Distributed-Memory Breadth-First Search on Massive Graphs

This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered direction optimizing algorithm. We analyze the performance and scalability trade-offs in using different local data structures such as CSR and DCSC, enabling in-node multithreading, and graph decompositions such as 1D and 2D decomposition.Comment: arXiv admin note: text overlap with arXiv:1104.451

The fast multipole method at exascale

This thesis presents a top to bottom analysis on designing and implementing fast algorithms for current and future systems. We present new analysis, algorithmic techniques, and implementations of the Fast Multipole Method (FMM) for solving N- body problems. We target the FMM because it is broadly applicable to a variety of scientific particle simulations used to study electromagnetic, fluid, and gravitational phenomena, among others. Importantly, the FMM has asymptotically optimal time complexity with guaranteed approximation accuracy. As such, it is among the most attractive solutions for scalable particle simulation on future extreme scale systems. We specifically address two key challenges. The first challenge is how to engineer fast code for today’s platforms. We present the first in-depth study of multicore op- timizations and tuning for FMM, along with a systematic approach for transforming a conventionally-parallelized FMM into a highly-tuned one. We introduce novel opti- mizations that significantly improve the within-node scalability of the FMM, thereby enabling high-performance in the face of multicore and manycore systems. The second challenge is how to understand scalability on future systems. We present a new algorithmic complexity analysis of the FMM that considers both intra- and inter- node communication costs. Using these models, we present results for choosing the optimal algorithmic tuning parameter. This analysis also yields the surprising prediction that although the FMM is largely compute-bound today, and therefore highly scalable on current systems, the trajectory of processor architecture designs, if there are no significant changes could cause it to become communication-bound as early as the year 2015. This prediction suggests the utility of our analysis approach, which directly relates algorithmic and architectural characteristics, for enabling a new kind of highlevel algorithm-architecture co-design. To demonstrate the scientific significance of FMM, we present two applications namely, direct simulation of blood which is a multi-scale multi-physics problem and large-scale biomolecular electrostatics. MoBo (Moving Boundaries) is the infrastruc- ture for the direct numerical simulation of blood. It comprises of two key algorithmic components of which FMM is one. We were able to simulate blood flow using Stoke- sian dynamics on 200,000 cores of Jaguar, a peta-flop system and achieve a sustained performance of 0.7 Petaflop/s. The second application we propose as future work in this thesis is biomolecular electrostatics where we solve for the electrical potential using the boundary-integral formulation discretized with boundary element methods (BEM). The computational kernel in solving the large linear system is dense matrix vector multiply which we propose can be calculated using our scalable FMM. We propose to begin with the two dielectric problem where the electrostatic field is cal- culated using two continuum dielectric medium, the solvent and the molecule. This is only a first step to solving biologically challenging problems which have more than two dielectric medium, ion-exclusion layers, and solvent filled cavities. Finally, given the difficulty in producing high-performance scalable code, productivity is a key concern. Recently, numerical algorithms are being redesigned to take advantage of the architectural features of emerging multicore processors. These new classes of algorithms express fine-grained asynchronous parallelism and hence reduce the cost of synchronization. We performed the first extensive performance study of a recently proposed parallel programming model, called Concurrent Collections (CnC). In CnC, the programmer expresses her computation in terms of application-specific operations, partially-ordered by semantic scheduling constraints. The CnC model is well-suited to expressing asynchronous-parallel algorithms, so we evaluate CnC using two dense linear algebra algorithms in this style for execution on state-of-the-art mul- ticore systems. Our implementations in CnC was able to match and in some cases even exceed competing vendor-tuned and domain specific library codes. We combine these two distinct research efforts by expressing FMM in CnC, our approach tries to marry performance with productivity that will be critical on future systems. Looking forward, we would like to extend this to distributed memory machines, specifically implement FMM in the new distributed CnC, distCnC to express fine-grained paral- lelism which would require significant effort in alternative models.Ph.D

On the design of architecture-aware algorithms for emerging applications

This dissertation maps various kernels and applications to a spectrum of programming models and architectures and also presents architecture-aware algorithms for different systems. The kernels and applications discussed in this dissertation have widely varying computational characteristics. For example, we consider both dense numerical computations and sparse graph algorithms. This dissertation also covers emerging applications from image processing, complex network analysis, and computational biology. We map these problems to diverse multicore processors and manycore accelerators. We also use new programming models (such as Transactional Memory, MapReduce, and Intel TBB) to address the performance and productivity challenges in the problems. Our experiences highlight the importance of mapping applications to appropriate programming models and architectures. We also find several limitations of current system software and architectures and directions to improve those. The discussion focuses on system software and architectural support for nested irregular parallelism, Transactional Memory, and hybrid data transfer mechanisms. We believe that the complexity of parallel programming can be significantly reduced via collaborative efforts among researchers and practitioners from different domains. This dissertation participates in the efforts by providing benchmarks and suggestions to improve system software and architectures.Ph.D.Committee Chair: Bader, David; Committee Member: Hong, Bo; Committee Member: Riley, George; Committee Member: Vuduc, Richard; Committee Member: Wills, Scot

Sparse matrix-vector multiplication on GPGPU clusters: A new storage format and a scalable implementation

Sparse matrix-vector multiplication (spMVM) is the dominant operation in many sparse solvers. We investigate performance properties of spMVM with matrices of various sparsity patterns on the nVidia "Fermi" class of GPGPUs. A new "padded jagged diagonals storage" (pJDS) format is proposed which may substantially reduce the memory overhead intrinsic to the widespread ELLPACK-R scheme. In our test scenarios the pJDS format cuts the overall spMVM memory footprint on the GPGPU by up to 70%, and achieves 95% to 130% of the ELLPACK-R performance. Using a suitable performance model we identify performance bottlenecks on the node level that invalidate some types of matrix structures for efficient multi-GPGPU parallelization. For appropriate sparsity patterns we extend previous work on distributed-memory parallel spMVM to demonstrate a scalable hybrid MPI-GPGPU code, achieving efficient overlap of communication and computation.Comment: 10 pages, 5 figures. Added reference to other recent sparse matrix format

High-Performance Computing Algorithms for Constructing Inverted Files on Emerging Multicore Processors

Current trends in processor architectures increasingly include more cores on a single chip and more complex memory hierarchies, and such a trend is likely to continue in the foreseeable future. These processors offer unprecedented opportunities for speeding up demanding computations if the available resources can be effectively utilized. Simultaneously, parallel programming languages such as OpenMP and MPI have been commonly used on clusters of multicore CPUs while newer programming languages such as OpenCL and CUDA have been widely adopted on recent heterogeneous systems and GPUs respectively. The main goal of this dissertation is to develop techniques and methodologies for exploiting these emerging parallel architectures and parallel programming languages to solve large scale irregular applications such as the construction of inverted files. The extraction of inverted files from large collections of documents forms a critical component of all information retrieval systems including web search engines. In this problem, the disk I/O throughput is the major performance bottleneck especially when intermediate results are written onto disks. In addition to the I/O bottleneck, a number of synchronization and consistency issues must be resolved in order to build the dictionary and postings lists efficiently. To address these issues, we introduce a dictionary data structure using a hybrid of trie and B-trees and a high-throughput pipeline strategy that completely avoids the use of disks as temporary storage for intermediate results, while ensuring the consumption of the input data at a high rate. The high-throughput pipelined strategy produces parallel parsed streams that are consumed at the same rate by parallel indexers. The pipelined strategy is implemented on a single multicore CPU as well as on a cluster of such nodes. We were able to achieve a throughput of more than 262MB/s on the ClueWeb09 dataset on a single node. On a cluster of 32 nodes, our experimental results show scalable performance using different metrics, significantly improving on prior published results. On the other hand, we develop a new approach for handling time-evolving documents using additional small temporal indexing structures. The lifetime of the collection is partitioned into multiple time windows, which guarantees a very fast temporal query response time at a small space overhead relative to the non-temporal case. Extensive experimental results indicate that the overhead in both indexing and querying is small in this more complicated case, and the query performance can indeed be improved using finer temporal partitioning of the collection. Finally, we employ GPUs to accelerate the indexing process for building inverted files and to develop a very fast algorithm for the highly irregular list ranking problem. For the indexing problem, the workload is split between CPUs and GPUs in such a way that the strengths of both architectures are exploited. For the list ranking problem involved in the decompression of inverted files, an optimized GPU algorithm is introduced by reducing the problem to a large number of fine grain computations in such a way that the processing cost per element is shown to be close to the best possible