Parallel Search with Extended Fibonacci Primitive

TL;DR

This paper models random search patterns in secondary storage as an extended Fibonacci series and evaluates parallel search primitives, demonstrating pointer jumping as the most efficient method in a PRAM model.

Contribution

Introduces a novel modeling of random walks using extended Fibonacci series and compares parallel search primitives in a PRAM environment.

Findings

Pointer jumping primitive outperforms others in efficiency.

Modeling random walk with Fibonacci series offers new analytical insights.

Simulation results validate the effectiveness of the proposed primitives.

Abstract

Search pattern experienced by the processor to search an element in secondary storage devices follows a random sequence. Formally, it is a random walk and its modeling is crucial in studying performance metrics like memory access time. In this paper, we first model the random walk using extended Fibonacci series. Our simulation is done on a parallel computing model (PRAM) with EREW strategy. Three search primitives are proposed under parallel computing model and each primitive is thoroughly tested on an array of size $10^7$ with the size of random walk being $10^4$. Our findings reveal that search primitive with pointer jumping is better than the other two primitives. Our key contribution lies in modeling random walk as an extended Fibonacci series generator and simulating the same with various search primitives.