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To extend network coverage and to possibly increase data packet throughput, the future wireless cellular networks could adopt relay nodes for multi-hop data transmission. This letter proposes a novel distributed scheduling algorithm for downlink relay networks. Soft-information indicating the probability of activating each network link is exchanged iteratively among neighboring network nodes to determine an efficient schedule. To ensure collision-free simultaneous data transmissions, collision-avoiding local constraint rules are enforced at each network node. To increase resource utility, the soft-information is weighted according to the urgency of data transmission across each link, which also helps maintain throughput fairness among network users.