graph. All our methods use at most O(n) total messages, where each message has O(logn) bits.