On the asymptotic behavior of some Algorithms
Philippe Robert (RAP UR-R)

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.
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