Variable Coded Batch Matrix Multiplication

A majority of coded matrix-matrix computation literature has broadly focused in two directions: matrix partitioning for computing a single task and batch processing multiple distinct tasks. While these works provide codes with good straggler resilience fast decoding their problem spaces, would not be able to take advantage the natural redundancy re-using matrices across jobs. In this paper, we introduce Variable Coded Distributed Batch Matrix Multiplication (VCDBMM) which tasks distributed system perform multiplication where are necessarily among Inspired part by Cross-Subspace Alignment codes, develop Flexible Alignments (FCSA) that flexible enough utilize redundancy. We full characterization FCSA allow wide variety complexities including decoding. theoretically demonstrate that, under certain practical conditions, within factor 2 optimal solution when it comes resilience. Furthermore, our simulations can achieve even better optimality gaps practice, going as low 1.7.