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In this paper, we consider the problem of minimizing the completion delay for instantly decodable network coding (IDNC) in wireless multicast and broadcast scenarios. We are interested in this class of network coding due to its numerous benefits, such as low decoding delay, low coding and decoding complexities, and simple receiver requirements. We first extend the IDNC graph, which represents all feasible IDNC coding opportunities, to efficiently operate in both multicast and broadcast scenarios. We then formulate the minimum completion delay problem for IDNC as a stochastic shortest path (SSP) problem. Although finding the optimal policy using SSP is intractable, we use this formulation to draw the theoretical guidelines for the policies that can minimize the completion delay in IDNC. Based on these guidelines, we design a maximum weight clique selection algorithm, which can efficiently reduce the IDNC …