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Abstract: Characterized by its distributive deployment, mobile edge computing (MEC) aims for providing the short-term response to diverse computing tasks. However, the benefit of MEC is not fully exploited, especially when the link used for offloading computational tasks is hampered. Since the recent time, intelligent reflecting surface (IRS) has been proposed to be a disruptive technology for enhancing both the spectral and energy efficiency. It comprises a large number of passive reflecting elements, each of which may impose a phase shift on the incident signal, thus collaboratively refining the signal propagation environment. In this paper, we investigate the beneficial role of the IRS in the MEC system, where single-antenna devices may opt to offload a fraction of their computational tasks to the edge computing node via a multi-antenna access point. We formulate a latency-minimization problem for both the single-device and multi-device scenarios, subject to both the the total edge computing resource and IRS phase shift constraints. To tackle this problem, we invoke the block coordinate descent (BCD) technique to decouple the original problem into several subproblems and alternatively optimize the computation offloading volume, the edge computing resource allocation, the multi-user detection matrix and the IRS phase shift vector. For each subproblem, we provide the corresponding solution. Extensive numerical results validate our algorithms and quantify the impact of the IRS on the latency performance in MEC systems.