Parallel graph generation algorithms for shared and distributed memory machines

Chapter 6 - Multiprocessor Machines

Graph algorithms are notorious for not getting good speedup on parallel architectures. These algorithms tend to suffer from irregular dependencies and a high synchronization cost that prevent an efficient execution on distributed memory machines. Hence such algorithms are mostly parallelized on shared memory machines. However, current commodity shared memory machines do not typically offer enough parallelism to process these problems. In this paper, we are presenting an early investigation of the scalability of such algorithms on Intel's upcoming Many Integrated Core (Intel MIC) architecture which, when it will be released in 2012, is expected to provide more than 50 physical cores with SMT capability. The Intel MIC architecture can be programmed through many programming models, here we investigate the three most popular of these models namely OpenMP, Cilk Plus and Intel's TBB. We present scalability results of a parallel graph coloring algorithm, three variations of a breadth-first search algorithm and a micro benchmark for irregular computations using these three programming models. Our results on a prototype board show that the multi-threaded architecture of Intel MIC can be effectively used for hiding latencies in irregular applications to achieve almost perfect speedup.

Among elliptic boundary value problems, the class of problems with separable variables can be solved fast and directly. Elliptic problems with separable variables usually assume that the computational domains are simple e.g., rectangle or circle, and constant coefficients [1]. This kind of problems can serve to generate preconditioners in iterative procedures for more complex methods. They can also be used in low-accuracy models similar to the ones used in Numerical Weather Simulations. A straightforward implementation of solvers for such problems makes them considered as too simple to pay much attention to them. For instance, NETLIB* contains the codes of various solvers for problems with separable variables. We are not aware if such solvers are provided as separate solvers in other software packages except NETLIB Fishpack* and Intel$\textcircled{\tiny{\,R}}$ Math Kernel Library (Intel$\textcircled{\tiny{\,R}}$ MKL) together with Intel$\textcircled{\tiny{\,R}}$ Cluster Poisson Solver Library (Intel$\textcircled{\tiny{\,R}}$ CPSL). The problems with the separable variables can be suboptimal in the sense that they require slightly more arithmetic operations (up to logarithmic factor) than the number of unknowns to compute the solution to the problem. This statement is true if, for example, the sizes of the discretized problems are powers of 2. Computational Mathematics suggests that we take into consideration not only arithmetic operations, but also the cost of memory operations as well. Modern computers can perform computations at a very high speed, while lacking the ability to deliver data to the computational units. Keeping in mind that a memory operation can easily be dozen to hundred times slower than an arithmetic one, a computationally optimal algorithm could compute the solution slower than memory optimal algorithm. The recent developments in processor industry resulted in multicore processors become standard processors not only for powerful clusters, but also for home computers and laptops. Therefore, the algorithm can also be non-optimal from the parallelization point of view. Optimality here can be understood in terms of the number of synchronization points and/or in terms of the amount of data that needs to be transferred between different cores/processors. In summary, the modern computational algorithm should focus on 3 key aspects, namely, parallelization, memory operations, and arithmetic costs. The purpose of this paper is to demonstrate on a simple 2D problem with separable variables that taking into account modern model the solution can be computed efficiently and fast. This would also help developers to compute solution to the problem with separable variables really negligible with respect to other computations. To complete our goal, we will evaluate software provided by Intel Corporation. In particular, we focus on the comparison (where possible) of NETLIB Fishpack* and Intel$\textcircled{\tiny{\,R}}$ CPSL provided at [2] as well as Intel$\textcircled{\tiny{\,R}}$ MKL provided at [3]. This paper is organized as follows. First we are solving a 2D Helmholtz problem using single precision on a shared memory machine with two 4-Core Intel$\textcircled{\tiny{\,R}}$ Xeon$\textcircled{\tiny{\,R}}$ Processors E5462. Next we do the same but use double precision arithmetic. Lastly we use double precision on a distributed memory machine using MPI.

Distributed memory parallel machines are increasingly being used by the scientific community to provide computational power for solving problems. Building a distributed memory parallel machine offers a tremendous advantage in terms of cost and scalability over building a shared memory parallel machine. Unfortunately, distributed memory machines are much more difficult to program, mainly due to the lack of a single global address space. Communication between processors in a distributed memory machine is accomplished by message passing. The time cost for acquiring data from another processor's memory is significantly greater than the time cost of acquiring data from local memory. To assist the programmer in using a distributed memory machine, compilers have been developed which alleviate the need for the programmer to manage the lack of a global address space. These compilers will generate semantically correct code containing communication routines to produce a logically shared memory machine on a physically distributed memory machine. However, the runtime performance of the code emitted from some of these compilers can be further improved. This thesis is primarily concerned with advanced compilation techniques which will provide better runtime performance of programs written in imperative languages for regular scientific programs. The optimization of communication generation for distributed memory machines is used to produce this result. We look at two "state of the art" compilation systems and find that improvement in the communication code generated by these compilers is still possible. We have simplified existing descriptions of the various formalisms found in these compilers, while still providing enough formalism to study the problems in depth. We have extended some existing optimization techniques by enhancing the elimination of masks, by extending the notion of relaxing the owner computes rule, by extending the notion of replicating computation, and by extending the notion of replicating data. This thesis has discussed a novel technique to split loops so that they do not contain any guarded statements. Finally, we have suggested avenues for future research, as it is clear from this thesis that more work is required before compilation systems for distributed memory parallel machines will be widely used for general purpose computing.

Recently, use of parallel machines in reservoir simulation has received considerable attention from the petroleum industry. This paper presents parallelization of a 3D compositional, equation-of-state reservoir simulator on the CM-5 and KSR-1. To the best of our knowledge, this is the first time that the parallelization of a compositional reservoir simulator has been performed on both the CM-5 and KSR-1. For new users of the CM-5 machines, the software and hardware of CM-5 architecture is presented, as well as details of the parallelization techniques. For example, domain decomposition, I/O's, phase equilibrium computations, and well model are described. The parallelism techniques on the KSR-1 are presented with the emphasis on the porting of the phase equilibrium calculation. The performance of each machine is evaluated by showing the speedup on different sets of processing nodes. Two test problems were used to explore the capability of the parallelized version of the code; one is a waterflood problem and the other is a CO2 multiple contact miscible flood, both in a West Texas oil field. These field problems were run on 1, 2, 4, 8, 16, and 32 processors to get insight into the locations of communication bottlenecks, generally occurring in the programming with distributed memory machines. The problems of latency and bandwidth which are associated with communication efficiency of the CM-5 are also addressed.

A number of computer scientists have contended that Linda cannot possibly be implemented efficiently on distributed memory machines because there is simply too much overhead. They believe that Linda will not be able to compete with message passing on such machines even for solving computationally intensive problems. The authors address this claim by discussing C-Linda's performance in solving a particular scientific computing problem, the shallow water equations. They have implemented and evaluated the performance of the Linda program on a variety of machines. They present results for shared memory machines (Sequent Symmetry and the Encore Multimax), for distributed memory machines (iPSC/2 and iPSC/860 hypercubes), and for a network of Sparcstations connected by an Ethernet. The same Linda program was executed on all these machines and its performance was evaluated and compared to that of implementations using alternative methods available on all machines. In the authors' experience, the Linda program has generally been easier and more convenient to write than the native versions for each machine. >

We present a system for functional parallel computing on distributed memory machines, which does dynamic load balancing and is totally symmetric. This means that every node can perform any computation and is client and server at the same time. Furthermore, the calling convention is similar to threads on shared memory machines to allow a uniform usage of parallel and distributed procedure calls. Finally the communication and computation is strictly separated for easy maintenance of the user program.

Algorithmic skeletons encapsulate typical parallel programming patterns such that they can be easily applied by users. Existing skeleton libraries usually work on distributed memory machines. We present an extension of our skeleton library Muesli which now allows to use the same application without modifications on a variety of parallel machines ranging from multi-processor distributed memory to many-core shared memory machines and combinations of those such as clusters of multi-core nodes. Internally, the skeletons are based on MPI and Open MP. We demonstrate the efficiency of our approach by providing experimental results.

The results produced by five different MPI benchmark programs on an SGI Altix 3700 are analyzed and compared. There are significant differences in the results for some MPI operations. We investigate the reasons for these discrepancies, which are due to differences in the measurement techniques, implementation details and default configurations of the different benchmarks. The variation in results on the Altix are generally much greater than on a distributed memory machine, due primarily to the ccNUMA architecture and the importance of cache effects, as well as some implementation details of the SGI MPI libraries.

In the past, efficient parallel algorithms have always been developed specifically for the successive generations of parallel systems (vector machines, shared-memory machines, distributed-memory machines, etc.). Today, due to many reasons, such as the inherent heterogeneity, the diversity, and the continuous evolution of the existing parallel execution supports, it is very hard to solve efficiently a target problem by using a single algorithm or to write portable programs that perform well on any computational supports. Toward this goal, we propose a generic framework based on communication models and adaptive approaches in order to adaptively model performances on grid computing environments. We apply this methodology on collective communication operations and show, by achieving experiments on a real platform, that the framework provides significant performances while determining the best combination model- algorithm depending on the problem and architecture parameters.

We present Talbot Suite, a C parallel software collection for the numerical inversion of Laplace Transforms, based onTalbot's method. It is designed to fit both single and multiple Laplace inversion problems, which arise in several application and research fields.In our software, we achieve high accuracy and efficiency, making full use of modern architectures and introducing two different levels of parallelism: coarse and fine grained parallelism. They offer a reasonable tradeoff between accuracy, the main aspect for a few inversions, and efficiency, the main aspect for multiple inversions. To take into account modern high-performance computing architectures, Talbot Suite provides different software versions: an OpenMP-based version for shared memory machines and a MPI-based version for distributed memory machines. Moreover, oriented to hybrid architectures, a combined MPI/OpenMP-based implementation is provided too. We describe our parallel algorithms and the software organization. We also report some performance results. Our software includes sample programs to call the Talbot Suite functions from C and from MATLAB.

Nonblocking data structures are an essential part of many parallel applications in that they can help to improve fault tolerance and performance. Although there are scores of nonblocking data structures, such as stacks, queues, double-ended queues (deques), lists, widely used in practice, most of them are designed to be used on shared-memory machines only, and cannot be used in a distributed-memory setting. Several recent studies focus on the development of novel tailor-made distributed nonblocking data structures and omit the potential for adapting a great wealth of existing shared-memory nonblocking ones for the distributed-memory case. Hence, we propose a general approach to bridge the gap between most existing nonblocking data structures and distributed-memory machines in this work. Several challenges, such as safe memory reclamation and solving the ABA problem, must be overcome. In this paper, we present a global memory management scheme to address these issues. The scheme takes advantage of hazard pointers which are widely used to tackle the problems in shared-memory environments. To demonstrate our general approach, we take stacks as a typical example of nonblocking data structures. This work also provides a survey of well-known nonblocking stack algorithms along with our analysis and evaluation in distributed-memory environments. Moreover, this paper depicts how to improve performance of a stack algorithm by making use of node information.

Parallel algorithms for reduction of a general matrix to upper Hessenberg form on a shared memory multiprocessor

Parallel algorithms for computing all possible subset regression models using the QR decomposition

Increasing the core count of CPUs to increase computational performance has been a significant trend for the better part of a decade. This has led to an unprecedented availability of large shared memory machines. Programming paradigms and systems are shifting to take advantage of this architectural change, so that intra-node parallelism can be fully utilized. Algorithms designed for parallel execution on distributed systems will also need to be modified to scale in these new shared and hybrid memory systems. In this paper, we reinvestigate parallel rendering algorithms with the goal of finding one that achieves favorable performance in this new environment. We test and analyze various methods, including sort-first, sort-last, and a hybrid scheme, to find an optimal parallel algorithm that maximizes shared memory performance.