Sparse computation, where sparse formats are used to compress nonzero values of big data, are commonly used in real world applications. However, the compiler-based data dependence analysis of sparse computations needed for automatic parallelization is difficult due to usage of indirect memory accesses through index arrays, e.g. col in val[col[j]], in these computations. One use of such data dependence analysis is to find opportunities for array privatization, which is an approach to increase available parallelism in a loop by providing each parallel thread its own copy of arrays where in each iteration the array reads are dominated by array writes in the same iteration. In this paper, we expand opportunities for compile-time array privatization in sparse computations by using newly formulated index array properties and a novel concept we call content-based privatization. Furthermore, we discuss existing opportunities to use our approach for detecting private arrays in existing library implementations of sparse computations.