On Demand Beaconless Planar Backbone Construction for Quasi Unit Disk Graphs

Beaconless topology control algorithms reduce message overhead of local topology constructions compared to conventional (beacon-based) local approaches by avoiding maintenance of neighborhood tables. Moreover, they construct a node´s adjacency in the desired topology on demand and only locally, i.e., Do not require network-wide operation. In this work, we present a beaconless topology control algorithm which enables a node to reactively construct a planar backbone graph in its geographic vicinity. This backbone graph is a constant node degree, constant stretch hop-spanner for the input quasi unit disk graph. Our contribution is novel, since all known algorithms with comparable outputs require maintenance of neighborhood tables and are designed for network-wide operation. In addition, it is of significance since there are several applications of it, e.g., In the context of geographic unicast and multicast routing with guaranteed delivery.