Related papers: Compatibility graphs in scheduling on batch proces…
This paper investigates concurrency-constrained scheduling problems, where the objective is to construct a schedule for a set of jobs subject to concurrency restrictions. Formally, we are given a conflict graph $G$ defined over a set of $n$…
In the paper we consider the problem of scheduling $n$ identical jobs on 4 uniform machines with speeds $s_1 \geq s_2 \geq s_3 \geq s_4,$ respectively. Our aim is to find a schedule with a minimum possible length. We assume that jobs are…
We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise…
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…
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…
In many manufacturing processes, batch processing is frequently needed for capacity reasons. This applies both to parallel and serial batching. However, while the serial batch processing is largely studied in the literature, as it is…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…
There is a long history of approximation schemes for the problem of scheduling jobs on identical machines to minimize the makespan. Such a scheme grants a $(1+\epsilon)$-approximation solution for every $\epsilon > 0$, but the running time…
We consider different online algorithms for a generalized scheduling problem for parallel machines, described in details in the first section. This problem is the generalization of the classical parallel machine scheduling problem, when the…
We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give linear-time algorithms to compute all non-dominated…
This paper presents a profound analysis of the robust job scheduling problem with uncertain release dates on unrelated machines. Our model involves minimizing the worst-case makespan and interval uncertainty where each release date belongs…
We consider the following special case of minimizing makespan. A set of jobs $J$ and a set of machines $M$ are given. Each job $j \in J$ can be scheduled on a machine from a subset $M_j$ of $M$. The processing time of $j$ is the same on all…
The task of scheduling jobs to machines while minimizing the total makespan, the sum of weighted completion times, or a norm of the load vector, are among the oldest and most fundamental tasks in combinatorial optimization. Since all of…
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…
We consider a natural extension of online makespan scheduling on identical parallel machines by introducing scenarios. A scenario is a subset of jobs, and the task of our problem is to find a global assignment of the jobs to machines so…
We study the problem of scheduling jobs on parallel machines minimizing the total completion time, with each job using exactly one resource. First, we derive fundamental properties of the problem and show that the problem is polynomially…
We study the problem of scheduling a set of jobs with release dates, deadlines and processing requirements (or works), on parallel speed-scaled processors so as to minimize the total energy consumption. We consider that both preemption and…
This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents some large data. A task can only be executed if all input and output data fit into memory, and a data can only…
In this paper, we explore the limits of graphics processors (GPUs) for general purpose parallel computing by studying problems that require highly irregular data access patterns: parallel graph algorithms for list ranking and connected…
We study a scheduling problem in which jobs may be split into parts, where the parts of a split job may be processed simultaneously on more than one machine. Each part of a job requires a setup time, however, on the machine where the job…