103 research outputs found
Geometry-Oblivious FMM for Compressing Dense SPD Matrices
We present GOFMM (geometry-oblivious FMM), a novel method that creates a
hierarchical low-rank approximation, "compression," of an arbitrary dense
symmetric positive definite (SPD) matrix. For many applications, GOFMM enables
an approximate matrix-vector multiplication in or even time,
where is the matrix size. Compression requires storage and work.
In general, our scheme belongs to the family of hierarchical matrix
approximation methods. In particular, it generalizes the fast multipole method
(FMM) to a purely algebraic setting by only requiring the ability to sample
matrix entries. Neither geometric information (i.e., point coordinates) nor
knowledge of how the matrix entries have been generated is required, thus the
term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme
for hierarchical matrix computations that reduces synchronization barriers. We
present results on the Intel Knights Landing and Haswell architectures, and on
the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1
Replicable parallel branch and bound search
Combinatorial branch and bound searches are a common technique for solving global optimisation and decision problems. Their performance often depends on good search order heuristics, refined over decades of algorithms research. Parallel search necessarily deviates from the sequential search order, sometimes dramatically and unpredictably, e.g. by distributing work at random. This can disrupt effective search order heuristics and lead to unexpected and highly variable parallel performance. The variability makes it hard to reason about the parallel performance of combinatorial searches.
This paper presents a generic parallel branch and bound skeleton, implemented in Haskell, with replicable parallel performance. The skeleton aims to preserve the search order heuristic by distributing work in an ordered fashion, closely following the sequential search order. We demonstrate the generality of the approach by applying the skeleton to 40 instances of three combinatorial problems: Maximum Clique, 0/1 Knapsack and Travelling Salesperson. The overheads of our Haskell skeleton are reasonable: giving slowdown factors of between 1.9 and 6.2 compared with a class-leading, dedicated, and highly optimised C++ Maximum Clique solver. We demonstrate scaling up to 200 cores of a Beowulf cluster, achieving speedups of 100x for several Maximum Clique instances. We demonstrate low variance of parallel performance across all instances of the three combinatorial problems and at all scales up to 200 cores, with median Relative Standard Deviation (RSD) below 2%. Parallel solvers that do not follow the sequential search order exhibit far higher variance, with median RSD exceeding 85% for Knapsack
Parallel source code transformation techniques using design patterns
Mención Internacional en el título de doctorIn recent years, the traditional approaches for improving performance, such as increasing
the clock frequency, has come to a dead-end. To tackle this issue, parallel architectures,
such as multi-/many-core processors, have been envisioned to increase
the performance by providing greater processing capabilities. However, programming
efficiently for this architectures demands big efforts in order to transform sequential
applications into parallel and to optimize such applications. Compared to
sequential programming, designing and implementing parallel applications for operating
on modern hardware poses a number of new challenges to developers such
as data races, deadlocks, load imbalance, etc.
To pave the way, parallel design patterns provide a way to encapsulate algorithmic
aspects, allowing users to implement robust, readable and portable solutions
with such high-level abstractions. Basically, these patterns instantiate parallelism
while hiding away the complexity of concurrency mechanisms, such as thread management,
synchronizations or data sharing. Nonetheless, frameworks following this
philosophy does not share the same interface and users require understanding different
libraries, and their capabilities, not only to decide which fits best for their
purposes but also to properly leverage them. Furthermore, in order to parallelize
these applications, it is necessary to analyze the sequential code in order to detect the
regions of code that can be parallelized that is a time consuming and complex task.
Additionally, different libraries targeted to specific devices provide some algorithms
implementations that are already parallel and highly-tuned. In these situations, it is
also necessary to analyze and determine which routine implementation is the most
suitable for a given problem.
To tackle these issues, this thesis aims at simplifying and minimizing the necessary
efforts to transform sequential applications into parallel. This way, resulting
codes will improve their performance by fully exploiting the available resources
while the development efforts will be considerably reduced. Basically, in this thesis,
we contribute with the following. First, we propose a technique to detect potential
parallel patterns in sequential code. Second, we provide a novel generic C++ interface
for parallel patterns which acts as a switch among existing frameworks. Third,
we implement a framework that is able to transform sequential code into parallel
using the proposed pattern discovery technique and pattern interface. Finally, we
propose mechanisms that are able to select the most suitable device and routine implementation
to solve a given problem based on previous performance information.
The evaluation demonstrates that using the proposed techniques can minimize the
refactoring and optimization time while improving the performance of the resulting
applications with respect to the original code.En los últimos años, las técnicas tradicionales para mejorar el rendimiento, como es
el caso del incremento de la frecuencia de reloj, han llegado a sus límites. Con el
fin de seguir mejorando el rendimiento, se han desarrollado las arquitecturas paralelas,
las cuales proporcionan un incremento del rendimiento al estar provistas de
mayores capacidades de procesamiento. Sin embargo, programar de forma eficiente
para estas arquitecturas requieren de grandes esfuerzos por parte de los desarrolladores.
Comparado con la programación secuencial, diseñar e implementar aplicaciones
paralelas enfocadas a trabajar en estas arquitecturas presentan una gran
cantidad de dificultades como son las condiciones de carrera, los deadlocks o el incorrecto
balanceo de la carga.
En este sentido, los patrones paralelos son una forma de encapsular aspectos
algorítmicos de las aplicaciones permitiendo el desarrollo de soluciones robustas,
portables y legibles gracias a las abstracciones de alto nivel. En general, estos patrones
son capaces de proporcionar el paralelismo a la vez que ocultan las complejidades
derivadas de los mecanismos de control de concurrencia necesarios como el
manejo de los hilos, las sincronizaciones o la compartición de datos. No obstante,
los diferentes frameworks que siguen esta filosofía no comparten una única interfaz
lo que conlleva que los usuarios deban conocer múltiples bibliotecas y sus capacidades,
con el fin de decidir cuál de ellos es mejor para una situación concreta y
como usarlos de forma eficiente. Además, con el fin de paralelizar aplicaciones existentes,
es necesario analizar e identificar las regiones del código que pueden ser paralelizadas,
lo cual es una tarea ardua y compleja. Además, algunos algoritmos ya se
encuentran implementados en paralelo y optimizados para arquitecturas concretas
en diversas bibliotecas. Esto da lugar a que sea necesario analizar y determinar que
implementación concreta es la más adecuada para solucionar un problema dado.
Para paliar estas situaciones, está tesis busca simplificar y minimizar el esfuerzo
necesario para transformar aplicaciones secuenciales en paralelas. De esta forma,
los códigos resultantes serán capaces de explotar los recursos disponibles a la vez
que se reduce considerablemente el esfuerzo de desarrollo necesario. En general,
esta tesis contribuye con lo siguiente. En primer lugar, se propone una técnica de
detección de patrones paralelos en códigos secuenciales. En segundo lugar, se presenta
una interfaz genérica de patrones paralelos para C++ que permite seleccionar
la implementación de dichos patrones proporcionada por frameworks ya existentes.
En tercer lugar, se introduce un framework de transformación de código secuencial
a paralelo que hace uso de las técnicas de detección de patrones y la interfaz
presentadas. Finalmente, se proponen mecanismos capaces de seleccionar la implementación
más adecuada para solucionar un problema concreto basándose en el
rendimiento obtenido en ejecuciones previas. Gracias a la evaluación realizada se ha
podido demostrar que uso de las técnicas presentadas pueden minimizar el tiempo
necesario para transformar y optimizar el código a la vez que mejora el rendimiento
de las aplicaciones transformadas.Programa Oficial de Doctorado en Ciencia y Tecnología InformáticaPresidente: David Expósito Singh.- Secretario: Rafael Asenjo Plaza.- Vocal: Marco Aldinucc
Architecture aware parallel programming in Glasgow parallel Haskell (GPH)
General purpose computing architectures are evolving quickly to become manycore
and hierarchical: i.e. a core can communicate more quickly locally than
globally. To be effective on such architectures, programming models must be
aware of the communications hierarchy. This thesis investigates a programming
model that aims to share the responsibility of task placement, load balance, thread
creation, and synchronisation between the application developer and the runtime
system.
The main contribution of this thesis is the development of four new architectureaware
constructs for Glasgow parallel Haskell that exploit information about task
size and aim to reduce communication for small tasks, preserve data locality, or to
distribute large units of work. We define a semantics for the constructs that specifies the sets of PEs that each construct identifies, and we check four properties
of the semantics using QuickCheck.
We report a preliminary investigation of architecture aware programming
models that abstract over the new constructs. In particular, we propose architecture
aware evaluation strategies and skeletons. We investigate three common
paradigms, such as data parallelism, divide-and-conquer and nested parallelism,
on hierarchical architectures with up to 224 cores. The results show that the
architecture-aware programming model consistently delivers better speedup and
scalability than existing constructs, together with a dramatic reduction in the
execution time variability.
We present a comparison of functional multicore technologies and it reports
some of the first ever multicore results for the Feedback Directed Implicit Parallelism
(FDIP) and the semi-explicit parallelism (GpH and Eden) languages. The
comparison reflects the growing maturity of the field by systematically evaluating
four parallel Haskell implementations on a common multicore architecture.
The comparison contrasts the programming effort each language requires with
the parallel performance delivered.
We investigate the minimum thread granularity required to achieve satisfactory
performance for three implementations parallel functional language on a
multicore platform. The results show that GHC-GUM requires a larger thread
granularity than Eden and GHC-SMP. The thread granularity rises as the number
of cores rises
ASKIT: Approximate Skeletonization Kernel-Independent Treecode in High Dimensions
We present a fast algorithm for kernel summation problems in high-dimensions.
These problems appear in computational physics, numerical approximation,
non-parametric statistics, and machine learning. In our context, the sums
depend on a kernel function that is a pair potential defined on a dataset of
points in a high-dimensional Euclidean space. A direct evaluation of the sum
scales quadratically with the number of points. Fast kernel summation methods
can reduce this cost to linear complexity, but the constants involved do not
scale well with the dimensionality of the dataset.
The main algorithmic components of fast kernel summation algorithms are the
separation of the kernel sum between near and far field (which is the basis for
pruning) and the efficient and accurate approximation of the far field.
We introduce novel methods for pruning and approximating the far field. Our
far field approximation requires only kernel evaluations and does not use
analytic expansions. Pruning is not done using bounding boxes but rather
combinatorially using a sparsified nearest-neighbor graph of the input. The
time complexity of our algorithm depends linearly on the ambient dimension. The
error in the algorithm depends on the low-rank approximability of the far
field, which in turn depends on the kernel function and on the intrinsic
dimensionality of the distribution of the points. The error of the far field
approximation does not depend on the ambient dimension.
We present the new algorithm along with experimental results that demonstrate
its performance. We report results for Gaussian kernel sums for 100 million
points in 64 dimensions, for one million points in 1000 dimensions, and for
problems in which the Gaussian kernel has a variable bandwidth. To the best of
our knowledge, all of these experiments are impossible or prohibitively
expensive with existing fast kernel summation methods.Comment: 22 pages, 6 figure
On Designing Multicore-aware Simulators for Biological Systems
The stochastic simulation of biological systems is an increasingly popular
technique in bioinformatics. It often is an enlightening technique, which may
however result in being computational expensive. We discuss the main
opportunities to speed it up on multi-core platforms, which pose new challenges
for parallelisation techniques. These opportunities are developed in two
general families of solutions involving both the single simulation and a bulk
of independent simulations (either replicas of derived from parameter sweep).
Proposed solutions are tested on the parallelisation of the CWC simulator
(Calculus of Wrapped Compartments) that is carried out according to proposed
solutions by way of the FastFlow programming framework making possible fast
development and efficient execution on multi-cores.Comment: 19 pages + cover pag
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