On Resource Pooling and Separation for LRU Caching

Caching systems using the Least Recently Used (LRU) principle have now become ubiquitous. A fundamental question for these systems is whether the cache space should be pooled together or divided to serve multiple flows of data item requests in order to minimize the miss probabilities. In this paper, we show that there is no straight yes or no answer to this question, depending on complex combinations of critical factors, including, e.g., request rates, overlapped data items across different request flows, data item popularities and their sizes. Specifically, we characterize the asymptotic miss probabilities for multiple competing request flows under resource pooling and separation for LRU caching when the cache size is large. Analytically, we show that it is asymptotically optimal to jointly serve multiple flows if their data item sizes and popularity distributions are similar and their arrival rates do not differ significantly; the self-organizing property of LRU caching automatically optimizes the resource allocation among them asymptotically. Otherwise, separating these flows could be better, e.g., when data sizes vary significantly. We also quantify critical points beyond which resource pooling is better than separation for each of the flows when the overlapped data items exceed certain levels. Technically, we generalize existing results on the asymptotic miss probability of LRU caching for a broad class of heavy-tailed distributions and extend them to multiple competing flows with varying data item sizes, which also validates the Che approximation under certain conditions. These results provide new insights on improving the performance of caching systems

Self-Improving Algorithms

We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we need to process a sequence I_1, I_2, ... of inputs I = (x_1, x_2, ..., x_n) of some fixed length n, where each x_i is drawn independently from some arbitrary, unknown distribution D_i. The goal is to design an algorithm for these inputs so that eventually the expected running time will be optimal for the input distribution D = D_1 * D_2 * ... * D_n. We give such self-improving algorithms for two problems: (i) sorting a sequence of numbers and (ii) computing the Delaunay triangulation of a planar point set. Both algorithms achieve optimal expected limiting complexity. The algorithms begin with a training phase during which they collect information about the input distribution, followed by a stationary regime in which the algorithms settle to their optimized incarnations.Comment: 26 pages, 8 figures, preliminary versions appeared at SODA 2006 and SoCG 2008. Thorough revision to improve the presentation of the pape

Reducing redundancy of real time computer graphics in mobile systems

The goal of this thesis is to propose novel and effective techniques to eliminate redundant computations that waste energy and are performed in real-time computer graphics applications, with special focus on mobile GPU micro-architecture. Improving the energy-efficiency of CPU/GPU systems is not only key to enlarge their battery life, but also allows to increase their performance because, to avoid overheating above thermal limits, SoCs tend to be throttled when the load is high for a large period of time. Prior studies pointed out that the CPU and especially the GPU are the principal energy consumers in the graphics subsystem, being the off-chip main memory accesses and the processors inside the GPU the primary energy consumers of the graphics subsystem. First, we focus on reducing redundant fragment processing computations by means of improving the culling of hidden surfaces. During real-time graphics rendering, objects are processed by the GPU in the order they are submitted by the CPU, and occluded surfaces are often processed even though they will end up not being part of the final image. When the GPU realizes that an object or part of it is not going to be visible, all activity required to compute its color and store it has already been performed. We propose a novel architectural technique for mobile GPUs, Visibility Rendering Order (VRO), which reorders objects front-to-back entirely in hardware to maximize the culling effectiveness of the GPU and minimize overshading, hence reducing execution time and energy consumption. VRO exploits the fact that the objects in graphics animated applications tend to keep its relative depth order across consecutive frames (temporal coherence) to provide the feeling of smooth transition. VRO keeps visibility information of a frame, and uses it to reorder the objects of the following frame. VRO just requires adding a small hardware to capture the visibility information and use it later to guide the rendering of the following frame. Moreover, VRO works in parallel with the graphics pipeline, so negligible performance overheads are incurred. We illustrate the benefits of VRO using various unmodified commercial 3D applications for which VRO achieves 27% speed-up and 14.8% energy reduction on average. Then, we focus on avoiding redundant computations related to CPU Collision Detection (CD). Graphics applications such as 3D games represent a large percentage of downloaded applications for mobile devices and the trend is towards more complex and realistic scenes with accurate 3D physics simulations. CD is one of the most important algorithms in any physics kernel since it identifies the contact points between the objects of a scene and determines when they collide. However, real-time accurate CD is very expensive in terms of energy consumption. We propose Render Based Collision Detection (RBCD), a novel energy-efficient high-fidelity CD scheme that leverages some intermediate results of the rendering pipeline to perform CD, so that redundant tasks are done just once. Comparing RBCD with a conventional CD completely executed in the CPU, we show that its execution time is reduced by almost three orders of magnitude (600x speedup), because most of the CD task of our model comes for free by reusing the image rendering intermediate results. Although not necessarily, such a dramatic time improvement may result in better frames per second if physics simulation stays in the critical path. However, the most important advantage of our technique is the enormous energy savings that result from eliminating a long and costly CPU computation and converting it into a few simple operations executed by a specialized hardware within the GPU. Our results show that the energy consumed by CD is reduced on average by a factor of 448x (i.e., by 99.8\%). These dramatic benefits are accompanied by a higher fidelity CD analysis (i.e., with finer granularity), which improves the quality and realism of the application.El objetivo de esta tesis es proponer técnicas efectivas y originales para eliminar computaciones inútiles que aparecen en aplicaciones gráficas, con especial énfasis en micro-arquitectura de GPUs. Mejorar la eficiencia energética de los sistemas CPU/GPU no es solo clave para alargar la vida de la batería, sino también incrementar su rendimiento. Estudios previos han apuntado que la CPU y especialmente la GPU son los principales consumidores de energía en el sub-sistema gráfico, siendo los accesos a memoria off-chip y los procesadores dentro de la GPU los principales consumidores de energía del sub-sistema gráfico. Primero, nos hemos centrado en reducir computaciones redundantes de la fase de fragment processing mediante la mejora en la eliminación de superficies ocultas. Durante el renderizado de gráficos en tiempo real, los objetos son procesados por la GPU en el orden en el que son enviados por la CPU, y las superficies ocultas son a menudo procesadas incluso si no no acaban formando parte de la imagen final. Cuando la GPU averigua que el objeto o parte de él no es visible, toda la actividad requerida para computar su color y guardarlo ha sido realizada. Proponemos una técnica arquitectónica original para GPUs móviles, Visibility Rendering Order (VRO), la cual reordena los objetos de delante hacia atrás por completo en hardware para maximizar la efectividad del culling de la GPU y así minimizar el overshading, y por lo tanto reducir el tiempo de ejecución y el consumo de energía. VRO explota el hecho de que los objetos de las aplicaciones gráficas animadas tienden a mantener su orden relativo en profundidad a través de frames consecutivos (coherencia temporal) para proveer animaciones con transiciones suaves. Dado que las relaciones de orden en profundidad entre objetos son testeadas en la GPU, VRO introduce costes mínimos en energía. Solo requiere añadir una pequeña unidad hardware para capturar la información de visibilidad. Además, VRO trabaja en paralelo con el pipeline gráfico, por lo que introduce costes insignificantes en tiempo. Ilustramos los beneficios de VRO usango varias aplicaciones 3D comerciales para las cuales VRO consigue un 27% de speed-up y un 14.8% de reducción de energía en media. En segundo lugar, evitamos computaciones redundantes relacionadas con la Detección de Colisiones (CD) en la CPU. Las aplicaciones gráficas animadas como los juegos 3D representan un alto porcentaje de las aplicaciones descargadas en dispositivos móviles y la tendencia es hacia escenas más complejas y realistas con simulaciones físicas 3D precisas. La CD es uno de los algoritmos más importantes entre los kernel de físicas dado que identifica los puntos de contacto entre los objetos de una escena. Sin embargo, una CD en tiempo real y precisa es muy costosa en términos de consumo energético. Proponemos Render Based Collision Detection (RBCD), una técnica energéticamente eficiente y preciso de CD que utiliza resultados intermedios del rendering pipeline para realizar la CD. Comparando RBCD con una CD convencional completamente ejecutada en la CPU, mostramos que el tiempo de ejecución es reducido casi tres órdenes de magnitud (600x speedup), porque la mayoría de la CD de nuestro modelo reusa resultados intermedios del renderizado de la imagen. Aunque no es así necesariamente, esta espectacular en tiempo puede resultar en mejores frames por segundo si la simulación de físicas está en el camino crítico. Sin embargo, la ventaja más importante de nuestra técnica es el enorme ahorro de energía que resulta de eliminar las largas y costosas computaciones en la CPU, sustituyéndolas por unas pocas operaciones ejecutadas en un hardware especializado dentro de la GPU. Nuestros resultados muestran que la energía consumida por la CD es reducidad en media por un factor de 448x. Estos dramáticos beneficios vienen acompañados de una mayor fidelidad en la CD (i.e. con granularidad más fina)Postprint (published version

Self-Customized BSP Trees for Collision Detection

The ability to perform efficient collision detection is essential in virtual reality environments and their applications, such as walkthroughs. In this paper we re-explore a classical structure used for collision detection -- the binary space partitioning tree. Unlike the common approach, which attributes equal likelihood to each possible query, we assume events that happened in the past are more likely to happen again in the future. This leads us to the definition of self-customized data structures. We report encouraging results obtained while experimenting with this concept in the context of self-customized bsp trees. Keywords: Collision detection, binary space partitioning, self-customization. 1 Introduction Virtual reality refers to the use of computer graphics to simulate physical worlds or to generate synthetic ones, where a user is to feel immersed in the environment to the extent that the user feels as if "objects" seen are really there. For example, "objects" should m..