Optimal parallel selection in sorted matrices

We present a parallel algorithm running in time O(log m log^{(Black star)} m (log log m + log(n/m))) time and O(m log(n/m)) operations on an EREW PRAM for the problem of selection in an m × n matrix with sorted rows and columns, m ≤ n. Our algorithm generalizes the result of Sarnath and He (1992) for selection in a sorted matrix of equal dimensions, and thus answers the open question they posted. The algorithm is work-optimal thus improving upon the result in (Sarnath and He, 1992) for the case of square matrices as well. Our algorithm can be generalized to solve the selection problem on a set of sorted matrices of arbitrary dimensions.