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Interprocessor communication with memory constraints 00

Interprocessor communication with memory constraints

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proceedings of the twelfth annual acm symposium on parallel algorithms and architectures

作者： Ali Pinar Bruce Hendrickson Department of Computer Science University of Illinois Urbana IL Parallel Computing Sciences Department Sandia National Laboratories Albuquerque NM

ISBN: (纸本)9781581131857

Many parallel applications require periodic redistribution of workloads and associated data. In a distributed memory computer, this redistribution can be difficult if limited memory is available for receiving messages. We propose a model for optimizing the exchange of messages under such circumstances which we call the minimum phase remapping problem. We first show that the problem is NP-Complete, and then analyze several methodologies for addressing it. First, we show how the problem can be phrased as an instance of multi-commodity flow. Next, we study a continuous approximation to the problem. We show that this continuous approximation has a solution which requires at most two more phases than the optimal discrete solution, but the question of how to consistently obtain a good discrete solution from the continuous problem remains open. Finally, we devise a simple and practical approximation algorithm for the problem with a bound of 1.5 times the optimal number of phases.

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Multithreaded algorithms for the fast Fourier transform 00

Multithreaded algorithms for the fast Fourier transform

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proceedings of the twelfth annual acm symposium on parallel algorithms and architectures

作者： Parimala Thulasiraman Kevin B. Theobald Ashfaq A. Khokhar Guang R. Gao Department of Electrical and Computer Engineering 140 Evans Hall University of Delaware Newark DE

ISBN: (纸本)9781581131857

In this paper we present fine-grained multithreaded algorithms and implementations for the Fast Fourier Transform (FFT) problem. The FFT problem has been formulated using two distinct approaches based on the dataflow concepts. The first approach, referred to as the receiver-initiated algorithm, realizes the FFAT iterations as a parent-child relationship while fully exploiting the underlying parallelism. The second approach, referred to as the sender-initiated algorithm, follows a data-flow model based on the producer-consumer style of programming and can be adopted to different architectural parameters for achieving high performance. The implementations of the proposed algorithms have been carried out on the EARTH (Efficient Architecture for Running THreads) platform. For both the algorithms, we analyze the ratio of remote vs local threads and study its impact on the experimental results. Our implementation results show that for certain block sizes on fixed problem size and machine size, the receiver-initiated approach performs better than the sender-initiated approach. For large number of processors, both the algorithms perform well, yielding execution times of only 10 msec for an input of 16 K data points on a 64 processor machine, assuming each processor running at 140 MHz clock speed.

关键词： parallel algorithms fine-grained non-preemptive multithreading dataflow architecture

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On the price of heterogeneity in parallel systems 06

On the price of heterogeneity in parallel systems

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proceedings of the eighteenth annual acm symposium on parallelism in algorithms and architectures

作者： P. Brighten Godfrey Richard M. Karp UC Berkeley Berkeley CA

ISBN: (纸本)9781595934529

Suppose we have a parallel or distributed system whose nodes have limited capacities, such as processing speed, bandwidth, memory, or disk space. How does the performance of the system depend on the amount of heterogeneity of its capacity distribution? We propose a general framework to quantify the worst-case effect of increasing heterogeneity in models of parallel systems. Given a cost function g(C,W) representing the system's performance as a function of its nodes' capacities C and workload W (such as the completion time of an optimum schedule of jobs W on machines C), we say that g has price of heterogeneity α when for any workload, cost cannot increase by more than a factor α if node capacities become arbitrarily more heterogeneous. We give constant bounds on the price of heterogeneity of several well-known job scheduling and graph degree/diameter problems, indicating that increasing heterogeneity can never be much of a disadvantage. On the other hand, with the introduction of timing constraints such as release times or precedence constraints on the jobs, the dependence on node capacities becomes more complex, so that increasing heterogeneity may be quite detrimental.

关键词： majorization scheduling heterogeneity

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Scheduling Cilk multithreaded parallel programs on processors of different speeds 00

Scheduling Cilk multithreaded parallel programs on processor...

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proceedings of the twelfth annual acm symposium on parallel algorithms and architectures

作者： Michael A. Bender Michael O. Rabin Department of Computer Science State University of New York at Stony Brook Stony Brook NY Division of Engineering and Applied Sciences Harvard University Cambridge MA

ISBN: (纸本)9781581131857

We study the problem of executing parallel programs, in particular Cilk programs, on a collection of processors of different speeds. We consider a model in which each processor maintains an estimate of its own speed, where communication between processors has a cost, and where all scheduling must be online. This problem has been considered previously in the fields of asynchronous parallel computing and scheduling theory. Our model is a bridge between the assumptions in these fields. We provide a new more accurate analysis of of an old scheduling algorithm called the maximum utilization scheduler. Based on this analysis, we generalize this scheduling policy and define the high utilization scheduler. We next focus on the Cilck platform and introduce a new algorithm for scheduling Cilk multithreaded parallel programs on heterogeneous processors. This scheduler is inspired by the high utilization scheduler and is modified to fit in a Cilk context. A crucial aspect of our algorithm is that it keeps the original spirit of the Cilk scheduler. In fact, when our new algorithm runs on homogeneous processors, it exactly mimics the dynamics of the original Cilk scheduler.

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Optimal schedules for data-parallel cycle-stealing in networks of workstations (extended abstract) 00

Optimal schedules for data-parallel cycle-stealing in networ...

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proceedings of the twelfth annual acm symposium on parallel algorithms and architectures

作者： Arnold L. Rosenberg Department of Computer Science University of Massachusetts Amherst MA

ISBN: (纸本)9781581131857

We refine the model underlying our prior work on scheduling cycle-stealing opportunities in NOWs [5, 16], obtaining a model wherein the scheduling guidelines of [16] produce optimal schedules for every such opportunity. Although computing optimal schedules usually requires the use of general (often inefficient) function-optimizing methods, we show how to compute optimal schedules efficiently for the broad class of opportunities whose durations come from a concave probability distribution. Even when no such efficient computation of an optimal schedule is available, our refined model always suggests a natural notion of approximately optimal schedule, which may be efficiently computable. We illustrate such efficient approximability via the important class of cycle-stealing opportunities whose durations come from a heavy-tailed distribution. Such opportunities do not admit any optimal schedule—nor even a natural notion of approximately optimal schedule—within the model of [5, 16]. Within our refined model, though, we derive computationally simple schedules for heavy-tailed opportunities, which can be “tuned” to have expected work-output that is arbitrarily close to optimal.

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An empirical study to compare two parallel programming models 06

An empirical study to compare two parallel programming model...

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proceedings of the eighteenth annual acm symposium on parallelism in algorithms and architectures

作者： Lorin Hochstein Victor R. Basili University of Maryland College Park MD

ISBN: (纸本)9781595934529

While there are strong beliefs within the community about whether one particular parallel programming model is easier to use than another, there has been little research to analyze these claims empirically. Currently, the most popular paradigm is message-passing, as implemented by the MPI library [1]. However, MPI is considered to be difficult for developing programs, because it forces the programmer to work at a very low level of abstraction. One alternative parallel programming model is the PRAM model, which supports fine-grained parallelism and has a substantial history of algorithmic theory [2]. It is not possible to program current parallel machines using the PRAM model because modern architectures are not designed to support such a model efficiently. However, current trends towards multicore chips suggest that large-scale, fine-grained uniform-memory access parallel machines may soon be feasible. XMT-C is an extension of the C language that supports parallel directives to provide a PRAM-like model to the programmer. A prototype compiler exists that generates code which runs on a simulator for an XMT architecture [3].To better understand how much benefit a PRAM-like model could provide over a message-passing model, we conducted a feasibility study in an academic setting to compare the effort required to solve a particular problem. The questions under study were: can we measure the effort in developing a program using these two programming models and can we differentiate the amount of effort for each model?.The subjects participating in the study were divided up into two groups. One group solved a problem using the MPI library in either C,C++, or Fortran, and the other group solved the problem using XMT-C. The task was to write a function to multiply a sparse matrix with a dense vector. To obtain subjects, we leveraged existing graduate-level parallel programming courses at two different universities: University of California, Santa Barbara (UCSB), and Universit

关键词： HPC message-passing PRAM XMT empirical study productivity effort parallel programming MPI

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An implementation report for parallel triangular decompositions 06

An implementation report for parallel triangular decompositi...

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proceedings of the eighteenth annual acm symposium on parallelism in algorithms and architectures

作者： Marc Moreno Maza Yuzhen Xie University of Western Ontario (UWO) London Ontario Canada

ISBN: (纸本)9781595934529

Since the discovery of Gröbner bases, the algorithmic advances in Commutative Algebra have made possible to tackle many classical problems in Algebraic Geometry that were previously out of reach. However, algorithmic progress is still desirable, for instance when solving symbolically a large system of algebraic non-linear equations. For such a system, in particular if its solution set consists of geometric components of different dimension (points, curves, surfaces, etc) it is necessary to combine Gröbner bases with decomposition techniques, such as triangular decompositions. Ideally, one would like each of the different components to be produced by an independent processor, or set of processors. In practice, the input polynomial system, which is hiding those components, requires some transformations in order to split the computations into sub-systems and, then, lead to the desired components. The efficiency of this approach depends on its ability to detect and exploit geometrical information during the solving *** work addresses two questions: How to discover geometrical information, at an early stage of the solving process, that would be favorable to parallel execution? How to ensure load balancing among the processors? We answer these questions in the context of triangular decompositions [2] which are a popular way of solving polynomial systems symbolically. These methods tend to split the input polynomial system into subsystems and, therefore, are natural candidate for parallel implementation. However, the only such method which has been parallelized so far is the Characteristic Set Method of Wu [5], as reported in [1, 6]. This approach suffers from several limitations. For instance, the solving of the second component cannot start before that of the first one is completed; this is a limitation in view of coarse-grain *** [4] an algorithm, called Triade, for TRIAngular DEcompositions, provides a good management of the intermediate computat

关键词： parallel execution polynomial system solver

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Infinite parallel job allocation (extended abstract) 00

Infinite parallel job allocation (extended abstract)

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proceedings of the twelfth annual acm symposium on parallel algorithms and architectures

作者： Petra Berenbrink Artur Czumaj Tom Friedetzky Nikita D. Vvedenskaya Dept. of Mathematics & Computer Science Paderborn University D-33095 Paderborn Germany Department of Computer and Information Science New Jersey Institute of Technology University Heights Newark NJ Institut für Informatik Technische Universität München D-80290 München Germany Institute of Information Transmission Problems Russian Academy of Science Moscow 101447 Russia

ISBN: (纸本)9781581131857

In recent years, the task of allocating jobs to servers has been studied with the “balls and bins” abstraction. Results in this area exploit the large decrease in maximum load that can be achieved by allowing each job (ball) a little freedom in choosing its destination server (bin).In this paper we examine an infinite and parallel allocation process (see [ABS98]) which is related to the “balls and bins” abstraction. The simple process can be used to model many problems arising in applications like load balancing, data accesses for parallel data servers, hashing, and PRAM ***, the parallel allocation process behaves in a highly non-uniform manner which makes its analysis challenging. Even the typically simple question of for which arrival rates the process is stable, is highly non-trivial. In order to cope with this non-uniform behavior we introduce a new sequential process and show (via simulations) that the sequential process models the behavior of the parallel one very accurately. We develop a system of ordinary differential equations in order to describe the behavior of our sequential process and present a thorough analysis of the performance this process. For example, we show that the queue length distribution decreases double-exponentially. Finally, we present simulation results indicating that the solutions to the differential equations very well predict the queue length distribution of our sequential process and the largest injection rate for which it is ***, we can conclude that in all the performance characteristics we have measured experimentally, the parallel and the sequential process are closely related. This indicates that the obtained solution of the differential equations and the results presented above are applicable to the parallel process, too.

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Delaunay graphs of point sets in the plane with respect to axis-parallel rectangles 08

Delaunay graphs of point sets in the plane with respect to a...

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proceedings of the nineteenth annual acm-SIAM symposium on Discrete algorithms

作者： Xiaomin Chen János Pach Mario Szegedy Gábor Tardos Google New York NY City College CUNY and Courant Institute NYU New York NY Rutgers University NJ Simon Fraser University Burnaby B.C. Canada and Rényi Institute Reáltanoda utca Hungary

Given a point set P in the plane, the Delaunay graph with respect to axis-parallel rectangles is a graph defined on the vertex set P, whose two points p,q ∈ P are connected by an edge if and only if there is a rectangle parallel to the coordinate axes that contains p and q, but no other elements of P. The following question of Even et al. [ELRS03] was motivated by a frequency assignment problem in cellular telephone networks. Does there exist a constant c > 0 such that the Delaunay graph of any set of n points in general position in the plane contains an independent set of size at least cn? We answer this question in the negative, by proving that the largest independent set in a randomly and uniformly selected point set in the unit square is O(n log2 log n/log n), with probability tending to 1. We also show that our bound is not far from optimal, as the Delaunay graph of a uniform random set of n points almost surely has an independent set of size at least cn/ log *** give two further applications of our methods. 1. We construct 2-dimensional n-element partially ordered sets such that the size of the largest independent sets of vertices in their Hasse diagrams is o(n). This answers a question of Matoušek and Přívětivý [MaP06] and improves a result of Kříž and Nešetřil [KrN91]. 2. For any positive integers c and d, we prove the existence of a planar point set with the property that no matter how we color its elements by c colors, we find an axis-parallel rectangle containing at least d points, all of which have the same color. This solves an old problem from [BrMP05].

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parallel depth first vs. work stealing schedulers on CMP architectures 06

Parallel depth first vs. work stealing schedulers on CMP arc...

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proceedings of the eighteenth annual acm symposium on parallelism in algorithms and architectures

作者： Vasileios Liaskovitis Shimin Chen Phillip B. Gibbons Anastassia Ailamaki Guy E. Blelloch Babak Falsafi Limor Fix Nikos Hardavellas Michael Kozuch Todd C. Mowry Chris Wilkerson Carnegie Mellon University Intel Research Pittsburgh Carnegie Mellon University and Intel Research Pittsburgh Intel Microprocessor Research Lab

ISBN: (纸本)9781595934529

In chip multiprocessors (CMPs), limiting the number of off-chip cache misses is crucial for good performance. Many multithreaded programs provide opportunities for constructive cache sharing, in which concurrently scheduled threads share a largely overlapping working set. In this brief announcement, we highlight our ongoing study [4] comparing the performance of two schedulers designed for fine-grained multithreaded programs: parallel Depth First (PDF) [2], which is designed for constructive sharing, and Work Stealing (WS) [3], which takes a more traditional *** of schedulers. In PDF, processing cores are allocated ready-to-execute program tasks such that higher scheduling priority is given to those tasks the sequential program would have executed earlier. As a result, PDF tends to co-schedule threads in a way that tracks the sequential execution. Hence, the aggregate working set is (provably) not much larger than the single thread working set [1]. In WS, each processing core maintains a local work queue of readyto-execute threads. Whenever its local queue is empty, the core steals a thread from the bottom of the first non-empty queue it finds. WS is an attractive scheduling policy because when there is plenty of parallelism, stealing is quite rare. However, WS is not designed for constructive cache sharing, because the cores tend to have disjoint working *** configurations studied. We evaluated the performance of PDF and WS across a range of simulated CMP configurations. We focused on designs that have fixed-size private L1 caches and a shared L2 cache on chip. For a fixed die size (240 mm2), we varied the number of cores from 1 to 32. For a given number of cores, we used a (default) configuration based on current CMPs and realistic projections of future CMPs, as process technologies decrease from 90nm to *** of findings. We studied a variety of benchmark programs to show the following *** several application classes, PDF enable

关键词： scheduling chip multiprocessors caches

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