Generalized parallel selection in sorted matrices

This paper presents a parallel algorithm running in time O(log m log* m(log log m+log(n/m))) time on an EREW PRAM with O(m/(log m log* m)) processors 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 for selection in a sorted matrix of equal dimensions, and thus answers the open question they posted. The algorithm is work-optimal when n≥m log m, and near optimal within O(log log m) factor otherwise. We show that our algorithm can be generalized to solve the selection problem on a set of sorted matrices of arbitrary dimensions.