It has been a challenge to develop efficient algorithms for relay selection and relay power optimization in arbitrarily large multi-hop wireless networks. In this paper, considering Gaussian networks with half-duplex decode-andforward relays, we develop a practical network-wide signal processing procedure with which the relay's data rate is not degraded by mutual interference. Multi-hop relaying is thus immune to mutual interference. Then, we develop an algorithm to find approximately the optimal hop count and the optimal relays for source-destination transmission rate maximization. With a quadratic complexity O(N 2 ), where N is the network size, this algorithm is efficient for arbitrarily large wireless networks. More interestingly, this algorithm is similar to the well-known Dijkstra's algorithm of wired networks.Keywords-successive interference cancellation, multi-hop relay, wireless networks, signal to noise and interference ratio, algorithm