  Coded matrix multiplication is a technique to enable straggler-resistant
multiplication of large matrices in distributed computing systems. In this
paper, we first present a conceptual framework to represent the division of
work amongst processors in coded matrix multiplication as a cuboid partitioning
problem. This framework allows us to unify existing methods and motivates new
techniques. Building on this framework, we apply the idea of hierarchical
coding (Ferdinand & Draper, 2018) to coded matrix multiplication. The
hierarchical scheme we develop is able to exploit the work completed by all
processors (fast and slow), rather than ignoring the slow ones, even if the
amount of work completed by stragglers is much less than that completed by the
fastest workers. On Amazon EC2, we achieve a 37% improvement in average
finishing time compared to non-hierarchical schemes.
