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We extend dominating-set-based routing to networks with unidirectional links. Specifically, an efficient localized algorithm for determining a dominating and absorbant set of vertices (mobile hosts) is given and this set can be easily updated when the network topology changes dynamically. A host ν is called a dominating neighbor (absorbant neighbor) of another host u if there is a directed edge from ν to u (from u to ν). A subset of vertices is dominating and absorbant if every vertex not in the subset has one dominating neighbor and one absorbant neighbor in the subset. The derived dominating and absorbant set exhibits good locality properties; that is, the change of a node status (dominating/dominated) affects only the status of nodes in the neighborhood. The notion of dominating and absorbant set can also be applied iteratively on the dominating and absorbant set itself, forming a hierarchy of dominating and absorbant sets. The effectiveness of our approach is confirmed and the locality of node status update is verified through simulation.