Near-Optimal Multicriteria Spanner Constructions in Wireless Ad Hoc Networks

In this paper, we study asymmetric power assignments that induce a low-energy k-strongly connected communication graph with spanner properties. We address two spanner models: energy and distance. The former serves as an indicator for the energy consumed in a message propagation between two nodes, while the latter reflects the geographic properties of routing in the induced communication graph. We consider a random wireless ad hoc network with IVI = n nodes distributed uniformly and independently in a unit square. For k ∈ {1, 2}, we propose several power assignments that obtain a good bicriteria approximation on the total cost and stretch factor under the two models. For k > 2, we analyze a power assignment developed by Carmi et al. and derive some interesting bounds on the stretch factor for both models as well. We also describe how to compute all the power assignments distributively, and we provide simulation results. To the best of our knowledge, these are the first provable theoretical bounds for low-cost spanners in wireless ad hoc networks.