Topology control in heterogeneous wireless networks: problems and solutions

Previous work on topology control usually assumes homogeneous wireless nodes with uniform transmission ranges. In this paper, we propose two localized topology control algorithms for heterogeneous wireless multihop networks with nonuniform transmission ranges: directed relative neighborhood graph (DRNG) and directed local minimum spanning tree (DLMST). In both algorithms, each node selects a set of neighbors based on the locally collected information. We prove that (1) the topologies derived under DRNG and DLMST preserve the network connectivity; (2) the out degree of any node in the resulting topology by DLMST is bounded; while the out degree of nodes in the topology by DRNG is not bounded; and (3) the topologies generated by DRNG and DLMST preserve the network bi-directionality.