“…Such aspects were mentioned, but not elaborated, in our recent companion paper [78]. We here aim to contribute in this direction, by providing a detailed analysis for a set of speci c operations and sketching transforms which are critical for various important problems in RandNLA and beyond, for example leverage scores computation [36,25,67,4,58,29,28,88,78], least squares regression [75,67,85,72,35,8,64,70], column subset selection [23,17,10,24,77,78], and rank computation [76,23,22,15,62]. Speci cally, given a talland-skinny matrix 𝐴 ∈ R 𝑛×𝑑 with 𝑛 𝑑, we present parallel algorithms, data structures and a numerical library for the following set of operations, all of which can be seen as special cases of sparse matrix multiplication:…”