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

Marc Agenis-Nevers; Neeraj Dhanraj Bokde; Zaher Mundher Yaseen; Mayur Shende

doi:10.1007/s11042-020-09471-8

Home/Archive/arXiv

arXiv · 1911.01420

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

Marc Agenis-Nevers·Neeraj Dhanraj Bokde·Zaher Mundher Yaseen·Mayur Shende

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.DS

Keep this discovery

BibTeX RIS

Marc Agenis-Nevers, Neeraj Dhanraj Bokde, Zaher Mundher Yaseen, Mayur Shende. 2019-11-04. An empirical estimation for time and memory algorithm complexities: newly developed R package. https://doi.org/10.1007/s11042-020-09471-8

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗