A Practical Hierarchial Model of Parallel Computation: The Model

We introduce a model of parallel computation that retains the ideal properties of the PRAM by using it as a sub-model, while simultaneously being more reflective of realistic parallel architectures by accounting for and providing abstract control over communication and synchronization costs. The Hierarchical PRAM (H-PRAM) model controls conceptual complexity in the face of asynchrony in two ways. First, by providing the simplifying assumption of synchronization to the design of algorithms, but allowing the algorithms to work asynchronously with each other; and organizing this control asynchrony via an implicit hierarchy relation. Second, by allowing the restriction of communication asynchrony in order to obtain determinate algorithms (thus greatly simplifying proofs of correctness). It is shown that the model is reflective of a variety of existing and proposed parallel architectures, particularly ones that can support massive parallelism. Relationships to programming languages are discussed. Since the PRAM is a sub-model, we can use PRAM algorithms as sub-algorithms in algorithms for the H-PRAM; thus results that have been established with respect to the PRAM are potentially transferable to this new model. The H-PRAM can be used as a flexible tool to investigate general degrees of locality (“neighborhoods of activity) in problems, considering communication and synchronization simultaneously. This gives the potential of obtaining algorithms that map more efficiently to architectures, and of increasing the number of processors that can efficiently be used on a problem (in comparison to a PRAM that charges for communication and synchronization). The model presents a framework in which to study the extent that general locality can be exploited in parallel computing. A companion paper demonstrates the usage of the H-PRAM via the design and analysis of various algorithms for computing the complete binary tree and the FFT/butterfly graph

A method for implementing lock-free shared data structures

We are interested in implementing data structures on shared memory multiprocessors. A natural model for these machines is an asynchronous parallel machine, in which the processors are subject to arbitrary delays. On such machines, it is desirable for algorithms to be {\em lock-free}, that is, they must allow concurrent access to data without using mutual exclusion. Efficient lock-free implementations are known for some specific data structures, but these algorithms do not generalize well to other structures. For most data structures, the only previously known lock-free algorithm is due to Herlihy. Herlihy presents a simple methodology to create a lock-free implementation of a general data structure, but his approach can be very expensive. We present a technique that provides the semantics of exclusive access to data without using mutual exclusion. Using this technique, we devise the {\em caching method}, a general method of implementing lock-free data structures that is provably better than Herlihy's methodology for many well-known data structures. The cost of one operation using the caching method is proportional to $T \log T$, where $T$ is the sequential cost of the operation. Under Herlihy's methodology, the cost is proportional to $T + C$, where $C$ is the time needed to make a logical copy of the data structure. For many data structures, such as arrays and {\em well connected} pointer-based structures (e.g., a doubly linked list), the best known value for $C$ is proportional to the size of the structure, making the copying time much larger than the sequential cost of an operation. The new method can also allow {\em concurrent updates} to the data structure; Herlihy's methodology cannot. A correct lock-free implementation can be derived from a correct sequential implementation in a straightforward manner using this method. The method is also flexible; a programmer can change many of the details of the default implementation to optimize for a particular pattern of data structure use

Fast Deterministic Consensus in a Noisy Environment

It is well known that the consensus problem cannot be solved deterministically in an asynchronous environment, but that randomized solutions are possible. We propose a new model, called noisy scheduling, in which an adversarial schedule is perturbed randomly, and show that in this model randomness in the environment can substitute for randomness in the algorithm. In particular, we show that a simplified, deterministic version of Chandra's wait-free shared-memory consensus algorithm (PODC, 1996, pp. 166-175) solves consensus in time at most logarithmic in the number of active processes. The proof of termination is based on showing that a race between independent delayed renewal processes produces a winner quickly. In addition, we show that the protocol finishes in constant time using quantum and priority-based scheduling on a uniprocessor, suggesting that it is robust against the choice of model over a wide range.Comment: Typographical errors fixe

Aspects of practical implementations of PRAM algorithms

The PRAM is a shared memory model of parallel computation which abstracts away from inessential engineering details. It provides a very simple architecture independent model and provides a good programming environment. Theoreticians of the computer science community have proved that it is possible to emulate the theoretical PRAM model using current technology. Solutions have been found for effectively interconnecting processing elements, for routing data on these networks and for distributing the data among memory modules without hotspots. This thesis reviews this emulation and the possibilities it provides for large scale general purpose parallel computation. The emulation employs a bridging model which acts as an interface between the actual hardware and the PRAM model. We review the evidence that such a scheme crn achieve scalable parallel performance and portable parallel software and that PRAM algorithms can be optimally implemented on such practical models. In the course of this review we presented the following new results: 1. Concerning parallel approximation algorithms, we describe an NC algorithm for finding an approximation to a minimum weight perfect matching in a complete weighted graph. The algorithm is conceptually very simple and it is also the first NC-approximation algorithm for the task with a sub-linear performance ratio. 2. Concerning graph embedding, we describe dense edge-disjoint embeddings of the complete binary tree with n leaves in the following n-node communication networks: the hypercube, the de Bruijn and shuffle-exchange networks and the 2-dimcnsional mesh. In the embeddings the maximum distance from a leaf to the root of the tree is asymptotically optimally short. The embeddings facilitate efficient implementation of many PRAM algorithms on networks employing these graphs as interconnection networks. 3. Concerning bulk synchronous algorithmics, we describe scalable transportable algorithms for the following three commonly required types of computation; balanced tree computations. Fast Fourier Transforms and matrix multiplications

On expressing different concurrency paradigms on virtual execution environment

Virtual execution environments (VEE) such as the Java Virtual Machine (JVM) and the Microsoft Common Language Runtime (CLR) have been designed when the dominant computer architecture featured a Von-Neumann interface to programs: a single processor hiding all the complexity of parallel computations inside its design. Programs are expressed in an intermediate form that is executed by the VEE that defines an abstract computational model in which the concurrency model has been influenced by these design choices and it basically exposes the multi-threading model of the underlying operating system. Recently computer systems have introduced computational units in which concurrency is explicit and under program control. Relevant examples are the Graphical Processing Units (GPU such as Nvidia or AMD) and the Cell BE architecture which allow for explicit control of single processing unit, local memories and communication channels. Unfortunately programs designed for Virtual Machines cannot access to these resources since are not available through the abstractions provided by the VEE. A major redesign of VEEs seems to be necessary in order to bridge this gap. In this thesis we study the problem of exposing non-von Neumann computing resources within the Virtual Machine without need for a redesign of the whole execution infrastructure. In this work we express parallel computations relying on extensible meta-data and reflection to encode information. Meta-programming techniques are then used to rewrite the program into an equivalent one using the special purpose underlying architecture. We provide a case study in which this approach is applied to compiling Common Intermediate Language (CIL) methods to multi-core GPUs; we show that it is possible to access these non-standard computing resources without any change to the virtual machine design

Toward optimised skeletons for heterogeneous parallel architecture with performance cost model

High performance architectures are increasingly heterogeneous with shared and distributed memory components, and accelerators like GPUs. Programming such architectures is complicated and performance portability is a major issue as the architectures evolve. This thesis explores the potential for algorithmic skeletons integrating a dynamically parametrised static cost model, to deliver portable performance for mostly regular data parallel programs on heterogeneous archi- tectures. The rst contribution of this thesis is to address the challenges of program- ming heterogeneous architectures by providing two skeleton-based programming libraries: i.e. HWSkel for heterogeneous multicore clusters and GPU-HWSkel that enables GPUs to be exploited as general purpose multi-processor devices. Both libraries provide heterogeneous data parallel algorithmic skeletons including hMap, hMapAll, hReduce, hMapReduce, and hMapReduceAll. The second contribution is the development of cost models for workload dis- tribution. First, we construct an architectural cost model (CM1) to optimise overall processing time for HWSkel heterogeneous skeletons on a heterogeneous system composed of networks of arbitrary numbers of nodes, each with an ar- bitrary number of cores sharing arbitrary amounts of memory. The cost model characterises the components of the architecture by the number of cores, clock speed, and crucially the size of the L2 cache. Second, we extend the HWSkel cost model (CM1) to account for GPU performance. The extended cost model (CM2) is used in the GPU-HWSkel library to automatically nd a good distribution for both a single heterogeneous multicore/GPU node, and clusters of heteroge- neous multicore/GPU nodes. Experiments are carried out on three heterogeneous multicore clusters, four heterogeneous multicore/GPU clusters, and three single heterogeneous multicore/GPU nodes. The results of experimental evaluations for four data parallel benchmarks, i.e. sumEuler, Image matching, Fibonacci, and Matrix Multiplication, show that our combined heterogeneous skeletons and cost models can make good use of resources in heterogeneous systems. Moreover using cores together with a GPU in the same host can deliver good performance either on a single node or on multiple node architectures