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This paper provides a polynomial time heuristic for the real-time communication scheduling problem in multi-hop wireless sensor networks.Wireless networks add a new dimension to the real-time communication problem because of interference: a transmission cannot be scheduled on a radio link if another transmission is scheduled on any interfering link. The problem being NP-hard in nature, we propose a novel heuristic that comes into two parts: (1) a scheduler that uses a topological analysis of the network to anticipate the effects of radio interference in order to improve scheduling prioritization, (2) an iterative route update scheme that pushes apart interfering streams and spreads them out over the network to reduce interference and improve schedulability while meeting the deadline requirements. The whole algorithm runs in polynomial time of O(N3d), where N and d are the number of streams and maximum deadline respectively. We use a simulation-based study to demonstrate that this algorithm produces near-optimal schedules for approximately 10 packet streams in a 100 node network, where the optimal schedule can be computed. We also show that the overall algorithm is able to schedule as much as 47% more steams than simple heuristics that takes only deadline or interference into account. Of this improvement, 4% - 26% contribution comes from the iterative route update scheme.