Distributed Computing with Heterogeneous Communication Constraints: The Worst-Case Computation Load and Proof by Contradiction

We consider a distributed computing framework where the distributed nodes have different communication capabilities, motivated by the heterogeneous networks in data centers and mobile edge computing systems. Following the structure of MapReduce, this framework consists of Map computation phase, Shuffle phase, and Reduce computation phase. The Shuffle phase allows distributed nodes to exchange intermediate values, in the presence of heterogeneous communication bottlenecks for different nodes (heterogeneous communication load constraints). Focusing on two-node and three-node (K=2, 3) distributed computing systems with heterogeneous communication load constraints, in this work we characterize the minimum total computation load, as well as the minimum worst-case computation load for some cases. The worst-case computation load depends on the computation load of a node with the heaviest job. Therefore, by minimizing the worst-case computation load it could potentially minimize the system latency. We show an interesting insight that, for some cases, there is a tradeoff between the minimum total computation load and the minimum worst-case computation load, in the sense that both cannot be achieved at the same time. The achievability schemes are proposed with careful design on the file assignment and data shuffling. Finally, beyond the cut-set bound, a novel converse is proposed using the proof by contradiction.