Narrow Results

In this paper, a parallel algorithm for all nearest smallers problem without using doubly logarithmic tree is described. It is shown that using only $O(loglogn)$ time routines for merging and prefix minima, we can easily get an $O(loglogn)$ time parallel algorithm for the all Nearest Smallers problem.

We prove that prefix sums of n integers of at most b bits can be found on a COMMON CRCW PRAM in time with a linear time-processor product. The algorithm is optimally fast, for any polynomial number of processors. In particular, if the time taken is . This is a generalisation of previous result. The previous time algorithm was valid only for O(log n)-bit numbers. Application of this algorithm to r-way parallel merge sort algorithm is also considered.

We also consider a more realistic PRAM variant, in which the word size, m, may be smaller than b (m≥log n). On this model, prefix sums can be found in optimal time.