The all nearest smaller values problem is deened as follows. Let A = (a 1 ; a 2 ; : : :; a n) be n elements drawn from a totally ordered domain. For each a i , 1 i n, nd the two nearest elements in A that are smaller than a i (if such exist): the left nearest smaller element a j (with j < i) and the right nearest smaller element a k (with k > i). We give an O(loglog n) time optimal parallel alg...