Related papers: Graham's Schedules and the Number Partition Proble…
We consider the following shared-resource scheduling problem: Given a set of jobs $J$, for each $j\in J$ we must schedule a job-specific processing volume of $v_j>0$. A total resource of $1$ is available at any time. Jobs have a resource…
A central problem in scheduling is to schedule $n$ unit size jobs with precedence constraints on $m$ identical machines so as to minimize the makespan. For $m=3$, it is not even known if the problem is NP-hard and this is one of the last…
In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are…
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…
We consider the problem of scheduling jobs with equal lengths on uniform parallel batch machines with non-identical capacities where each job can only be processed on a specified subset of machines called its processing set. For the case of…
The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
This paper considers the scheduling of stochastic jobs on parallel identical machines to minimize the expected total weighted completion time. While this is a classical problem with a significant body of research on approximation algorithms…
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…
We investigate the scheduling of $n$ jobs divided into $c$ classes on $m$ identical parallel machines. For every class there is a setup time which is required whenever a machine switches from the processing of one class to another class.…
We study the problem of executing an application represented by a precedence task graph on a parallel machine composed of standard computing cores and accelerators. Contrary to most existing approaches, we distinguish the allocation and the…
We propose a Boolean Linear Programming model for the preemptive single machine scheduling problem with equal processing times, arbitrary release dates and weights(priorities) minimizing the total weighted completion time. Almost always an…
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 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 $1.5$…
Topic modeling is a very powerful technique in data analysis and data mining but it is generally slow. Many parallelization approaches have been proposed to speed up the learning process. However, they are usually not very efficient because…
We consider a natural scheduling problem which arises in many distributed computing frameworks. Jobs with diverse resource requirements (e.g. memory requirements) arrive over time and must be served by a cluster of servers, each with a…
The rigid gang task model is based on the idea of executing multiple threads simultaneously on a fixed number of processors to increase efficiency and performance. Although there is extensive literature on global rigid gang scheduling,…
The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining different sets is optimized. In this paper we simplify a known…