  We consider the problem of dominating set-based virtual backbone used for
routing in asymmetric wireless ad-hoc networks. These networks have non-uniform
transmission ranges and are modeled using the well-established disk graphs. The
corresponding graph theoretic problem seeks a strongly connected
dominating-absorbent set of minimum cardinality in a digraph. A subset of nodes
in a digraph is a strongly connected dominating-absorbent set if the subgraph
induced by these nodes is strongly connected and each node in the graph is
either in the set or has both an in-neighbor and an out-neighbor in it.
Distributed algorithms for this problem are of practical significance due to
the dynamic nature of ad-hoc networks. We present a first distributed
approximation algorithm, with a constant approximation factor and O(Diam)
running time, where Diam is the diameter of the graph. Moreover we present a
simple heuristic algorithm and conduct an extensive simulation study showing
that our heuristic outperforms previously known approaches for the problem.
