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Terminal devices (TDs) connect to networks through access points (APs)integrated into the edge server. This provides a prerequisite for TDs to uploadtasks to cloud data centers or offload them to edge servers for execution. Inthis process, signal coverage, data transmission, and task execution consumeenergy, and the energy consumption of signal coverage increases sharply as theradius increases. Lower power leads to less energy consumption in a given timesegment. Thus, power control for APs is essential for reducing energyconsumption. Our objective is to determine the power assignment for each APwith same capacity constraints such that all TDs are covered, and the totalpower is minimized. We define this problem as a \emph{minimum power capacitatedcover } (MPCC) problem and present a \emph{minimum local ratio} (MLR) powercontrol approach for this problem to obtain accurate results in polynomialtime. Power assignments are chosen in a sequence of rounds. In each round, wechoose the power assignment that minimizes the ratio of its power to the numberof currently uncovered TDs it contains. In the event of a tie, we pick anarbitrary power assignment that achieves the minimum ratio. We continuechoosing power assignments until all TDs are covered. Finally, variousexperiments verify that this method can outperform another greedy-based way.

A Local-Ratio-Based Power Control Approach for Capacitated Access Points in Mobile Edge Computing