Related papers: Parameterized Complexity of Scheduling Problems in…
In this paper, we consider the parameterized complexity of the following scheduling problem. We must schedule a number of jobs on $m$ machines, where each job has unit length, and the graph of precedence constraints consists of a set of…
We study the problem of non-preemptively scheduling $n$ jobs, each job $j$ with a release time $t_j$, a deadline $d_j$, and a processing time $p_j$, on $m$ parallel identical machines. Cieliebak et al. (2004) considered the two constraints…
In this study, we investigate a robust single-machine scheduling problem under processing time uncertainty. The uncertainty is modeled using the budgeted approach, where each job has a nominal and deviation processing time, and the number…
We study the parameterized complexity of scheduling unit-time jobs on parallel, identical machines under generalized precedence constraints for minimization of the makespan and the sum of completion times. In our setting, each job is…
Since its development in the early 90's, parameterized complexity has been widely used to analyze the tractability of many NP-hard combinatorial optimization problems with respect to various types of problem parameters. While the generic…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open…
The Windows Scheduling Problem, also known as the Pinwheel Problem, is to schedule periodic jobs subject to their processing frequency demands. Instances are given as a set of jobs that have to be processed infinitely often such that the…
We study the fundamental scheduling problem $1\mid r_j\mid\sum w_j U_j$: schedule a set of $n$ jobs with weights, processing times, release dates, and due dates on a single machine, such that each job starts after its release date and we…
In this work, we study the computational (parameterized) complexity of $P \mid r_j, p_j=p \mid \sum_j w_j U_j$. Here, we are given $m$ identical parallel machines and $n$ jobs with equal processing time, each characterized by a release…
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…
Negatively answering a question posed by Mnich and Wiese (Math. Program. 154(1-2):533-562), we show that P2|prec,$p_j{\in}\{1,2\}$|$C_{\max}$, the problem of finding a non-preemptive minimum-makespan schedule for precedence-constrained jobs…
Scheduling theory is an old and well-established area in combinatorial optimization, whereas the much younger area of parameterized complexity has only recently gained the attention of the community. Our aim is to bring these two areas…
We provide new (parameterized) computational hardness results for Interval Scheduling on Unrelated Machines. It is a classical scheduling problem motivated from just-in-time or lean manufacturing, where the goal is to complete jobs exactly…
In this paper, we study the parameterized complexity of several variants of scheduling with precedence constraints between jobs. Namely, we consider the single machine setting with delay values on top of the precedence constraints. Such…
In contrast to the fixed parameter analysis (FPA), in the variable parameter analysis (VPA) the value of the target problem parameter is not fixed, it rather depends on the structure of a given problem instance and tends to have a favorable…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
In this paper we study the classical single machine scheduling problem where the objective is to minimize the total weight of tardy jobs. Our analysis focuses on the case where one or more of three natural parameters is either constant or…
The $1|B,r_j|\sum w_jU_j$ scheduling problem takes as input a batch setup time $\Delta$ and a set of $n$ jobs, each having a processing time, a release date, a weight, and a due date; the task is to find a sequence of batches that minimizes…
We consider scheduling on identical and unrelated parallel machines with job assignment restrictions. These problems are NP-hard and they do not admit polynomial time approximation algorithms with approximation ratios smaller than $1.5$…