Hierarchical coded matrix multiplication in heterogeneous multi-hop networks

The performance of distributed computing is restricted by the slowest worker nodes, known as stragglers, in the system. Coded computation has emerged as an efficient technique to mitigate the straggler effects in distributed computing. Most existing works only considered the computation straggler for single-hop networks. However, in multi-hop networks, the straggler effects will occur not only on worker nodes but also on relay nodes. In this paper, we consider a heterogeneous multi-hop network. The nodes in the network are heterogeneous, i.e., their computation capacities and transmission capacities are different. We propose a hierarchical coding scheme for such a network. Firstly, we reorganize it into a hierarchical network containing multiple layers. Each layer in the network consists of several groups. Then, a new hierarchical coding scheme is proposed, where coding is applied to each group to mitigate the stragglers. By taking both the computation time and transmission time into consideration, the overall task completion time is derived. To improve the performance of the network, heterogeneous hierarchical coded computation (HHCC) algorithm is proposed to provide an asymptotically optimal task allocation strategy. Compared with existing uniform uncoded, load balanced uncoded, and heterogeneous coded matrix multiplication schemes, HHCC has significant improvement