Distributed Matrix Tiling Using A Hypergraph Labeling Formulation

Abstract

Partitioning large matrices is an important problem in distributed linear algebra computing (used in ML among others). Briefly, our goal is to perform a sequence of matrix algebra operations in a distributed manner (whenever possible) on these large matrices. However, not all partitioning schemes work well with different matrix algebra operations and their implementations (algorithms). This is a type of data tiling problem. In this work we consider a theoretical model for a version of the matrix tiling problem in the setting of hypergraph labeling. We prove some hardness results and give a theoretical characterization of its complexity on random instances. Additionally we develop a greedy algorithm and experimentally show its efficacy.