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Many signaling or data forwarding operations (e.g., the route discovery process in on-demand routing protocols) involve the broadcasting of packets, which incurs considerable collisions in ad hoc networks based on a contention-based channel access protocol. We propose the three-hop horizon pruning (THP) algorithm to reduce the impact of broadcasting. THP can either compute a connected dominating set (CDS) or a two-hop connected dominating set (TCDS). Each node uses THP to select the smallest subset of its one-hop neighbors that use its two-hop neighbors to reach other nodes three hops away. When all nodes need to be covered (i.e., a CDS is needed), additional relays are selected to cover those two-hop neighbors left uncovered. We compare THP against the best-performing broadcasting algorithms, and show through extensive simulations that THP is more efficient. To show how THP can improve the route discovery process of an on demand routing protocol, we apply THP to AODV (the new variant is named AODV-THP), and also provide a version of THP that provides added redundancy. Simulation results show that, for networks with low mobility, AODV-THP improves over AODVs performance in all aspects: better delivery ratio, lower control overhead, fewer packet collisions, and smaller end-to-end delays.