Scheduling and Tuning Kernels for High-performance on Heterogeneous Processor Systems

Accelerated parallel computing techniques using devices such as GPUs and Xeon Phis (along with CPUs) have proposed promising solutions of extending the cutting edge of high-performance computer systems. A significant performance improvement can be achieved when suitable workloads are handled by the accelerator. Traditional CPUs can handle those workloads not well suited for accelerators. Combination of multiple types of processors in a single computer system is referred to as a heterogeneous system. This dissertation addresses tuning and scheduling issues in heterogeneous systems. The first section presents work on tuning scientific workloads on three different types of processors: multi-core CPU, Xeon Phi massively parallel processor, and NVIDIA GPU; common tuning methods and platform-specific tuning techniques are presented. Then, analysis is done to demonstrate the performance characteristics of the heterogeneous system on different input data. This section of the dissertation is part of the GeauxDock project, which prototyped a few state-of-art bioinformatics algorithms, and delivered a fast molecular docking program. The second section of this work studies the performance model of the GeauxDock computing kernel. Specifically, the work presents an extraction of features from the input data set and the target systems, and then uses various regression models to calculate the perspective computation time. This helps understand why a certain processor is faster for certain sets of tasks. It also provides the essential information for scheduling on heterogeneous systems. In addition, this dissertation investigates a high-level task scheduling framework for heterogeneous processor systems in which, the pros and cons of using different heterogeneous processors can complement each other. Thus a higher performance can be achieve on heterogeneous computing systems. A new scheduling algorithm with four innovations is presented: Ranked Opportunistic Balancing (ROB), Multi-subject Ranking (MR), Multi-subject Relative Ranking (MRR), and Automatic Small Tasks Rearranging (ASTR). The new algorithm consistently outperforms previously proposed algorithms with better scheduling results, lower computational complexity, and more consistent results over a range of performance prediction errors. Finally, this work extends the heterogeneous task scheduling algorithm to handle power capping feature. It demonstrates that a power-aware scheduler significantly improves the power efficiencies and saves the energy consumption. This suggests that, in addition to performance benefits, heterogeneous systems may have certain advantages on overall power efficiency

Relajaciones de ejecución definidas por el usuario para la mejora de la programabilidad en computación paralela de altas prestaciones

Tesis de la Universidad Complutense de Madrid, Facultad de Informática, leída el 22-11-2019This thesis proposes the development and implementation of a new programming model basedon execution relaxations, and focused on High-Performance Parallel Computing. Specifically,the main goals of the thesis are:1. Advocate a development methodology in which users define the basic computing units(tasks), together with a set of relaxations in, possibly, multiple dimensions. These relaxationswill be translated, at execution time, into expanded (and complex) scheduling opportunitiesdepending on the underlying architectural features, yielding improvements in termsof desired output metrics (e.g., performance or energy consumption).2. Abstract away users from the complexity of the underlying heterogeneous hardware, delegatingthe proper exploitation of expanded scheduling choices to a system software component(typically referred as a runtime). This piece of software, armed with knowledge fromstatic architectural characteristics and dynamic status of the hardware at execution time,will exploit those combinations considered optimal among those relaxations proposed bythe user for each task ready for execution.3. Extend this abstraction in order to describe both computing systems, by means of executor/ allocator hierarchies that describe the heterogeneous computing architecture, and applications,in terms of sets of interdependent tasks. In addition, the relations between executorsand tasks are categorized into a new task-executor taxonomy, which motivates ambiguityfreeHPC programming frontends based on the STSE, Single Task - Single Executor classification,distinguished from fully-automated runtime backends.4. Propose a new programming model (STEEL) based on previous ideas, that gathers featuresconsidered to be basic for future task-based programming models, namely: performance,composability, expressivity and hard-to-misuse interfaces.5. Specify an API to support the STEEL programming model, and a runtime implementationleveraging techniques and programming paradigms supported by modern C++, illustratingits flexibility, ease of use and performance impact by means of simple use cases and examples.Hence, the proposed methodology stands for a clear and strict separation of concerns betweenthe involved actors in a parallel executions: user / codes and underlying hardware. This kind ofabstractions allows a delegation of the expert knowledge from the user toward the system software(runtime) in a systematic way, and facilitates the integration of mechanisms to automate optimizations,adapting performance to the specificities of the heterogeneous parallel architecture in whichthe code is instantiated and executed.From this perspective, the thesis designs, implements and validates mechanisms to perform aso-called complexity formalization, classifying many actions that are currently done by the userand building a framework in which these complexities can be delegated to the runtime system. Thedelegation of these decisions is already a step forward to next generation of programming modelsseeking performance, expressivity, programmability and portability...La presente tesis doctoral propone el diseño e implementación de un nuevo modelo de programación basado en relajaciones de ejecución y enfocado al ámbito de la Computación Paralela de Altas Prestaciones. Concretamente, los objetivos principales de la tesis son:1. Abogar por una metodología de desarrollo en la que el usuario define las unidades básicas de computo (tareas), junto con un conjunto de relajaciones en, posiblemente, múltiples dimensiones. Estas relajaciones se traducirán, en tiempo de ejecución, en oportunidades expandidas(y complejas) de planificación en función de la arquitectura subyacente, impactando así en métricas como rendimiento o consumo energético.2. Abstraer al usuario de la complejidad del hardware subyacente, delegando la correcta explotación de dichas posibilidades de planificación expandidas a un componente software de sistema (típicamente conocido como runtime). Dicho software, dotado de conocimiento tanto de las características estáticas de la arquitectura subyacente como del estado puntual de la misma en el momento de la ejecución, explotará las combinaciones consideradas optimas de entre las relajaciones propuestas por el usuario para cada tarea lista para set ejecutada.3. Extender dicha abstracción para describir tanto sistemas de cómputo, en forma de jerarquía de ejecutores y alojadores de memoria que en ´ultimo término describen una arquitectura de cómputo heterogénea, como aplicaciones, en forma de un conjunto de tareas interrelacionadas. Además, las relaciones entre ejecutores y tareas son clasificadas en una nueva taxonomía tarea-ejecutor, la cual motiva frontends de programación HPC sin ambigüedad basados en la clasificación STSE, Single Task - Single Executor, separada de backends runtime totalmente automatizados.4. Proponer un nuevo modelo de programación (STEEL) basado en la clasificación STSE que aglutine ciertas características consideradas básicas de cara al éxito de los futuros modelos de programación basados en tareas: rendimiento, facilidad de composición, expresividad e interfaces no permisivos ante fallos.5. Especificar una API que dé soporte al modelo de programación, así como una implementación runtime del mismo aprovechando técnicas y paradigmas soportados en el lenguaje C++ de última generación, e ilustrar su uso, flexibilidad e impacto en el rendimiento a través de ejemplos y casos de uso sencillos .La metodología que se propugna aboga por una clara y estricta separación de conceptos entre los actores básicos que componen una ejecución paralela: usuario / código y hardware subyacente. Este tipo de abstracciones permite delegar el conocimiento experto desde el usuario hacia el software de sistema, proporcionando así mecanismos para mecanizar y automatizar su optimización ,y adaptar su rendimiento a la arquitectura paralela sobre la que se instanciarán los códigos. Desde este punto de vista, la tesis diseña, implementa y valida mecanismos para llevar a cabo una formalización de la complejidad inherente a la programación paralela heterogénea, clasificando aquellas acciones que en la actualidad se llevan a cabo por parte del usuario en el proceso de desarrollo y optimización de código, y proporcionando un marco de trabajo en el que dicha complejidad puede ser delegada, de forma eficiente y consistente, a un runtime...Fac. de InformáticaTRUEunpu

Parallel optimization algorithms for high performance computing : application to thermal systems

The need of optimization is present in every field of engineering. Moreover, applications requiring a multidisciplinary approach in order to make a step forward are increasing. This leads to the need of solving complex optimization problems that exceed the capacity of human brain or intuition. A standard way of proceeding is to use evolutionary algorithms, among which genetic algorithms hold a prominent place. These are characterized by their robustness and versatility, as well as their high computational cost and low convergence speed. Many optimization packages are available under free software licenses and are representative of the current state of the art in optimization technology. However, the ability of optimization algorithms to adapt to massively parallel computers reaching satisfactory efficiency levels is still an open issue. Even packages suited for multilevel parallelism encounter difficulties when dealing with objective functions involving long and variable simulation times. This variability is common in Computational Fluid Dynamics and Heat Transfer (CFD & HT), nonlinear mechanics, etc. and is nowadays a dominant concern for large scale applications. Current research in improving the performance of evolutionary algorithms is mainly focused on developing new search algorithms. Nevertheless, there is a vast knowledge of sequential well-performing algorithmic suitable for being implemented in parallel computers. The gap to be covered is efficient parallelization. Moreover, advances in the research of both new search algorithms and efficient parallelization are additive, so that the enhancement of current state of the art optimization software can be accelerated if both fronts are tackled simultaneously. The motivation of this Doctoral Thesis is to make a step forward towards the successful integration of Optimization and High Performance Computing capabilities, which has the potential to boost technological development by providing better designs, shortening product development times and minimizing the required resources. After conducting a thorough state of the art study of the mathematical optimization techniques available to date, a generic mathematical optimization tool has been developed putting a special focus on the application of the library to the field of Computational Fluid Dynamics and Heat Transfer (CFD & HT). Then the main shortcomings of the standard parallelization strategies available for genetic algorithms and similar population-based optimization methods have been analyzed. Computational load imbalance has been identified to be the key point causing the degradation of the optimization algorithm¿s scalability (i.e. parallel efficiency) in case the average makespan of the batch of individuals is greater than the average time required by the optimizer for performing inter-processor communications. It occurs because processors are often unable to finish the evaluation of their queue of individuals simultaneously and need to be synchronized before the next batch of individuals is created. Consequently, the computational load imbalance is translated into idle time in some processors. Several load balancing algorithms have been proposed and exhaustively tested, being extendable to any other population-based optimization method that needs to synchronize all processors after the evaluation of each batch of individuals. Finally, a real-world engineering application that consists on optimizing the refrigeration system of a power electronic device has been presented as an illustrative example in which the use of the proposed load balancing algorithms is able to reduce the simulation time required by the optimization tool.El aumento de las aplicaciones que requieren de una aproximación multidisciplinar para poder avanzar se constata en todos los campos de la ingeniería, lo cual conlleva la necesidad de resolver problemas de optimización complejos que exceden la capacidad del cerebro humano o de la intuición. En estos casos es habitual el uso de algoritmos evolutivos, principalmente de los algoritmos genéticos, caracterizados por su robustez y versatilidad, así como por su gran coste computacional y baja velocidad de convergencia. La multitud de paquetes de optimización disponibles con licencias de software libre representan el estado del arte actual en tecnología de optimización. Sin embargo, la capacidad de adaptación de los algoritmos de optimización a ordenadores masivamente paralelos alcanzando niveles de eficiencia satisfactorios es todavía una tarea pendiente. Incluso los paquetes adaptados al paralelismo multinivel tienen dificultades para gestionar funciones objetivo que requieren de tiempos de simulación largos y variables. Esta variabilidad es común en la Dinámica de Fluidos Computacional y la Transferencia de Calor (CFD & HT), mecánica no lineal, etc. y es una de las principales preocupaciones en aplicaciones a gran escala a día de hoy. La investigación actual que tiene por objetivo la mejora del rendimiento de los algoritmos evolutivos está enfocada principalmente al desarrollo de nuevos algoritmos de búsqueda. Sin embargo, ya se conoce una gran variedad de algoritmos secuenciales apropiados para su implementación en ordenadores paralelos. La tarea pendiente es conseguir una paralelización eficiente. Además, los avances en la investigación de nuevos algoritmos de búsqueda y la paralelización son aditivos, por lo que el proceso de mejora del software de optimización actual se verá incrementada si se atacan ambos frentes simultáneamente. La motivación de esta Tesis Doctoral es avanzar hacia una integración completa de las capacidades de Optimización y Computación de Alto Rendimiento para así impulsar el desarrollo tecnológico proporcionando mejores diseños, acortando los tiempos de desarrollo del producto y minimizando los recursos necesarios. Tras un exhaustivo estudio del estado del arte de las técnicas de optimización matemática disponibles a día de hoy, se ha diseñado una librería de optimización orientada al campo de la Dinámica de Fluidos Computacional y la Transferencia de Calor (CFD & HT). A continuación se han analizado las principales limitaciones de las estrategias de paralelización disponibles para algoritmos genéticos y otros métodos de optimización basados en poblaciones. En el caso en que el tiempo de evaluación medio de la tanda de individuos sea mayor que el tiempo medio que necesita el optimizador para llevar a cabo comunicaciones entre procesadores, se ha detectado que la causa principal de la degradación de la escalabilidad o eficiencia paralela del algoritmo de optimización es el desequilibrio de la carga computacional. El motivo es que a menudo los procesadores no terminan de evaluar su cola de individuos simultáneamente y deben sincronizarse antes de que se cree la siguiente tanda de individuos. Por consiguiente, el desequilibrio de la carga computacional se convierte en tiempo de inactividad en algunos procesadores. Se han propuesto y testado exhaustivamente varios algoritmos de equilibrado de carga aplicables a cualquier método de optimización basado en una población que necesite sincronizar los procesadores tras cada tanda de evaluaciones. Finalmente, se ha presentado como ejemplo ilustrativo un caso real de ingeniería que consiste en optimizar el sistema de refrigeración de un dispositivo de electrónica de potencia. En él queda demostrado que el uso de los algoritmos de equilibrado de carga computacional propuestos es capaz de reducir el tiempo de simulación que necesita la herramienta de optimización

Task-based multifrontal QR solver for heterogeneous architectures

Afin de s'adapter aux architectures multicoeurs et aux machines de plus en plus complexes, les modèles de programmations basés sur un parallélisme de tâche ont gagné en popularité dans la communauté du calcul scientifique haute performance. Les moteurs d'exécution fournissent une interface de programmation qui correspond à ce paradigme ainsi que des outils pour l'ordonnancement des tâches qui définissent l'application. Dans cette étude, nous explorons la conception de solveurs directes creux à base de tâches, qui représentent une charge de travail extrêmement irrégulière, avec des tâches de granularités et de caractéristiques différentes ainsi qu'une consommation mémoire variable, au-dessus d'un moteur d'exécution. Dans le cadre du solveur qr mumps, nous montrons dans un premier temps la viabilité et l'efficacité de notre approche avec l'implémentation d'une méthode multifrontale pour la factorisation de matrices creuses, en se basant sur le modèle de programmation parallèle appelé "flux de tâches séquentielles" (Sequential Task Flow). Cette approche, nous a ensuite permis de développer des fonctionnalités telles que l'intégration de noyaux dense de factorisation de type "minimisation de cAfin de s'adapter aux architectures multicoeurs et aux machines de plus en plus complexes, les modèles de programmations basés sur un parallélisme de tâche ont gagné en popularité dans la communauté du calcul scientifique haute performance. Les moteurs d'exécution fournissent une interface de programmation qui correspond à ce paradigme ainsi que des outils pour l'ordonnancement des tâches qui définissent l'application. Dans cette étude, nous explorons la conception de solveurs directes creux à base de tâches, qui représentent une charge de travail extrêmement irrégulière, avec des tâches de granularités et de caractéristiques différentes ainsi qu'une consommation mémoire variable, au-dessus d'un moteur d'exécution. Dans le cadre du solveur qr mumps, nous montrons dans un premier temps la viabilité et l'efficacité de notre approche avec l'implémentation d'une méthode multifrontale pour la factorisation de matrices creuses, en se basant sur le modèle de programmation parallèle appelé "flux de tâches séquentielles" (Sequential Task Flow). Cette approche, nous a ensuite permis de développer des fonctionnalités telles que l'intégration de noyaux dense de factorisation de type "minimisation de cAfin de s'adapter aux architectures multicoeurs et aux machines de plus en plus complexes, les modèles de programmations basés sur un parallélisme de tâche ont gagné en popularité dans la communauté du calcul scientifique haute performance. Les moteurs d'exécution fournissent une interface de programmation qui correspond à ce paradigme ainsi que des outils pour l'ordonnancement des tâches qui définissent l'application. !!br0ken!!ommunications" (Communication Avoiding) dans la méthode multifrontale, permettant d'améliorer considérablement la scalabilité du solveur par rapport a l'approche original utilisée dans qr mumps. Nous introduisons également un algorithme d'ordonnancement sous contraintes mémoire au sein de notre solveur, exploitable dans le cas des architectures multicoeur, réduisant largement la consommation mémoire de la méthode multifrontale QR avec un impacte négligeable sur les performances. En utilisant le modèle présenté ci-dessus, nous visons ensuite l'exploitation des architectures hétérogènes pour lesquelles la granularité des tâches ainsi les stratégies l'ordonnancement sont cruciales pour profiter de la puissance de ces architectures. Nous proposons, dans le cadre de la méthode multifrontale, un partitionnement hiérarchique des données ainsi qu'un algorithme d'ordonnancement capable d'exploiter l'hétérogénéité des ressources. Enfin, nous présentons une étude sur la reproductibilité de l'exécution parallèle de notre problème et nous montrons également l'utilisation d'un modèle de programmation alternatif pour l'implémentation de la méthode multifrontale. L'ensemble des résultats expérimentaux présentés dans cette étude sont évalués avec une analyse détaillée des performance que nous proposons au début de cette étude. Cette analyse de performance permet de mesurer l'impacte de plusieurs effets identifiés sur la scalabilité et la performance de nos algorithmes et nous aide ainsi à comprendre pleinement les résultats obtenu lors des tests effectués avec notre solveur.To face the advent of multicore processors and the ever increasing complexity of hardware architectures, programming models based on DAG parallelism regained popularity in the high performance, scientific computing community. Modern runtime systems offer a programming interface that complies with this paradigm and powerful engines for scheduling the tasks into which the application is decomposed. These tools have already proved their effectiveness on a number of dense linear algebra applications. In this study we investigate the design of task-based sparse direct solvers which constitute extremely irregular workloads, with tasks of different granularities and characteristics with variable memory consumption on top of runtime systems. In the context of the qr mumps solver, we prove the usability and effectiveness of our approach with the implementation of a sparse matrix multifrontal factorization based on a Sequential Task Flow parallel programming model. Using this programming model, we developed features such as the integration of dense 2D Communication Avoiding algorithms in the multifrontal method allowing for better scalability compared to the original approach used in qr mumps. In addition we introduced a memory-aware algorithm to control the memory behaviour of our solver and show, in the context of multicore architectures, an important reduction of the memory footprint for the multifrontal QR factorization with a small impact on performance. Following this approach, we move to heterogeneous architectures where task granularity and scheduling strategies are critical to achieve performance. We present, for the multifrontal method, a hierarchical strategy for data partitioning and a scheduling algorithm capable of handling the heterogeneity of resources. Finally we present a study on the reproducibility of executions and the use of alternative programming models for the implementation of the multifrontal method. All the experimental results presented in this study are evaluated with a detailed performance analysis measuring the impact of several identified effects on the performance and scalability. Thanks to this original analysis, presented in the first part of this study, we are capable of fully understanding the results obtained with our solver

MULTI-SCALE SCHEDULING TECHNIQUES FOR SIGNAL PROCESSING SYSTEMS

A variety of hardware platforms for signal processing has emerged, from distributed systems such as Wireless Sensor Networks (WSNs) to parallel systems such as Multicore Programmable Digital Signal Processors (PDSPs), Multicore General Purpose Processors (GPPs), and Graphics Processing Units (GPUs) to heterogeneous combinations of parallel and distributed devices. When a signal processing application is implemented on one of those platforms, the performance critically depends on the scheduling techniques, which in general allocate computation and communication resources for competing processing tasks in the application to optimize performance metrics such as power consumption, throughput, latency, and accuracy. Signal processing systems implemented on such platforms typically involve multiple levels of processing and communication hierarchy, such as network-level, chip-level, and processor-level in a structural context, and application-level, subsystem-level, component-level, and operation- or instruction-level in a behavioral context. In this thesis, we target scheduling issues that carefully address and integrate scheduling considerations at different levels of these structural and behavioral hierarchies. The core contributions of the thesis include the following. Considering both the network-level and chip-level, we have proposed an adaptive scheduling algorithm for wireless sensor networks (WSNs) designed for event detection. Our algorithm exploits discrepancies among the detection accuracy of individual sensors, which are derived from a collaborative training process, to allow each sensor to operate in a more energy efficient manner while the network satisfies given constraints on overall detection accuracy. Considering the chip-level and processor-level, we incorporated both temperature and process variations to develop new scheduling methods for throughput maximization on multicore processors. In particular, we studied how to process a large number of threads with high speed and without violating a given maximum temperature constraint. We targeted our methods to multicore processors in which the cores may operate at different frequencies and different levels of leakage. We develop speed selection and thread assignment schedulers based on the notion of a core's steady state temperature. Considering the application-level, component-level and operation-level, we developed a new dataflow based design flow within the targeted dataflow interchange format (TDIF) design tool. Our new multiprocessor system-on-chip (MPSoC)-oriented design flow, called TDIF-PPG, is geared towards analysis and mapping of embedded DSP applications on MPSoCs. An important feature of TDIF-PPG is its capability to integrate graph level parallelism and actor level parallelism into the application mapping process. Here, graph level parallelism is exposed by the dataflow graph application representation in TDIF, and actor level parallelism is modeled by a novel model for multiprocessor dataflow graph implementation that we call the Parallel Processing Group (PPG) model. Building on the contribution above, we formulated a new type of parallel task scheduling problem called Parallel Actor Scheduling (PAS) for chip-level MPSoC mapping of DSP systems that are represented as synchronous dataflow (SDF) graphs. In contrast to traditional SDF-based scheduling techniques, which focus on exploiting graph level (inter-actor) parallelism, the PAS problem targets the integrated exploitation of both intra- and inter-actor parallelism for platforms in which individual actors can be parallelized across multiple processing units. We address a special case of the PAS problem in which all of the actors in the DSP application or subsystem being optimized can be parallelized. For this special case, we develop and experimentally evaluate a two-phase scheduling framework with three work flows --- particle swarm optimization with a mixed integer programming formulation, particle swarm optimization with a simulated annealing engine, and particle swarm optimization with a fast heuristic based on list scheduling. Then, we extend our scheduling framework to support general PAS problem which considers the actors cannot be parallelized

High-Performance and Time-Predictable Embedded Computing

Nowadays, the prevalence of computing systems in our lives is so ubiquitous that we live in a cyber-physical world dominated by computer systems, from pacemakers to cars and airplanes. These systems demand for more computational performance to process large amounts of data from multiple data sources with guaranteed processing times. Actuating outside of the required timing bounds may cause the failure of the system, being vital for systems like planes, cars, business monitoring, e-trading, etc. High-Performance and Time-Predictable Embedded Computing presents recent advances in software architecture and tools to support such complex systems, enabling the design of embedded computing devices which are able to deliver high-performance whilst guaranteeing the application required timing bounds. Technical topics discussed in the book include: Parallel embedded platforms Programming models Mapping and scheduling of parallel computations Timing and schedulability analysis Runtimes and operating systems The work reflected in this book was done in the scope of the European project P SOCRATES, funded under the FP7 framework program of the European Commission. High-performance and time-predictable embedded computing is ideal for personnel in computer/communication/embedded industries as well as academic staff and master/research students in computer science, embedded systems, cyber-physical systems and internet-of-things.info:eu-repo/semantics/publishedVersio

High Performance Embedded Computing

Nowadays, the prevalence of computing systems in our lives is so ubiquitous that we live in a cyber-physical world dominated by computer systems, from pacemakers to cars and airplanes. These systems demand for more computational performance to process large amounts of data from multiple data sources with guaranteed processing times. Actuating outside of the required timing bounds may cause the failure of the system, being vital for systems like planes, cars, business monitoring, e-trading, etc. High-Performance and Time-Predictable Embedded Computing presents recent advances in software architecture and tools to support such complex systems, enabling the design of embedded computing devices which are able to deliver high-performance whilst guaranteeing the application required timing bounds. Technical topics discussed in the book include: Parallel embedded platforms Programming models Mapping and scheduling of parallel computations Timing and schedulability analysis Runtimes and operating systemsThe work reflected in this book was done in the scope of the European project P SOCRATES, funded under the FP7 framework program of the European Commission. High-performance and time-predictable embedded computing is ideal for personnel in computer/communication/embedded industries as well as academic staff and master/research students in computer science, embedded systems, cyber-physical systems and internet-of-things

Independent tasks on 2 resources with co-scheduling effects

Concurrent kernel execution is a relatively new feature in modern GPUs, which was designed to improve hardware utilization and the overall system throughput. However, the decision on the simultaneous execution of tasks is performed by the hardware with a leftover policy, that assigns as many resources as possible for one task and then assigns the remaining resources to the next task. This can lead to unreasonable use of resources. In this work, we tackle the problem of co-scheduling for GPUs with and without preemption, with the focus on determining the kernels submission order to reduce the number of preemptions and the kernels makespan, respectively. We propose a graph-based theoretical model to build preemptive and non-preemptive schedules. We show that the optimal preemptive makespan can be computed by solving a Linear Program in polynomial time, and we propose an algorithm based on this solution which minimizes the number of preemptions. We also propose an algorithm that transforms a preemptive solution of optimal makespan into a non-preemptive solution with the smallest possible preemption overhead. We show, however, that finding the minimal amount of preemptions among all preemptive solutions of optimal makespan is a NP-hard problem, and computing the optimal non-preemptive schedule is also NP-hard. In addition, we study the non-preemptive problem, without searching first for a good preemptive solution, and present a Mixed Integer Linear Program solution to this problem. We performed experiments on real-world GPU applications and our approach can achieve optimal makespan by preempting 6 to 9% of the tasks. Our non-preemptive approach, on the other side, obtains makespan within 2.5% of the optimal preemptive schedules, while previous approaches exceed the preemptive makespan by 5 to 12%