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 (∑) 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 , ..., in the range 1.., store the integers 1, ..., in an array of () cells such that for all ∈ {1, ...,}, all elements of {: 1 ≤ ≤ and = } occur together, separated only by empty cells. Integer chain-sorting: Given integers , ..., in the range 1.., construct a linked list containing the integers 1, ..., such that for all , ∈ {1, ..., }, if precedes in the list, then ≤ .

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