(quasi) Spanners for Mobile Ad Hoc Networks

We introduce the notion of t-quasi-spanners as an alternative to classical t-spanners. Our motivation for quasi-spanners comes from the problem of computing a sparse backbone for ad hoc wireless networks with fixed transmission ranges. We study the computational complexity of the problem of computing the sparsest quasi-spanner. Then we concentrate on the case t = 2 and give a distributed algorithm for computing a 2-quasi-spanner with linear number of edges. Note that for 2-spanners no distributed algorithm is known. Finally, we improve our algorithm on a class of random ad hoc networks.