Normalized Delivery Time of Wireless MapReduce

We consider a full-duplex wireless Distributed Computing (DC) system under the MapReduce framework. New upper and lower bounds on the optimal tradeoff between Normalized Delivery Time (NDT) and computation load are presented. The upper bound strictly improves over the previous reported upper bounds and is based on two novel interference alignment (IA) schemes tailored to the interference cancellation capabilities of the nodes. Our second IA scheme additionally applies a zero-forcing strategy that allows to accumulate all interference at any of the nodes on the same (small) subspace, leaving the remaining space for useful signals. The lower bound is proved through information-theoretic converse arguments based on carefully chosen multi-access channel (MAC) type arguments and by finding solutions to the optimization problems resulting from these arguments. The lower bound matches an existing upper bound based on zero-forcing and interference cancellation (but no IA) in the regime where each node can store at least half of the files. While optimal in this regime, zero-forcing and interference cancellation are not sufficient to obtain the optimal NDT in scenarios where each node cannot store half of the files. This follows from the previously established optimal NDT under zero-forcing and interference cancellation and our new IA-schemes.