Matrix multiplication is a fundamental building block in various distributed computing algorithms. In order to multiply large matrices, it is common practice to distribute the computation into multiple tasks running on different nodes. In order to tolerate stragglers among such nodes, various coding schemes have been proposed by adding additional coded tasks. However, most existing coding schemes for matrix multiplication are constructed for only one matrix multiplication, while batch matrix multiplication is common in large-scale distributed computing workloads. In this paper, we propose Rook Coding (RC), a novel polynomial-based coding framework for computing the multiplication of$n$pairs of matrices in batch. Designed to achieve lower encoding time in practice, we construct RC as polynomials of much simpler forms than existing coding schemes for batch matrix multiplication, achieving a recovery threshold of$O(n^{\log _{2} ~3})$. Compared to existing coding schemes, RC achieves a lower encoding complexity in practice, because of its simpler forms in the encoding polynomials. Through extensive experiments, we show that RC can save the time of the whole job thanks to its low overhead of encoding.

The matrix multiplication is a fundamental building block in many machine learning models. As the input matrices may be too large to be multiplied on a single server, it is common to split input matrices into multiple submatrices and execute the multiplications on different servers. However, in a distributed infrastructure it is common to observe stragglers whose performance is lower than other servers at some time. In order to mitigate the adversarial effects of potential stragglers, various coding schemes for the distributed matrix multiplication have been recently proposed. While most existing works have only considered the simplest case where only two matrices are multiplied, we investigate a more general case in this paper where multiple matrices are multiplied, and propose a coding scheme that the result can be directly decoded in one round, instead of in multiple rounds of computation. Compared to completing the matrix chain multiplication in multiple rounds, our coding scheme can achieve significant savings of completion time by up to 90.3%.