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

Jude-Thaddeus Ojiaku
University of Liverpool
University of Liverpool, 2017


   title={A study of time and energy efficient algorithms for parallel and heterogeneous computing},

   author={Ojiaku, Jude-Thaddeus},


   school={University of Liverpool}


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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.
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