Coded Sequential Matrix Multiplication For Straggler Mitigation

In this work, we consider a sequence of $J$ matrix multiplication jobs which needs to be distributed by a master across multiple worker nodes. For $i\in \{1,2,\ldots,J\}$, job-$i$ begins in round-$i$ and has to be completed by round-$(i+T)$. Previous works consider only the special case of $T=0$ and focus on coding across workers. We propose here two schemes with $T>0$, which feature coding across workers as well as the dimension of time. Our first scheme is a modification of the polynomial coding scheme introduced by Yu et al. and places no assumptions on the straggler model. Exploitation of the temporal dimension helps the scheme handle a larger set of straggler patterns than the polynomial coding scheme, for a given computational load per worker per round. The second scheme assumes a particular straggler model to further improve performance (in terms of encoding/decoding complexity). We develop theoretical results establishing (i) optimality of our proposed schemes for a certain class of straggler patterns and (ii) improved performance for the case of i.i.d. stragglers. These are further validated by experiments, where we implement our schemes to train neural networks.