On the Computation of 2-Dimensional Recurrence Equations

TL;DR

This paper presents a method to reduce 2D recurrence problems to 1D, enabling efficient computation using the Kogge and Stone algorithm with logarithmic time complexity.

Contribution

It introduces a novel reduction technique transforming 2D recurrence equations into 1D form suitable for parallel algorithms.

Findings

Reduction from 2D to 1D recurrence is feasible

Computation time scales with log_2(2n-1)

Applicable to parallel processing algorithms

Abstract

The paper demonstrates how a 2-dimensional recurrence problem can be reduced to a mono-dimensional recurrence problem where the Kogge and Stone algorithm is applicable, with the computation time - excluding the reduction step - becoming proportional to $log_2(2n-1)$.