Over-the-Air Computation of Large-Scale Nomographic Functions in MapReduce Over the Edge Cloud Network

Abstract

Motivated by increasing powerful edge devices with data-intensive computing and limited storage size, we study a MapReduce-based wireless distributed computing framework by allocating a portion of files in the remote data center to the network edge and utilizing computation and memory resources at the edge. Our framework is composed of three step phases: 1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Map</i> ; 2) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Shuffle</i> ; and 3) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Reduce</i> . However, in the data shuffling stage, shuffling many data accounts for a large amount of the total running time over wireless interference networks will degrade its performance. Moreover, data shuffling between pervasive edge devices with limited spectrum bandwidth is very challenging. Today, many devices focus on computing functions rather than collecting all the individual wireless data centers. Therefore, we can use over-the-air computation (AirComp) technology to reliably compute multiple target functions by harnessing interference in the multiple-access channel with a higher computation efficiency than the traditional orthogonal multiaccess scheme that combats interference. We study a mixed-timescale optimization of the transmitting–receiving (Tx-Rx) policy and file allocation to minimize the averaged computation mean-squared error (MSE) under the power constraint of each device. File allocation control is adaptive to the long-term statistical channel state information (CSI), while the Tx-Rx policy is adaptive to the CSI and file allocation strategy. We decompose the problem into a short-term Tx-Rx policy and a long-term file allocation control problem to tackle the joint nonconvex optimization. Simulation results indicate the effectiveness of our proposed two-timescale algorithm and the advantages of our computation framework over the state-of-the-art baselines.