In an ad hoc network, each host assumes the role of a router and relays packets toward final destinations. This paper studies efficient routing mechanisms for packet flooding in ad hoc wireless networks. Because a packet is broadcast to all neighboring nodes, the optimality criteria of wireless network routing are different from that of the wired network routing. We show that the minimum cost flooding tree problem is similar to MCDS (Minimum Connected Dominating Set) problem and prove the NP-completeness of the minimum cost flooding tree problem. Then, we propose two flooding methods: self-pruning and dominant pruning. Both methods utilize the neighbor information to reduce redundant transmissions. Performance analysis shows that both methods perform significantly better than the blind flooding. Especially, dominant pruning performs close to the practically achievable best performance limit.