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LogP: Towards a Realistic Model of Parallel Computation
, 1993
"... A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding developme ..."
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Cited by 497 (14 self)
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A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding development of techniques that yield performance across a range of current and future parallel machines. This paper offers a new parallel machine model, called LogP, that reflects the critical technology trends underlying parallel computers. It is intended to serve as a basis for developing fast, portable parallel algorithms and to offer guidelines to machine designers. Such a model must strike a balance between detail and simplicity in order to reveal important bottlenecks without making analysis of interesting problems intractable. The model is based on four parameters that specify abstractly the computing bandwidth, the communication bandwidth, the communication delay, and the efficiency of coupling communication and computation. Portable parallel algorithms typically adapt to the machine configuration, in terms of these parameters. The utility of the model is demonstrated through examples that are implemented on the CM5.
LogGP: Incorporating Long Messages into the LogP Model  One step closer towards a realistic model for parallel computation
, 1995
"... We present a new model of parallel computationthe LogGP modeland use it to analyze a number of algorithms, most notably, the single node scatter (onetoall personalized broadcast). The LogGP model is an extension of the LogP model for parallel computation [CKP + 93] which abstracts the comm ..."
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Cited by 236 (1 self)
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We present a new model of parallel computationthe LogGP modeland use it to analyze a number of algorithms, most notably, the single node scatter (onetoall personalized broadcast). The LogGP model is an extension of the LogP model for parallel computation [CKP + 93] which abstracts the communication of fixedsized short messages through the use of four parameters: the communication latency (L), overhead (o), bandwidth (g), and the number of processors (P ). As evidenced by experimental data, the LogP model can accurately predict communication performance when only short messages are sent (as on the CM5) [CKP + 93, CDMS94]. However, many existing parallel machines have special support for long messages and achieve a much higher bandwidth for long messages compared to short messages (e.g., IBM SP2, Paragon, Meiko CS2, Ncube/2). We extend the basic LogP model with a linear model for long messages. This combination, which we call the LogGP model of parallel computation, has o...
WaitFree Data Structures in the Asynchronous PRAM Model
 In Proceedings of the 2nd Annual Symposium on Parallel Algorithms and Architectures
, 2000
"... In the asynchronous PRAM model, processes communicate by atomically reading and writing shared memory locations. This paper investigates the extent to which asynchronous PRAM permits longlived, highly concurrent data structures. An implementation of a concurrent object is waitfree if every operati ..."
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Cited by 65 (13 self)
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In the asynchronous PRAM model, processes communicate by atomically reading and writing shared memory locations. This paper investigates the extent to which asynchronous PRAM permits longlived, highly concurrent data structures. An implementation of a concurrent object is waitfree if every operation will complete in a finite number of steps, and it is kbounded waitfree, for some k > 0, if every operation will complete within k steps. In the first part of this paper, we show that there are objects with waitfree implementations but no kbounded waitfree implementations for any k, and that there is an infinite hierarchy of objects with implementations that are kbounded waitfree but not Kbounded waitfree for some K > k. In the second part of the paper, we give an algebraic characterization of a large class of objects that do have waitfree implementations in asynchronous PRAM, as well as a general algorithm for implementing them. Our tools include simple iterative algorithms for waitfree approximate agreement and atomic snapshot.
CommunicationEfficient Parallel Sorting
, 1996
"... We study the problem of sorting n numbers on a pprocessor bulksynchronous parallel (BSP) computer, which is a parallel multicomputer that allows for general processortoprocessor communication rounds provided each processor sends and receives at most h items in any round. We provide parallel sort ..."
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Cited by 64 (2 self)
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We study the problem of sorting n numbers on a pprocessor bulksynchronous parallel (BSP) computer, which is a parallel multicomputer that allows for general processortoprocessor communication rounds provided each processor sends and receives at most h items in any round. We provide parallel sorting methods that use internal computation time that is O( n log n p ) and a number of communication rounds that is O( log n log(h+1) ) for h = \Theta(n=p). The internal computation bound is optimal for any comparisonbased sorting algorithm. Moreover, the number of communication rounds is bounded by a constant for the (practical) situations when p n 1\Gamma1=c for a constant c 1. In fact, we show that our bound on the number of communication rounds is asymptotically optimal for the full range of values for p, for we show that just computing the "or" of n bits distributed evenly to the first O(n=h) of an arbitrary number of processors in a BSP computer requires\Omega\Gammaqui n= log(h...
Designing Efficient Sorting Algorithms for Manycore GPUs
, 2009
"... We describe the design of highperformance parallel radix sort and merge sort routines for manycore GPUs, taking advantage of the full programmability offered by CUDA. Our radix sort is the fastest GPU sort and our merge sort is the fastest comparisonbased sort reported in the literature. Our radix ..."
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Cited by 55 (4 self)
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We describe the design of highperformance parallel radix sort and merge sort routines for manycore GPUs, taking advantage of the full programmability offered by CUDA. Our radix sort is the fastest GPU sort and our merge sort is the fastest comparisonbased sort reported in the literature. Our radix sort is up to 4 times faster than the graphicsbased GPUSort and greater than 2 times faster than other CUDAbased radix sorts. It is also 23 % faster, on average, than even a very carefully optimized multicore CPU sorting routine. To achieve this performance, we carefully design our algorithms to expose substantial finegrained parallelism and decompose the computation into independent tasks that perform minimal global communication. We exploit the highspeed onchip shared memory provided by NVIDIAâ€™s GPU architecture and efficient dataparallel primitives, particularly parallel scan. While targeted at GPUs, these algorithms should also be wellsuited for other manycore processors.
A Randomized Parallel 3D Convex Hull Algorithm For Coarse Grained Multicomputers
 In Proc. ACM Symp. on Parallel Algorithms and Architectures
, 1995
"... We present a randomized parallel algorithm for constructing the 3D convex hull on a generic pprocessor coarse grained multicomputer with arbitrary interconection network and n=p local memory per processor, where n=p p 2+ffl (for some arbitrarily small ffl ? 0). For any given set of n points in ..."
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Cited by 50 (11 self)
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We present a randomized parallel algorithm for constructing the 3D convex hull on a generic pprocessor coarse grained multicomputer with arbitrary interconection network and n=p local memory per processor, where n=p p 2+ffl (for some arbitrarily small ffl ? 0). For any given set of n points in 3space, the algorithm computes the 3D convex hull, with high probaility, in O( n log n p ) local computation time and O(1) communication phases with at most O(n=p) data sent/received by each processor. That is, with high probability, the algorithm computes the 3D convex hull of an arbitrary point set in time O( n logn p + \Gamma n;p ), where \Gamma n;p denotes the time complexity of one communication phase. The assumption n p p 2+ffl implies a coarse grained, limited parallelism, model which is applicable to most commercially available multiprocessors. In the terminology of the BSP model, our algorithm requires, with high probability, O(1) supersteps, synchronization period L = \Th...
Waitfree Parallel Algorithms for the UnionFind Problem
 In Proc. 23rd ACM Symposium on Theory of Computing
, 1994
"... We are interested in designing efficient data structures for a shared memory multiprocessor. In this paper we focus on the UnionFind data structure. We consider a fully asynchronous model of computation where arbitrary delays are possible. Thus we require our solutions to the data structure problem ..."
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Cited by 50 (0 self)
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We are interested in designing efficient data structures for a shared memory multiprocessor. In this paper we focus on the UnionFind data structure. We consider a fully asynchronous model of computation where arbitrary delays are possible. Thus we require our solutions to the data structure problem have the waitfree property, meaning that each thread continues to make progress on its operations, independent of the speeds of the other threads. In this model efficiency is best measured in terms of the total number of instructions used to perform a sequence of data structure operations, the work performed by the processors. We give a waitfree implementation of an efficient algorithm for UnionFind. In addition we show that the worst case performance of the algorithm can be improved by simulating a synchronized algorithm, or by simulating a larger machine if the data structure requests support sufficient parallelism. Our solutions apply to a much more general adversary model than has be...
Modeling Parallel Computers as Memory Hierarchies
 In Proc. Programming Models for Massively Parallel Computers
, 1993
"... A parameterized generic model that captures the features of diverse computer architectures would facilitate the development of portable programs. Specific models appropriate to particular computers are obtained by specifying parameters of the generic model. A generic model should be simple, and for ..."
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Cited by 45 (6 self)
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A parameterized generic model that captures the features of diverse computer architectures would facilitate the development of portable programs. Specific models appropriate to particular computers are obtained by specifying parameters of the generic model. A generic model should be simple, and for each machine that it is intended to represent, it should have a reasonably accurate specific model. The Parallel Memory Hierarchy (PMH) model of computation uses a single mechanism to model the costs of both interprocessor communication and memory hierarchy traffic. A computer is modeled as a tree of memory modules with processors at the leaves. All data movement takes the form of block transfers between children and their parents. This paper assesses the strengths and weaknesses of the PMH model as a generic model. 1 Introduction The raw computing power of multiprocessor computers is exploding. The challenge is to create software that can take advantage of this computing power. The diversit...
Can a SharedMemory Model Serve as a Bridging Model for Parallel Computation?
, 1999
"... There has been a great deal of interest recently in the development of generalpurpose bridging models for parallel computation. Models such as the BSP and LogP have been proposed as more realistic alternatives to the widely used PRAM model. The BSP and LogP models imply a rather different style fo ..."
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Cited by 42 (11 self)
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There has been a great deal of interest recently in the development of generalpurpose bridging models for parallel computation. Models such as the BSP and LogP have been proposed as more realistic alternatives to the widely used PRAM model. The BSP and LogP models imply a rather different style for designing algorithms when compared with the PRAM model. Indeed, while many consider data parallelism as a convenient style, and the sharedmemory abstraction as an easytouse platform, the bandwidth limitations of current machines have diverted much attention to messagepassing and distributedmemory models (such as the BSP and LogP) that account more properly for these limitations. In this paper we consider the question of whether a sharedmemory model can serve as an effective bridging model for parallel computation. In particular, can a sharedmemory model be as effective as, say, the BSP? As a candidate for a bridging model, we introduce the Queuing SharedMemory (QSM) model, which accounts for limited communication bandwidth while still providing a simple sharedmemory abstraction. We substantiate the ability of the QSM to serve as a bridging model by providing a simple workpreserving emulation of the QSM on both the BSP, and on a related model, the (d, x)BSP. We present evidence that the features of the QSM are essential to its effectiveness as a bridging model. In addition, we describe scenarios