Parallel Machine Scheduling with Nested Processing Set Restrictions and Job Delivery Times

The problem of scheduling jobs with delivery times on parallel machines is studied, where each job can only be processed on a specific subset of the machines called its processing set. Two distinct processing sets are either nested or disjoint; that is, they do not partially overlap. All jobs are available for processing at time 0. The goal is to minimize the time by which all jobs are delivered, which is equivalent to minimizing the maximum lateness from the optimization viewpoint. A list scheduling approach is analyzed and its approximation ratio of 2 is established. In addition, a polynomial time approximation scheme is derived

Inapproximability Results for Scheduling with Interval and Resource Restrictions

In the restricted assignment problem, the input consists of a set of machines and a set of jobs each with a processing time and a subset of eligible machines. The goal is to find an assignment of the jobs to the machines minimizing the makespan, that is, the maximum summed up processing time any machine receives. Herein, jobs should only be assigned to those machines on which they are eligible. It is well-known that there is no polynomial time approximation algorithm with an approximation guarantee of less than 1.5 for the restricted assignment problem unless P=NP. In this work, we show hardness results for variants of the restricted assignment problem with particular types of restrictions. For the case of interval restrictions - where the machines can be totally ordered such that jobs are eligible on consecutive machines - we show that there is no polynomial time approximation scheme (PTAS) unless P=NP. The question of whether a PTAS for this variant exists was stated as an open problem before, and PTAS results for special cases of this variant are known. Furthermore, we consider a variant with resource restriction where the sets of eligible machines are of the following form: There is a fixed number of (renewable) resources, each machine has a capacity, and each job a demand for each resource. A job is eligible on a machine if its demand is at most as big as the capacity of the machine for each resource. For one resource, this problem has been intensively studied under several different names and is known to admit a PTAS, and for two resources the variant with interval restrictions is contained as a special case. Moreover, the version with multiple resources is closely related to makespan minimization on parallel machines with a low rank processing time matrix. We show that there is no polynomial time approximation algorithm with a rate smaller than 48/47 ? 1.02 or 1.5 for scheduling with resource restrictions with 2 or 4 resources, respectively, unless P=NP. All our results can be extended to the so called Santa Claus variants of the problems where the goal is to maximize the minimal processing time any machine receives

Scheduling with processing set restrictions : a survey

2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

The Glasgow Parallel Reduction Machine: Programming Shared-memory Many-core Systems using Parallel Task Composition

We present the Glasgow Parallel Reduction Machine (GPRM), a novel, flexible framework for parallel task-composition based many-core programming. We allow the programmer to structure programs into task code, written as C++ classes, and communication code, written in a restricted subset of C++ with functional semantics and parallel evaluation. In this paper we discuss the GPRM, the virtual machine framework that enables the parallel task composition approach. We focus the discussion on GPIR, the functional language used as the intermediate representation of the bytecode running on the GPRM. Using examples in this language we show the flexibility and power of our task composition framework. We demonstrate the potential using an implementation of a merge sort algorithm on a 64-core Tilera processor, as well as on a conventional Intel quad-core processor and an AMD 48-core processor system. We also compare our framework with OpenMP tasks in a parallel pointer chasing algorithm running on the Tilera processor. Our results show that the GPRM programs outperform the corresponding OpenMP codes on all test platforms, and can greatly facilitate writing of parallel programs, in particular non-data parallel algorithms such as reductions.Comment: In Proceedings PLACES 2013, arXiv:1312.221

Algorithms for Hierarchical and Semi-Partitioned Parallel Scheduling

We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming formulation of the problem and leverage its fractional relaxation to obtain a polynomial-time 2-approximation algorithm. Extensions that incorporate memory capacity constraints are also discussed

Polly's Polyhedral Scheduling in the Presence of Reductions

The polyhedral model provides a powerful mathematical abstraction to enable effective optimization of loop nests with respect to a given optimization goal, e.g., exploiting parallelism. Unexploited reduction properties are a frequent reason for polyhedral optimizers to assume parallelism prohibiting dependences. To our knowledge, no polyhedral loop optimizer available in any production compiler provides support for reductions. In this paper, we show that leveraging the parallelism of reductions can lead to a significant performance increase. We give a precise, dependence based, definition of reductions and discuss ways to extend polyhedral optimization to exploit the associativity and commutativity of reduction computations. We have implemented a reduction-enabled scheduling approach in the Polly polyhedral optimizer and evaluate it on the standard Polybench 3.2 benchmark suite. We were able to detect and model all 52 arithmetic reductions and achieve speedups up to 2.21$\times$ on a quad core machine by exploiting the multidimensional reduction in the BiCG benchmark.Comment: Presented at the IMPACT15 worksho

Reallocation Problems in Scheduling

In traditional on-line problems, such as scheduling, requests arrive over time, demanding available resources. As each request arrives, some resources may have to be irrevocably committed to servicing that request. In many situations, however, it may be possible or even necessary to reallocate previously allocated resources in order to satisfy a new request. This reallocation has a cost. This paper shows how to service the requests while minimizing the reallocation cost. We focus on the classic problem of scheduling jobs on a multiprocessor system. Each unit-size job has a time window in which it can be executed. Jobs are dynamically added and removed from the system. We provide an algorithm that maintains a valid schedule, as long as a sufficiently feasible schedule exists. The algorithm reschedules only a total number of O(min{log^* n, log^* Delta}) jobs for each job that is inserted or deleted from the system, where n is the number of active jobs and Delta is the size of the largest window.Comment: 9 oages, 1 table; extended abstract version to appear in SPAA 201