On expanding the toolkit of locality-based coded computation to the coordinates of inputs.

The tail latency of large-scale distributed computations, such as matrix multiplication, is adversely affected by unavailable workers. A technique called "coded computation" alleviates this problem by using extra workers to evaluate the function being computed at coded inputs and substitute the extra workers for the unavailable ones. Most of the literature on coded computation of multivariate polynomials applies to arbitrary inputs and ignores the structure of the inputs. However, a recent work introduced a locality-based coded computation framework and showed how to leverage the structure of inputs to reduce the overhead of coded computation. Our work expands the toolkit of locality-based approaches to coded computation beyond linearly dependent input points for the class of m-homogeneous polynomials. Specifically, we present new methods to exploit the structure of each coordinate of the inputs. Finally, we apply our new tools to multiplying upper (or lower) triangular matrices and show a reduction in the number of workers needed compared to the best known coded computation schemes.