Lecture 8 : Pseudorandomness and Sketching

Thus far we have been considered linear sketching algorithms for data streams where the sketch is given by an S ×M random matrix A where S is small and at most the space bound and M is huge. So far, as in the Count-Min, Count, and Tug-of-War sketches, the matrix A has been defined implicitly using pairwise or 4-wise independence using a very small number of random bits that contribute only a small amount to the space bound. If we required truly M -wise independent random entries in A then it would cost too much to store them during the algorithm.