Energy-efficient algorithms for non-preemptive speed-scaling

We improve complexity bounds for energy-efficient speed scheduling problems for both the single processor and multi-processor cases. Energy conservation has become a major concern, so revisiting traditional scheduling problems to take into account the energy consumption has been part of the agenda of the scheduling community for the past few years. We consider the energy minimizing speed scaling problem introduced by Yao et al. where we wish to schedule a set of jobs, each with a release date, deadline and work volume, on a set of identical processors. The processors may change speed as a function of time and the energy they consume is the $\alpha$th power of its speed. The objective is then to find a feasible schedule which minimizes the total energy used. We show that in the setting with an arbitrary number of processors where all work volumes are equal, there is a $2(1+\varepsilon)(5(1+\varepsilon))^{\alpha -1}\tilde{B}_{\alpha}=O_{\alpha}(1)$ approximation algorithm, where $\tilde{B}_{\alpha}$ is the generalized Bell number. This is the first constant factor algorithm for this problem. This algorithm extends to general unequal processor-dependent work volumes, up to losing a factor of $(\frac{(1+r)r}{2})^{\alpha}$ in the approximation, where $r$ is the maximum ratio between two work volumes. We then show this latter problem is APX-hard, even in the special case when all release dates and deadlines are equal and $r$ is 4. In the single processor case, we introduce a new linear programming formulation of speed scaling and prove that its integrality gap is at most $12^{\alpha -1}$. As a corollary, we obtain a $(12(1+\varepsilon))^{\alpha -1}$ approximation algorithm where there is a single processor, improving on the previous best bound of $2^{\alpha-1}(1+\varepsilon)^{\alpha}\tilde{B}_{\alpha}$ when $\alpha \ge 25$

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

Online-Bearbeitung kritischer Aufgaben : Deadline-Scheduling und Convex-Body-Chasing

In this thesis, we study two fundamental online optimization problems in which tasks arrive over time and require to be processed either immediately or until a certain deadline. The goal is to finish all tasks and minimize some cost function. In the real world, such an optimization problem has to be solved for instance by an on-board computer of a car that needs to handle safety-relevant and thus time-critical tasks.In der vorliegenden Arbeit betrachten wir zwei fundamentale Probleme aus der Online-Optimierung, in denen Jobs, die nach und nach ankommen, entweder sofort oder bis zu einer bestimmten Deadline bearbeitet werden müssen. Das Ziel ist es, alle Jobs rechtzeitig zu erledigen und dabei eine bestimmte Kostenfunktion zu minimieren. In der Praxis müssen solche Probleme zum Beispiel von dem Bordcomputer eines Autos gelöst werden, der sicherheitsrelevante und daher zeitkritische Jobs bearbeiten muss.DFG, GRK 1408, Methods for Discrete StructuresDFG, ME 3825-1, Scheduling under Uncertainty: On Performance-Adaptivity Tradeoff

Approximation Algorithms for Modern Multi-Processor Scheduling Problems

This thesis is devoted to the design and analysis of algorithms for scheduling problems. These problems are ubiquitous in the modern world. Examples include the optimization of local transportation, managing access to concurrent resources like runways at airports and efficient execution of computing tasks on server systems. Problem instances that appear in the real world often are so large and complex that it is not possible to solve them “by hand”. This rises the need for strong algorithmic approaches, which motivates our focus of study. In this work we consider two types of scheduling problems which gained in importance due to recent technological advances. The first problem comes from the avionics industry and deals with scheduling periodically recurring tasks in a parallel computer network on a plane: Each task comes with a period p and execution time c, and needs to use a processor exclusively for c time units every p time units. The scheduling problem is to assign starting offsets for the first execution of the tasks so that no collision occurs. The second problem is a scheduling problem that arises in highly parallelized processing environments with a shared common resource, e.g., modern multi-core computer architectures. In addition to classical makespan minimization problems such as scheduling on identical machines, each job has an additional resource constraint. The scheduler must ensure that at no time, the accumulated requirement of all active jobs at that time exceeds a given limit. For both types of problems we study their algorithmic complexity in a mathematical, rigorous way by designing approximation algorithms and establishing inapproximability results. We thereby give a characterization of the approximation landscape of these problems. We also consider a more practical perspective: For an engineer from the industry, a rigorous proof that an algorithm finds a solution of certain guaranteed quality for all possible kinds of problem instances is usually not that relevant. It is rather of interest to find “good enough” or even optimal solutions for particular instances that actually appear in the real world in “reasonable” time. We show that structural insights gained in the more theoretical process of designing approximation algorithms can be highly beneficial also for obtaining practical results. In particular, we develop integer programming formulations for the avionics problem based on structural properties revealed in the design of approximation algorithms. These formulations lead to strong tools that, for the first time, enable to algorithmically solve real-world instances from our industrial partner

Parallel and Distributed Computing

The 14 chapters presented in this book cover a wide variety of representative works ranging from hardware design to application development. Particularly, the topics that are addressed are programmable and reconfigurable devices and systems, dependability of GPUs (General Purpose Units), network topologies, cache coherence protocols, resource allocation, scheduling algorithms, peertopeer networks, largescale network simulation, and parallel routines and algorithms. In this way, the articles included in this book constitute an excellent reference for engineers and researchers who have particular interests in each of these topics in parallel and distributed computing

Advances and Technologies in High Voltage Power Systems Operation, Control, Protection and Security

The electrical demands in several countries around the world are increasing due to the huge energy requirements of prosperous economies and the human activities of modern life. In order to economically transfer electrical powers from the generation side to the demand side, these powers need to be transferred at high-voltage levels through suitable transmission systems and power substations. To this end, high-voltage transmission systems and power substations are in demand. Actually, they are at the heart of interconnected power systems, in which any faults might lead to unsuitable consequences, abnormal operation situations, security issues, and even power cuts and blackouts. In order to cope with the ever-increasing operation and control complexity and security in interconnected high-voltage power systems, new architectures, concepts, algorithms, and procedures are essential. This book aims to encourage researchers to address the technical issues and research gaps in high-voltage transmission systems and power substations in modern energy systems

Scheduling techniques to improve the worst-case execution time of real-time parallel applications on heterogeneous platforms

The key to providing high performance and energy-efficient execution for hard real-time applications is the time predictable and efficient usage of heterogeneous multiprocessors. However, schedulability analysis of parallel applications executed on unrelated heterogeneous multiprocessors is challenging and has not been investigated adequately by earlier works. The unrelated model is suitable to represent many of the multiprocessor platforms available today because a task (i.e., sequential code) may exhibit a different work-case-execution-time (WCET) on each type of processor on an unrelated heterogeneous multiprocessors platform. A parallel application can be realistically modeled as a directed acyclic graph (DAG), where the nodes are sequential tasks and the edges are dependencies among the tasks. This thesis considers a sporadic DAG model which is used broadly to analyze and verify the real-time requirements of parallel applications. A global work-conserving scheduler can efficiently utilize an unrelated platform by executing the tasks of a DAG on different processor types. However, it is challenging to compute an upper bound on the worst-case schedule length of the DAG, called makespan, which is used to verify whether the deadline of a DAG is met or not. There are two main challenges. First, because of the heterogeneity of the processors, the WCET for each task of the DAG depends on which processor the task is executing on during actual runtime. Second, timing anomalies are the main obstacle to compute the makespan even for the simpler case when all the processors are of the same type, i.e., homogeneous multiprocessors. To that end, this thesis addresses the following problem: How we can schedule multiple sporadic DAGs on unrelated multiprocessors such that all the DAGs meet their deadlines. Initially, the thesis focuses on homogeneous multiprocessors that is a special case of unrelated multiprocessors to understand and tackle the main challenge of timing anomalies. A novel timing-anomaly-free scheduler is proposed which can be used to compute the makespan of a DAG just by simulating the execution of the tasks based on this proposed scheduler. A set of representative task-based parallel OpenMP applications from the BOTS benchmark suite are modeled as DAGs to investigate the timing behavior of real-world applications. A simulation framework is developed to evaluate the proposed method. Furthermore, the thesis targets unrelated multiprocessors and proposes a global scheduler to execute the tasks of a single DAG to an unrelated multiprocessors platform. Based on the proposed scheduler, methods to compute the makespan of a single DAG are introduced. A set of representative parallel applications from the BOTS benchmark suite are modeled as DAGs that execute on unrelated multiprocessors. Furthermore, synthetic DAGs are generated to examine additional structures of parallel applications and various platform capabilities. A simulation framework that simulates the execution of the tasks of a DAG on an unrelated multiprocessor platform is introduced to assess the effectiveness of the proposed makespan computations. Finally, based on the makespan computation of a single DAG this thesis presents the design and schedulability analysis of global and federated scheduling of sporadic DAGs that execute on unrelated multiprocessors

A Study of Time and Energy Efficient Algorithms for Parallel and Heterogeneous Computing

This PhD project is motivated by the need to develop and achieve better and energy efficient computing through the use of parallelism and heterogeneous systems. Our contribution consists of both theoretical aspects, as well as in-depth and comprehensive empirical studies that aim to provide more insight into parallel and heterogeneous computing. Our first problem is a theoretical problem that focuses on the scheduling of a special category of jobs known as deteriorating jobs. These kind of jobs will require more effort to complete them if postponed to a later time. They are intended to model several industrial processes including steel production, fire-fighting and financial management. We study the problem in the context of parallel machine scheduling in an online setting where jobs have arbitrary release times. Our main results show that List Scheduling is $(1+b_{max})$-competitive and that no deterministic algorithm is better than $(1+b_{max})^{1-\frac{1}{m}}$, where $b_{max}$ is the largest deteriorating rate. We also extend our results to online deterministic algorithms and show that no deterministic online algorithm is better than $(1+b_{max})$-competitive. Our next study concerns the scheduling of $n$ jobs with precedence constraints on $m$ parallel machines. We are interested in the precedence constraint known as chain precedence constraint where each job can have at most one predecessor and at most one successor. The jobs are modelled as directed acyclic graphs where nodes represent the jobs and edges represent the precedence constraints between jobs. The jobs have a strict deadline that must be met. The parallel machines are considered to be unrelated and a communication network connects each pair of machines. Execution of the jobs on the machines as well as communication across the network incurs costs in the form of time and energy. These costs are given by cost matrices that covers processing and communication. The goal is to construct a feasible schedule that minimizes the total energy required to execute the chain of jobs on the machines, such that all deadlines are met. We present a dynamic programming solution to the problem that leads to a pseudo polynomial time algorithm with running time $O(nm^2d_{max})$, where $d_{max}$ is the largest deadline. We show that the algorithm computes an optimal schedule where one exists. We then proceed to a similar problem that involves the scheduling of jobs to minimize flow time plus energy. This problem is based on a dynamic speed scaling heuristic in literature that is able to adjust the speed of a processor based on the number of \emph{active jobs}, called AJC. We present a comprehensive empirical study that consists of several job selection, speed selection and processor allocation heuristics. We also consider both single processor and multi processor settings. Our main goal is to investigate the viability of designing a fixed-speed counterpart for AJC, that is not as computationally intensive as AJC, while being very simple. We also evaluate the performance of this fixed speed heuristic and compare it with that of AJC. Our fourth and final study involves the use of graphics processing unit (GPU) as an accelerator for compute intensive tasks. The GPU has become a very popular multi processor for heterogeneous computing both from an economical point of view and performance standpoint. Firstly, we contribute to the development of a Bioinformatics tool, called GapsMis, by implementing a heterogeneous version that uses graphics processors for acceleration. GapsMis is a tool designed for the alignment of sequences, like protein and DNA sequences, and allows for the insertion of gaps in the alignment. Then we present a case study that aims to highlight the various aspects, including benefits and challenges, involved in developing heterogeneous applications that is vendor-agnostic. In order to do this we select four algorithms as case studies including GapsMis and the algorithm presented in our second problem. The other two algorithms are based on the Velocity-Verlet integration and the Fruchterman-Reingold force-based method for graph layout. We make use of the Open Computing Language (OpenCL) and C++ for implementation of the algorithms on a range of graphics processors from Advanced Micro Devices (AMD) and NVIDIA Corporation. We evaluate several factors that can affect performance of these applications on each hardware. We also compare the performance of our algorithms in a multi-GPU setting and against single and multi-core CPU implementations. Furthermore, several metrics are defined to capture several aspects of performance including execution time of application kernel(s), execution time of application including communication times, throughput, power and energy consumption