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Mobile-edge computing (MEC) is expected to provide low-latency computationservice for wireless devices (WDs). However, when WDs are located at cell edgeor communication links between base stations (BSs) and WDs are blocked, theoffloading latency will be large. To address this issue, we propose anintelligent reflecting surface (IRS)-assisted cell-free MEC system consistingof multiple BSs and IRSs for improving the transmission environment.Consequently, we formulate a min-max latency optimization problem by jointlydesigning multi-user detection (MUD) matrices, IRSs' reflecting beamformingvectors, WDs' transmit power and edge computing resource, subject toconstraints on edge computing capability and IRSs phase shifts. To solve it, analternating optimization algorithm based on the block coordinate descent (BCD)technique is proposed, in which the original non-convex problem is decoupledinto two subproblems for alternately optimizing computing and communicationparameters. In particular, we optimize the MUD matrix based on the second-ordercone programming (SOCP) technique, and then develop two efficient algorithms tooptimize IRSs' reflecting vectors based on the semi-definite relaxation (SDR)and successive convex approximation (SCA) techniques, respectively. Numericalresults show that employing IRSs in cell-free MEC systems outperformsconventional MEC systems, resulting in up to about 60% latency reduction can beattained. Moreover, numerical results confirm that our proposed algorithmsenjoy a fast convergence, which is beneficial for practical implementation.

Min-Max Latency Optimization for IRS-aided Cell-Free Mobile Edge Computing Systems