  In this paper, we consider the mobile edge offloading scenario consisting of
one mobile device (MD) with multiple independent tasks and various remote edge
devices. In order to save energy, the user's device can offload the tasks to
available access points for edge computing. Data compression is applied to
reduce offloaded data size prior to wireless transmission to minimize the
execution latency. The problem of jointly optimizing the task allocation
decision and the data compression ratio to minimize the total tasks' execution
latency and the MD's energy consumption concurrently is proposed. We show that
the design problem is a non-convex optimization one but it can be transformed
into a convex one through a semidefinite relaxation (SDR) based approach.
Numerical simulations demonstrate the outperformance of the proposed scheme
compared to the benchmark one.
