Space Efficient Formats for Structure of Sparse Matrices Based on Tree Structures

Very large sparse matrices are often processed on massively parallel computer systems with distributed memory architectures consisting of tens or hundreds of thousands of processor cores. The problem occurs when we want or need to load/store these matrices from/to a distributed file system. This paper deals with the design of new formats for storing very large sparse matrices suitable for parallel I/O systems. The first one is based on arithmetic coding and the second one is based on binary tree format. We compare the space complexity of common storage formats and our new formats and prove that the latter are considerably more space efficient.