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Related papers: On the extension complexity of scheduling

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Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel and distributed platforms. It is inherently centralized. However, with the increasing number of processors, the cost for managing a single…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-07-20 Marc Tchiboukdjian , Nicolas Gast , Denis Trystram

We consider the classical makespan minimization scheduling problem where $n$ jobs must be scheduled on $m$ identical machines. Using weighted random sampling, we developed two sublinear time approximation schemes: one for the case where $n$…

Data Structures and Algorithms · Computer Science 2026-05-05 Bin Fu , Yumei Huo , Hairong Zhao

This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…

Logic in Computer Science · Computer Science 2025-10-17 S Hitarth , Alessio Mansutti , Guruprerana Shabadi

Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the…

Data Structures and Algorithms · Computer Science 2023-05-16 Sebastian Berndt , Hauke Brinkop , Klaus Jansen , Matthias Mnich , Tobias Stamm

In the moldable job scheduling problem one has to assign a set of $n$ jobs to $m$ machines, in order to minimize the time it takes to process all jobs. Each job is moldable, so it can be assigned not only to one but any number of the equal…

Data Structures and Algorithms · Computer Science 2023-03-03 Kilian Grage , Klaus Jansen , Felix Ohnesorge

The class $(r,2)$-CSP, or simply Max 2-CSP, consists of constraint satisfaction problems with at most two $r$-valued variables per clause. For instances with $n$ variables and $m$ binary clauses, we present an $O(n r^{5+19m/100})$-time…

Discrete Mathematics · Computer Science 2008-03-26 Alexander D. Scott , Gregory B. Sorkin

We consider a natural generalization of scheduling $n$ jobs on $m$ parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches…

Data Structures and Algorithms · Computer Science 2018-09-28 Klaus Jansen , Marten Maack , Alexander Mäcker

We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…

Discrete Mathematics · Computer Science 2023-09-07 Khaoula Bouakaz , Mourad Boudhar

The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…

Data Structures and Algorithms · Computer Science 2017-12-01 Simon Bruggmann , Rico Zenklusen

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…

Data Structures and Algorithms · Computer Science 2026-01-07 Klaus Jansen , Felix Ohnesorge

One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…

Discrete Mathematics · Computer Science 2015-03-17 José Verschae , Andreas Wiese

We study the classical scheduling problem of minimizing the makespan of a set of unit size jobs with precedence constraints on parallel identical machines. Research on the problem dates back to the landmark paper by Graham from 1966 who…

Data Structures and Algorithms · Computer Science 2025-01-17 Syamantak Das , Andreas Wiese

In online makespan minimization a sequence of jobs $\sigma = J_1,..., J_n$ has to be scheduled on $m$ identical parallel machines so as to minimize the maximum completion time of any job. We investigate the problem with an essentially new…

Data Structures and Algorithms · Computer Science 2013-04-23 Susanne Albers , Matthias Hellwig

We consider the classic problem of scheduling jobs with precedence constraints on a set of identical machines to minimize the makespan objective function. Understanding the exact approximability of the problem when the number of machines is…

Data Structures and Algorithms · Computer Science 2020-04-30 Janardhan Kulkarni , Shi Li , Jakub Tarnawski , Minwei Ye

The Makespan Scheduling problem is an extensively studied NP-hard problem, and its simplest version looks for an allocation approach for a set of jobs with deterministic processing times to two identical machines such that the makespan is…

Neural and Evolutionary Computing · Computer Science 2025-04-25 Feng Shi , Daoyu Huang , Xiankun Yan , Frank Neumann

In this work, the online printing shop scheduling problem is considered. This challenging real problem, that appears in the nowadays printing industry, can be seen as a flexible job shop scheduling problem with sequence flexibility in which…

Optimization and Control · Mathematics 2022-02-22 Willian T. Lunardi , Ernesto G. Birgin , Philippe Laborie , Débora P. Ronconi , Holger Voos

We consider Johnson's rule for minimizing the makespan in the two-machine flow shop problem. Although its worst-case time complexity is O(n log n), we show that it is possible to detect in linear time whether a full sorting of jobs can be…

Optimization and Control · Mathematics 2026-01-08 Federico Della Croce , Quentin Schau

Integer Linear Programming with $n$ binary variables and $m$ many $0/1$-constraints can be solved in time $2^{\tilde O(m^2)} \text{poly}(n)$ and it is open whether the dependence on $m$ is optimal. Several seemingly unrelated problems,…

Data Structures and Algorithms · Computer Science 2024-09-06 Lars Rohwedder , Karol Węgrzycki

This paper considers scheduling on identical machines. The scheduling objective considered in this paper generalizes most scheduling minimization problems. In the problem, there are $n$ jobs and each job $j$ is associated with a…

Data Structures and Algorithms · Computer Science 2019-04-23 Benjamin Moseley

We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…

Data Structures and Algorithms · Computer Science 2020-10-02 Jesper Nederlof , Céline Swennenhuis