A Practical 73/50 Approximation for Contiguous Monotone Moldable Job Scheduling

Klaus Jansen; Felix Ohnesorge

Home/Archive/arXiv

arXiv · 2601.02836

A Practical 73/50 Approximation for Contiguous Monotone Moldable Job Scheduling

Klaus Jansen·Felix Ohnesorge

View original source ↗Read source document ↗Export metadata ↓

Abstract

In moldable job scheduling, we are provided $m$ identical machines and $n$ jobs that can be executed on a variable number of machines. The execution time of each job depends on the number of machines assigned to execute that job. For the specific problem of monotone moldable job scheduling, jobs are assumed to have a processing time that is non-increasing in the number of machines. The previous best-known algorithms are: (1) a polynomial-time approximation scheme with time complexity $\Omega(n^{g(1/\varepsilon)})$, where $g(\cdot)$ is a super-exponential function [Jansen and Th\"ole '08; Jansen and Land '18], (2) a fully polynomial approximation scheme for the case of $m \geq 8\frac{n}{\varepsilon}$ [Jansen and Land '18], and (3) a $\frac{3}{2}$ approximation with time complexity $O(nm\log(mn))$ [Wu, Zhang, and Chen '23]. We present a new practically efficient algorithm with an approximation ratio of $\approx (1.4593 + \varepsilon)$ and a time complexity of $O(nm \log \frac{1}{\varepsilon})$. Our result also applies to the contiguous variant of the problem. In addition to our theoretical results, we implement the presented algorithm and show that the practical performance is significantly better than the theoretical worst-case approximation ratio.

Explore related subjects

cs.DS

Keep this discovery

BibTeX RIS

Klaus Jansen, Felix Ohnesorge. 2026-01-06. A Practical 73/50 Approximation for Contiguous Monotone Moldable Job Scheduling. https://arxiv.org/abs/2601.02836

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↗