Cover-Free Families and Topology-Transparent Scheduling for MANETs

We examine the combinatorial requirements of topology-transparent transmission schedules in a mobile ad hoc network (MANET). Specifically, if each of the N nodes has at most D active neighbors, we require the schedule to guarantee a collision-free transmission to each neighbor. This requirement is met by a cover-free family. We show that existing constructions for topology-transparent schedules correspond to an orthogonal array. Moreover, we show that Steiner systems support the largest number of nodes for a given schedule length. Both of these combinatorial objects are special cases of cover-free families. Analytically and numerically, we examine slot guarantees, expected throughput, and normalized expected throughput for systems of small strength, exploring the sensitivity of the response to D. Expected throughput provides a better performance metric than the minimum throughput results obtained earlier. The impact of a more realistic model of acknowledgments is also examined. The extension of the schedule to multiple frames returns us to the orthogonal arrays. The very density of Steiner systems that afforded an improvement over orthogonal arrays in one frame impedes the best extension to more frames.