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In this paper, we consider the problem of minimizing the mean completion delay in wireless broadcast for instantly decodable network coding. We first formulate the problem as a stochastic shortest path (SSP) problem. Although finding the packet selection policy using SSP is intractable, we use this formulation to draw the theoretical properties of efficient selection algorithms. Based on these properties, we propose a simple online selection algorithm that efficiently minimizes the mean completion delay of a frame of broadcast packets, compared to the random and greedy selection algorithms with a similar computational complexity. Simulation results show that our proposed algorithm indeed outperforms these random and greedy selection algorithms.