Localized Algorithms for Energy Efficient Topology in Wireless Ad Hoc Networks

We propose several novel localized algorithms to construct energy efficient routing structures for homogeneous wireless ad hoc networks, where all nodes have same maximum transmission ranges. Our first structure has the following attractive properties: (1) It is energy efficient: given any two nodes u and v, there is a path connecting them in the structure with total energy cost at most ρ = 1/1-(2sin π/k)β times of the energy cost of any path connecting them in original communication graph; (2) Its node degree is bounded from above by a positive constant k+5 where k>6 is an adjustable parameter; (3) It is a planar structure, which enables several localized routing algorithms; (4) It can be constructed and maintained locally and dynamically. Moreover, by assuming that the node ID and its position can be represented in O(log n) bits each for a wireless network of n nodes, we show that the structure can be constructed using at most 24n messages, where each message is O(log n) bits. Our second method improves the degree bound to k, relaxes the theoretical power spanning ratio to ρ = √2 β/1 -(2√2sinπ/k)β, where k›8 is an adjustable parameter, and keeps all other properties. We show that the second structure can be constructed using at most 3n messages, where each message has size of O(log n) bit.We also experimentally evaluate the performance of these new energy efficient network topologies. The theoretical results are corroborated by the simulations: these structures are more efficient in practice, compared with other known structures used in wireless ad hoc networks and are easier to construct. In addition, the power assignment based on our new structures shows low energy cost and small interference at each wireless node.