An empirical estimation for time and memory algorithm complexities: newly developed R package

TL;DR

GuessCompx is an R package that empirically estimates the time and memory complexities of algorithms using sample data, fitting complexity functions and predicting resource usage without needing the target code.

Contribution

It introduces a novel, practical R tool for empirical complexity estimation that does not require access to the algorithm's code, filling a gap in computational complexity analysis.

Findings

Successfully fits various complexity functions to empirical data

Predicts total computation time and memory usage accurately

Provides visualizations and significance tests for complexity assessment

Abstract

This article introduces GuessCompx which is an R package that performs an empirical estimation on the time and memory complexities of an algorithm or a function. It tests multiple increasing-sizes samples of the user's data and attempts to fit one of seven complexity functions: O(N), O(N^2), O(log(N)), etc. Based on a best fit procedure using LOO-MSE (leave one out-mean squared error), it also predicts the full computation time and memory usage on the whole dataset. Conceptually, it relies on the base R functions system.time and memory.size, the latter being only suitable for Windows users. Together with this results, a plot and a significance test are returned. Complexity is assessed with regard to the user's actual dataset through its size (and no other parameter). This article provides several examples demonstrating several cases (e.g., distance function, time series and custom function) and optimal parameters tuning. The subject of the empirical computational complexity has been relatively little studied in computer sciences, and such a package provides a reliable, convenient and simple procedure for estimation process. Further, the package does not require to have the code of the target function.