Fast parallel space allocation, estimation, and integer sorting

Abstract

The following problems are shown to be solvable in O(log* n) time with optimal speedup with high probability on a randomized CRCW PRAM using O(n) space: · Space allocation: Given nonnegative integers., allocate nonoverlapping blocks of consecutive memory cells of sizes., from a base segment of O(Σnj=1xj) consecutive memory cells. · Estimation: Given integers in the range 1., compute “good” estimates of the number of occurrences of each value in the range 1. · Semisorting: Given integers, 1.n, in the range 1.n, store the integers 1., n, in an array of O(n) cells such that for all iϵ(1., n), all elements of (j:1≤j≤n and xj=i) occur together, separated only by empty cells. · Integer chain-sorting: Given integers., in the range 1.n, construct a linked list containing the integers 1., n, such that for all, i, jϵ(1., n), if precedes in the list, then xi≤xj. Moreover, given slightly superlinear processor and space bounds, these problems or variations of them can be solved in constant time with high probability. As a corollary of the integer chain-sorting result, it follows that n integers in the range 1.n can be sorted in O(log n/log log n) time with optimal speedup with high probability. © 1995 Academic Press, Inc.