New approaches to storing and manipulating multi-dimensional sparse arrays

In this paper, we introduce some storage schemes for multi-dimensional sparse arrays (MDSAs) that handle the sparsity of the array with two primary goals; reducing the storage overhead and maintaining efficient data element access. Four schemes are proposed. These are: i.) The PATRICIA trie compressed storage method (PTCS) which uses PATRICIA trie to store the valid non-zero array elements; ii.)The extended compressed row storage (xCRS) which extends CRS method for sparse matrix storage to sparse arrays of higher dimensions and achieves the best data element access efficiency of all the methods; iii.) The bit encoded xCRS (BxCRS) which optimizes the storage utilization of xCRS by applying data compression methods with run length encoding, while maintaining its data access efficiency; and iv.) a hybrid approach that provides a desired balance between the storage utilization and data manipulation efficiency by combining xCRS and the Bit Encoded Sparse Storage (BESS). These storage schemes were evaluated and compared on three basic array operations; constructing the storage scheme, accessing a random element and retrieving a sub-array, using a set of synthetic sparse multi-dimensional arrays.