On the asymptotic behavior of some Algorithms

TL;DR

This paper introduces a straightforward method to analyze the long-term behavior of algorithms with tree structures, revealing oscillations and providing explicit formulas for periodic functions without complex analysis.

Contribution

It presents a novel, simpler approach to study asymptotic oscillations in algorithms with tree structures, avoiding complex analysis techniques.

Findings

Precise analysis of asymptotic oscillations

Explicit representation of periodic functions

Simplified approach to asymptotic behavior

Abstract

A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis techniques as it is usually done in this context. A new explicit representation of periodic functions involved is obtained at the same time.