Journal of Interconnection Networks ❢c World Scientific Publishing Company (QUASI) SPANNERS FOR MOBILE AD HOC NETWORKS

We introduce a notion of t-quasi-spanner as an alternative to classical t-spanners. Our motivation for quasi-spanner comes from a problem of computing a sparse backbone for ad hoc wireless networks with fixed transmission ranges. We study computational complexity of the problem of computing 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. Finally, we give a modification of our algorithm which performs well on a class of random ad hoc networks