  This paper studies a mobile edge computing (MEC) assisted integrated sensing
and communication (ISAC), where reconfigurable intelligent surface (RIS) is
used to alleviate the attenuation of communication links during computational
offloading. In this paradigm, the dual function radar and communication
(DFRC)-enabled user equipments (UEs) simultaneously perform radar sensing and
communication tasks, facilitating the offloading of partial computational tasks
to an edge computing server (ECS) through an RIS. To satisfy the critical need
for time-efficient sensing, we investigate the latency minimization problem for
both single-UE and multi-UE scenarios, subject to constraints on UEs' transmit
power, radar signal-to-interference-plus-noise-ratio (SINR), RIS phase shift,
and computation capability. To address the formulated non-convex problem, we
propose an algorithm based on the block coordinate descent (BCD) method to
decouple the original problem into two subproblems, where the computational and
beamforming settings are optimized alternately. Specifically, we employ the
Lagrangian method for the optimization of computational settings. In addition,
two equivalent transformations are applied to transform the objective function
(OF) of the subproblem for active and passive beamforming into a form of
weighted sum-rate. Then, a combination of minimum variance distortionless
response (MVDR), successive convex approximation (SCA),
majorization-minimization (MM), and weighted minimum mean-square error (WMMSE)
techniques are applied to tackle this subproblem. Moreover, a closed-form
solution is obtained in the simplified single UE scenario. Finally, simulation
results substantiate the effectiveness of the proposed system.
