An O(1) Solution to the Prefix Sum Problem on a Specialized Memory Architecture

TL;DR

This paper presents an O(1) time solution for the prefix sum problem on a specialized memory architecture where bits can be shared, and also provides optimal solutions for two variants in the comparison-based model.

Contribution

It introduces an O(1) time algorithm for prefix sums on shared-bit memory architecture and optimal solutions for variants in the comparison model.

Findings

O(1) update and retrieval on shared-bit memory architecture

Optimal $ heta( ext{lg} N)$ solutions for problem variants in comparison model

Advances understanding of prefix sum solutions in specialized memory models

Abstract

In this paper we study the Prefix Sum problem introduced by Fredman. We show that it is possible to perform both update and retrieval in O(1) time simultaneously under a memory model in which individual bits may be shared by several words. We also show that two variants (generalizations) of the problem can be solved optimally in $\Theta(\lg N)$ time under the comparison based model of computation.