Efficient parallel algorithms for selection and searching on sorted matrices

Parallel algorithms for more general versions of the well known selection and searching problems are formulated. The authors look at these problems when the set of elements can be represented as an n ×n matrix with sorted rows and columns. The selection algorithm takes O(lognloglogn log* n) time with O(n/log nlog* n) processors on an EREW PRAM. The searching algorithm takes O(loglogn) time with O(n/loglogn ) processors on a CREW PRAM, which is optimal. The authors also show that no algorithm using at most n log^c n processors, c⩾1, can solve the matrix search problem in time faster than Ω(log log n)