Optimal representation of sparse matrices

This paper introduces a novel data structure used to store sparse matrices optimally – minimizing the space of the matrix representation and the time complexity of an access to the matrix element. The size of our data structure is close to the information theoretic minimum – it differs in the second order term – and permits constant access to the matrix elements and a constant amortized time with a high probability for the insertion of a new element in the matrix and a deletion of an existing element. We tested our solution in a setup of mixed model equations that is used for genetic evaluation of breeding values and estimation of dispersion parameters. The coefficient matrices are large (over 1 mio. of equations) and sparse. The new algorithm reduced the number of accesses to the data structure (at most two accesses) and reduced the time for building the equation system, especially in theworst cases.