We study the off-line efficient mobile edge computing (EMEC) problem for a joint computing to process a task both locally and remotely with the objective of minimizing the finishing time. When computing remotely, the time will include the communication and computing time. We first describe the time model, formulate EMEC, prove NPcompleteness of EMEC, and show the lower bound. We then provide an integer linear programming (ILP) based algorithm to achieve the optimal solution and give results for small-scale cases. A fully polynomialtime approximation scheme (FPTAS), named Approximation Partition (AP), is provided through converting ILP to the subset sum problem. Numerical results show that both the total data length and the movement have great impact on the time for mobile edge computing. Numerical results also demonstrate that our AP algorithm obtain the finishing time, which is close to the optimal solution.

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