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In a wireless multi-hop relay network, the optimal routing scheme with exhaustive path search entails high computational complexity and large storage requirement, and is impractical for a large number of hops. In this paper, we propose a suboptimal path selection scheme, based on amplify-and-forward (AF) protocol, that has outage performance close to the optimal routing scheme, but with much less complexity. The proposed scheme draws on the analogy between the node distribution of a commonly used relay network model and the trellis of a convolutional code, and applies the Viterbi algorithm in selecting a path to maximize the end-to-end signal-to-noise ratio (SNR). In specific, the relay network topology is first mapped to the trellis diagram of a convolutional code. In the trellis, the branch metric is defined as the inverse of the instantaneous SNR of the channel connecting two relays in two adjacent clusters. Consequently, the path metric is equal to the inverse of the equivalent SNR of the path. Then, the sliding window Viterbi algorithm is used to select a path from the source to the destination. Simulation results show that when the window size is five times the total encoder memory or more, the proposed routing scheme achieves near optimal outage performance. The proposed scheme has a polynomial complexity and low communication overhead. Therefore, it is very efficient for relay networks with a large number of hops.