Related papers: A $(4/3+\varepsilon)$-Approximation for Preemptive…
We are concerned with the problem of scheduling $n$ jobs onto $m$ identical machines. Each machine has to be in operation for a prescribed time, and the objective is to minimize the total machine working time. Precisely, let $c_i$ be the…
Motivated by modern parallel computing applications, we consider the problem of scheduling parallel-task jobs with heterogeneous resource requirements in a cluster of machines. Each job consists of a set of tasks that can be processed in…
We consider here the MultiBot problem for the scheduling and the resource parametrization of jobs related to the production or the transportation of different products inside a given time horizon. Those jobs must meet known in advance…
Parameterizing by the largest processing time $p_{max}$ and the number of different job processing times $d$, we propose a proximity technique for High-Multiplicity Scheduling on Uniform Machines for the objectives Makespan Minimization…
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…
Scheduling with testing is a recent online problem within the framework of explorable uncertainty motivated by environments where some preliminary action can influence the duration of a task. Jobs have an unknown processing time that can be…
Machine scheduling problems involving conflict jobs can be seen as a constrained version of the classical scheduling problem, in which some jobs are conflict in the sense that they cannot be proceeded simultaneously on different machines.…
We introduce the following elementary scheduling problem. We are given a collection of n jobs, where each job has an integer length as well as a set Ti of time intervals in which it can be feasibly scheduled. Given a parameter B, the…
We study ordinal makespan scheduling on small numbers of identical machines, with respect to two parallel solutions. In ordinal scheduling, it is known that jobs are sorted by non-increasing sizes, but the specific sizes are not known in…
We study the precedence-constrained resource scheduling problem [SICOMP'75]. There are $n$ jobs where each job takes a certain time to finish and has a resource requirement throughout the execution time. There are precedence among the jobs.…
An optimal solution to the problem of scheduling real-time tasks on a set of identical processors is derived. The described approach is based on solving an equivalent uniprocessor real-time scheduling problem. Although there are other…
In this paper the problem of scheduling of jobs on parallel machines under incompatibility relation is considered. In this model a binary relation between jobs is given and no two jobs that are in the relation can be scheduled on the same…
Consider a scheduling problem in which jobs need to be processed on a single machine. Each job has a weight and is composed of several operations belonging to different families. The machine needs to perform a setup between the processing…
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…
Scheduling jobs with given processing times on identical parallel machines so as to minimize their total completion time is one of the most basic scheduling problems. We study interesting generalizations of this classical problem involving…
Scheduling jobs with precedence constraints on a set of identical machines to minimize the total processing time (makespan) is a fundamental problem in combinatorial optimization. In practical settings such as cloud computing, jobs are…
This paper examines scheduling problem denoted as $P|seq, ser|C_{max}$ in Graham's notation; in other words, scheduling of tasks on parallel identical machines ($P$) with sequence-dependent setups ($seq$) each performed by one of the…
Given a hierarchical plan (or schedule) with uncertain task times, we propose a deterministic polynomial (time and memory) algorithm for estimating the probability that its meets a deadline, or, alternately, that its {\em makespan} is less…
Structural properties of optimal preemptive schedules have been studied in a number of recent papers with a primary focus on two structural parameters: the minimum number of preemptions necessary, and a tight lower bound on `shifts', i.e.,…
We consider the classic problem of scheduling jobs with precedence constraints on identical machines to minimize makespan, in the presence of communication delays. In this setting, denoted by $\mathsf{P} \mid \mathsf{prec}, c \mid…