Abstract: We are concerned with designing feedback-based adaptive Instantly Decodable Network Coding (IDNC) schemes with the aim of minimizing retransmission times in wireless multicast and broadcast scenarios. In this paper, we first analyze the multiple factors influencing the transmission times and give the quantitative formula. Meantime, we introduce the concept of Cache-based Instantly Decodable Network Coding (C-IDNC) that the correctly received undecodable retransmission packets are waited in the cache for a future network decoding opportunity rather than delete. Then, we construct an IDNC graph, and formulate the retransmission times minimization problem as an max-weight search problem and propose efficient algorithms for finding its optimal solution. Further, we propose a heuristic algorithms with worst case linear execution complexity based on sorting and iteration. Simulation results show that our proposed algorithms significantly reduce the IDNC retransmission times compared to previous works.