Priority-grouping method for parallel multi-scheduling in Grid

With the advent in multicore computers, the scheduling of Grid jobs can be made more effective if scaled to fully utilize the underlying hardware, and parallelized to benefit from the exploitation of multicores. The fact that sequential algorithms do not scale with multicore systems nor benefit from parallelism remains a major obstacle to scheduling in the Grid. As multicore systems become ever more pervasive in our computing lives, over reliance on such systems for passive parallelism does not offer the best option in harnessing the benefits of their multiprocessors for Grid scheduling. An explicit means of exploiting parallelism for Grid scheduling is required. The Group-based Parallel Multi-scheduler, introduced in this paper, is aimed at effectively exploiting the benefits of multicore systems for Grid scheduling by splitting jobs and machines into paired groups and independently scheduling jobs in parallel from those groups. We implemented two job grouping methods, Execution Time Balanced (ETB) and Execution Time Sorted then Balanced (ETSB), and two machine grouping methods, Evenly Distributed (EvenDist) and Similar Together (SimTog). For each method, we varied the number of groups between 2, 4 and 8. We then executed the MinMin Grid scheduling algorithm independently within the groups. We demonstrated that by sharing jobs and machines into groups before scheduling, the computation time for the scheduling process drastically improved by magnitudes of 85% over the ordinary MinMin algorithm when implemented on a HPC system. We also found that our balanced group based approach achieved better results than our previous Priority based grouping approach

Group-based parallel multi-scheduler for grid computing

With the advent in multicore computers, the scheduling of Grid jobs can be made more effective if scaled to fully utilize the underlying hardware, and parallelized to benefit from the exploitation of multicores. The fact that sequential algorithms do not scale with multicore systems nor benefit from parallelism remains a major obstacle to scheduling in the Grid. As multicore systems become ever more pervasive in our computing lives, over reliance on such systems for passive parallelism does not offer the best option in harnessing the benefits of their multiprocessors for Grid scheduling. An explicit means of exploiting parallelism for Grid scheduling is required. The Group-based Parallel Multi-scheduler, introduced in this paper, is aimed at effectively exploiting the benefits of multicore systems for Grid scheduling by splitting jobs and machines into paired groups and independently scheduling jobs in parallel from those groups. We implemented two job grouping methods, Execution Time Balanced (ETB) and Execution Time Sorted then Balanced (ETSB), and two machine grouping methods, Evenly Distributed (EvenDist) and Similar Together (SimTog). For each method, we varied the number of groups between 2, 4 and 8. We then executed the MinMin Grid scheduling algorithm independently within the groups. We demonstrated that by sharing jobs and machines into groups before scheduling, the computation time for the scheduling process drastically improved by magnitudes of 85% over the ordinary MinMin algorithm when implemented on a HPC system. We also found that our balanced group based approach achieved better results than our previous Priority based grouping approach

Preemptive scheduling on two identical parallel machines with a single transporter

We consider a scheduling problem on two identical parallel machines, in which the jobs are moved between the machines by an uncapacitated transporter. In the processing preemption is allowed. The objective is to minimize the time by which all completed jobs are collected together on board the transporter. We identify the structural patterns of an optimal schedule and design an algorithm that either solves the problem to optimality or in the worst case behaves as a fully polynomial-time approximation scheme

Energy Efficient Scheduling and Routing via Randomized Rounding

We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speed-scaling setting. We apply our framework to various scheduling and routing problems in heterogeneous computing and networking environments. We first consider the energy minimization problem of scheduling a set of jobs on a set of parallel speed scalable processors in a fully heterogeneous setting. For both the preemptive-non-migratory and the preemptive-migratory variants, our approach allows us to obtain solutions of almost the same quality as for the homogeneous environment. By exploiting the result for the preemptive-non-migratory variant, we are able to improve the best known approximation ratio for the single processor non-preemptive problem. Furthermore, we show that our approach allows to obtain a constant-factor approximation algorithm for the power-aware preemptive job shop scheduling problem. Finally, we consider the min-power routing problem where we are given a network modeled by an undirected graph and a set of uniform demands that have to be routed on integral routes from their sources to their destinations so that the energy consumption is minimized. We improve the best known approximation ratio for this problem.Comment: 27 page

Approximation Schemes for Machine Scheduling

In the classical problem of makespan minimization on identical parallel machines, or machine scheduling for short, a set of jobs has to be assigned to a set of machines. The jobs have a processing time and the goal is to minimize the latest finishing time of the jobs. Machine scheduling is well known to be NP-hard and thus there is no polynomial time algorithm for this problem that is guaranteed to find an optimal solution unless P=NP. There is, however, a polynomial time approximation scheme (PTAS) for machine scheduling, that is, a family of approximation algorithms with ratios arbitrarily close to one. Whether a problem admits an approximation scheme or not is a fundamental question in approximation theory. In the present work, we consider this question for several variants of machine scheduling. We study the problem where the machines are partitioned into a constant number of types and the processing time of the jobs is also dependent on the machine type. We present so called efficient PTAS (EPTAS) results for this problem and variants thereof. We show that certain cases of machine scheduling with assignment restrictions do not admit a PTAS unless P=NP. Moreover, we introduce a graph framework based on the restrictions of the jobs and use it in the design of approximation schemes for other variants. We introduce an enhanced integer programming formulation for assignment problems, show that it can be efficiently solved, and use it in the EPTAS design for variants of machine scheduling with setup times. For one of the problems, we show that there is also a PTAS in the case with uniform machines, where machines have speeds influencing the processing times of the jobs. We consider cases in which each job requires a certain amount of a shared renewable resource and the processing time is depended on the amount of resource it receives or not. We present so called asymptotic fully polynomial time approximation schemes (AFPTAS) for the problems

Scheduling Parallel Jobs with Linear Speedup

We consider a scheduling problem where a set of jobs is distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g., personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3+e)-approximation algorithm for that problem, for any e>0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve in general. We also briefly discuss variants of the problem and derive lower bounds.operations research and management science;

Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan

The energy scheduling problem: Industrial case-study and constraint propagation techniques

This paper deals with production scheduling involving energy constraints, typically electrical energy. We start by an industrial case-study for which we propose a two-step integer/constraint programming method. From the industrial problem we derive a generic problem,the Energy Scheduling Problem (EnSP). We propose an extension of specific resource constraint propagation techniques to efficiently prune the search space for EnSP solving. We also present a branching scheme to solve the problem via tree search.Finally,computational results are provided