Bivariate Polynomial Coding for Efficient Distributed Matrix Multiplication

Coded computing is an effective technique to mitigate “stragglers” in large-scale and distributed matrix multiplication. In particular, univariate polynomial codes have been shown be straggler mitigation by making the computation time depend only on fastest workers. However, these schemes completely ignore work done straggling workers resulting a waste of computational resources. To reduce amount left unfinished at workers, one can further decompose multiplication task into smaller sub-tasks, assign multiple sub-tasks each worker, possibly heterogeneously, better fit their particular storage capacities. this work, we propose novel family bivariate codes efficiently exploit carried out We show that bivariate bring significant advantages terms upload communication costs efficiency, measured number computed per worker. two coding schemes. The first exploits fact interpolation always possible rectangular grid evaluation points. obtain such points cost adding some redundant computations. For second scheme, relax decoding constraints require decodability for almost all choices present sets satisfying conditions certain configurations Our numerical results considerably reduces average believe opens up new class previously unexplored efficient coded computation.