The proposed representation of sparse matrices in compressed form. (Panel A) General scheme for sparse matrices with abstract attributes, where the nonassigned attributes are eliminated by an indicator binary matrix stored in a compressed representation (e.g., multi-BRWT), supporting the rank operation on its columns to enable the access to the corresponding attribute for any given cell of the matrix. These attributes are stored separately, typically in the form of compressed arrays. (Panel B) The scheme applied to a single column with integer values (e.g., k-mer counts) and the query algorithm (e.g., the count of k-mer i is retrieved as A1[rank(B1, i)]). Empty cells in gray represent zeros. (Panel C) The scheme applied to a single column where each cell is a set of numbers, or a tuple (e.g., representing k-mer coordinates). The “zero” attributes (empty sets) are eliminated with an indicator bitmap, and the nonempty sets are encoded in an array that holds all numbers together with a delimiting bitmap.
