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Improved Worst -Case Deterministic parallel Dynamic Minimum Spanning Forest 18

Improved Worst -Case Deterministic Parallel Dynamic Minimum ...

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30th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Kopelowitz, Tsvi Porat, Ely Rosenmutter, Yair Bar Ilan Univ Ramat Gan Israel

ISBN: (纸本)9781450357999

This paper gives a new deterministic algorithm for the dynamic Minimum Spanning Forest (MSF) problem in the EREW PRAM model, where the goal is to maintain a MSF of a weighted graph with n vertices and m edges while supporting edge insertions and deletions. We show that one can solve the dynamic MSF problem using O(jt) processors and O(log n) worst-case update time, for a total of ONT. log n) work. This improves on the work of Ferragina [IPPS 1995] which costs O(log n) worst-case update time and 0(n213 log);171) work.

关键词： dynamic connectivity minimum spanning forest dynamic graph algorithms pram model

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Brief Announcement: Open Cilk 18

Brief Announcement: Open Cilk

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30th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Schardl, Tao B. Lee, I-Ting Angelina Leiserson, Charles E. MIT CSAIL Cambridge MA 02139 USA Washington Univ St Louis MO 63110 USA

ISBN: (纸本)9781450357999

Open Cilk is a new open-source platform to support Cilk multi-threaded programming, especially for researchers and teachers. Open Cilk aims to provide a full-featured implementation of Cilk that is easy to modify and extend. Based on the award-winning Tapir/LLVM compiler, Open Cilk will provide a streamlined run-time system and feature comprehensive static instrumentation for dynamic-analysis tools. As a community-infrastructure project, Open Cilk encourages contributions from researchers in the areas of languages, compilers, runtime systems, tools, libraries, and benchmarks.

关键词： Cilk multicore programming parallel algorithms parallel languages productivity tools

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A Simple and Efficient parallel Laplacian Solver 23

A Simple and Efficient Parallel Laplacian Solver

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35th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Sachdeva, Sushant Zhao, Yibin Univ Toronto Toronto ON Canada

ISBN: (纸本)9781450395458

A symmetric matrix is called a Laplacian if it has nonpositive off-diagonal entries and zero row sums. Since the seminal work of Spielman and Teng (2004) on solving Laplacian linear systems in nearly linear time, several algorithms have been designed for the task. Yet, the work of Kyng and Sachdeva (2016) remains the simplest and most practical sequential solver. They presented a solver purely based on random sampling and without graph-theoretic constructions such as low-stretch trees and sparsifiers. In this work, we extend the result of Kyng and Sachdeva to a simple parallel Laplacian solver with O(m log(3) n log log n) or O((m + n log(5) n) log n log log n) work and O(log(2) n log log n) depth using the ideas of block Cholesky factorization from Kyng et al. (2016). Compared to the best known parallel Laplacian solvers that achieve polylogarithmic depth due to Lee et al. (2015), our solver achieves both better depth and, for dense graphs, better work.

关键词： Laplacian Linear Systems parallel algorithms Linear System Solvers

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Scheduling Irregular parallel Computations on Hierarchical Caches 11

Scheduling Irregular Parallel Computations on Hierarchical C...

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23rd annual symposium on parallelism in algorithms and architectures

作者： Blelloch, Guy E. Fineman, Jeremy T. Gibbons, Phillip B. Simhadri, Harsha Vardhan Carnegie Mellon Univ Pittsburgh PA 15213 USA

ISBN: (纸本)9781450307437

For nested-parallel computations with low depth (span, critical path length) analyzing the work, depth, and sequential cache complexity suffices to attain reasonably strong bounds on the parallel runtime and cache complexity on machine models with either shared or private caches. These bounds, however, do not extend to general hierarchical caches, due to limitations in (i) the cache-oblivious (CO) model used to analyze cache complexity and (ii) the schedulers used to map computation tasks to processors. This paper presents the parallel cache-oblivious (PCO) model, a relatively simple modification to the CO model that can be used to account for costs on a broad range of cache hierarchies. The first change is to avoid capturing artificial data sharing among parallel threads, and the second is to account for parallelism-memory imbalances within tasks. Despite the more restrictive nature of PCO compared to CO, many algorithms have the same asymptotic cache complexity bounds. The paper then describes a new scheduler for hierarchical caches, which extends recent work on "space-bounded schedulers" to allow for computations with arbitrary work imbalance among parallel subtasks. This scheduler attains provably good cache performance and runtime on parallel machine models with hierarchical caches, for nested-parallel computations analyzed using the PCO model. We show that under reasonable assumptions our scheduler is "work efficient" in the sense that the cost of the cache misses are evenly balanced across the processors-i.e., the runtime can be determined within a constant factor by taking the total cost of the cache misses analyzed for a computation and dividing it by the number of processors. In contrast, to further support our model, we show that no scheduler can achieve such bounds (optimizing for both cache misses and runtime) if work, depth, and sequential cache complexity are the only parameters used to analyze a computation.

关键词： parallel hierarchical memory Cost models Schedulers Analysis of parallel algorithms Cache complexity

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Brief announcement: RedRem: A parallel redundancy remover 11

Brief announcement: RedRem: A parallel redundancy remover

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Proceedings of the twenty-third annual acm symposium on parallelism in algorithms and architectures

作者： Acharya, Hrishikesh Gouda, Mohamed University of Texas at Austin Austin TX United States National Science Foundation Washington DC United States

ISBN: (纸本)9781450307437

Policies defined by a sequence of predicate-decision rules, with first-match semantics, are widely used;a notable example is their use in firewalls, where the rules are used to decide whether to accept or discard each packet. Owing to the critical importance of correctness of such policies, as well as the need for high performance, they have been the subject of considerable analysis. In earlier work, we have demonstrated that the problem of removing redundant rules from firewalls is theoretically equivalent to verifying that a firewall satisfies a property, and proposed that this theorem be used to build a high performance redundancy remover. In this paper, we realize this promise, and build a fast linear-space redundancy remover, one to three orders of magnitude faster than current approaches. Further, we show that our algorithm is easy to parallelize- there exists a natural way to partition a large instance of the problem into independent small ones. © 2011 Authors.

关键词： Redundancy

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Bandwidth Optimized parallel algorithms for Sparse Matrix-Matrix Multiplication using Propagation Blocking 20

Bandwidth Optimized Parallel Algorithms for Sparse Matrix-Ma...

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32nd acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Gu, Zhixiang Moreira, Jose Edelsohn, David Azad, Ariful Indiana Univ Bloomington IN 47405 USA IBM Corp Armonk NY 10504 USA Facebook Inc Menlo Pk CA 94025 USA

ISBN: (纸本)9781450369350

Sparse matrix-matrix multiplication (SpGEMM) is a widely used kernel in various graph, scientific computing and machine learning algorithms. It is well known that SpGEMM is a memory-bound operation, and its peak performance is expected to be bound by the memory bandwidth. Yet, existing algorithms fail to saturate the memory bandwidth, resulting in suboptimal performance under the Roofline model. In this paper, we characterize existing SpGEMM algorithms based on their memory access patterns and develop practical lower and upper bounds for SpGEMM performance. We then develop an SpGEMM algorithm based on the outer product. The newly developed algorithm called PB-SpGEMM saturates memory bandwidth by using the propagation blocking technique and by performing in-cache sorting and merging. For many practical matrices, PB-SpGEMM runs 20%-50% faster than the state-of-the-art heap and hash SpGEMM algorithms on modern multicore processors. Most importantly, PB-SpGEMM attains performance predicted by the Roofline model, and its performance remains stable with respect to matrix size and sparsity.

关键词： parallel algorithm SpGEMM

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Field-Split parallel Architecture for High Performance Multi-Match Packet Classification Using FPGAs 09

Field-Split Parallel Architecture for High Performance Multi...

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21st acm symposium on parallelism in algorithms and architectures

作者： Jiang, Weirong Prasanna, Viktor K. Univ So Calif Ming Hsieh Dept Elect Engn Los Angeles CA 90089 USA

ISBN: (纸本)9781605586069

Multi-match packet classification is a critical function in network intrusion detection systems (NIDS), where all matching rules for a packet need to be reported. Most of the previous work is based on ternary content addressable memories (TCAMs) which are expensive and are not scalable with respect to clock rate, power consumption, and circuit area. This paper studies the characteristics of real-life Snort NIDS rule sets, and proposes a novel SRAM-based architecture. The proposed architecture is called field-split parallel bit vector (FSBV) where some header fields of a packet are further split into bit-level subfields. Unlike previous multi-match packet classification algorithms which suffer from memory explosion, the memory requirement of FSBV is linear in the number of rules. FPGA technology is exploited to provide high throughput and to support dynamic updates. Implementation results show that our architecture can store on a single Xilinx Virtex-5 FPGA the full set of packet header rules extracted from the latest Snort NIDS and sustains 100 Gbps throughput for minimum size (40 bytes) packets. The design achieves 1.25x improvement in throughput while the power consumption is approximately one fourth that of the state-of-the-art solutions.

关键词： FPGA multi-match packet classification NIDS SRAM

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Space-efficient scheduling of parallelism with synchronization variables 97

Space-efficient scheduling of parallelism with synchronizati...

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Proceedings of the 1997 9th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Blelloch, Guy E. Gibbons, Phillip B. Matias, Yossi Narlikar, Girija J. Carnegie Mellon Pittsburgh PA United States

ISBN: (纸本)9780897918909

Recent work on scheduling algorithms has resulted in provable bounds on the space taken by parallel computations in relation to the space taken by sequential computations. The results for online versions of these algorithms, however, have been limited to computations in which threads can only synchronize with ancestor or sibling threads. Such computations do not include languages with futures or user-specified synchronization constraints. Here we extend the results to languages with synchronization variables. Such languages include languages with futures, such as Multilisp and Cool, as well as other languages such as ID. The main result is an online scheduling algorithm which, given a computation with w work (total operations), σ synchronizations, d depth (critical path) and s1 sequential space, will run in O(w/p+σlog(pd)/p+d log(pd)) time and s1+O(pd log (pd)) space, on a p-processor CRCW PRAM with a fetch-and-add primitive. This includes all time and space costs for both the computation and the scheduler. The scheduler is non-preemptive in the sense that it will only move a thread if the thread suspends on a synchronization, forks a new thread, or exceeds a threshold when allocating space. For the special case where the computation is a planar graph with left-to-right synchronization edges, the scheduling algorithm can be implemented in O(w/p+d log p) time and s1+O(pd log p) space. These are the first non-trivial space bounds described for such languages.

关键词： parallel algorithms

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Communication-optimal parallel minimum spanning tree algorithms extended abstract

Communication-optimal parallel minimum spanning tree algorit...

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Proceedings of the 1998 10th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Adler, M. Dittrich, W. Juurlink, B. Kutylowski, M. Rieping, I. Univ of Toronto Toronto Ont Canada

Lower and upper bounds for finding a minimum spanning tree (MST) in a weighted undirected graph on the BSP model are presented. We provide the first non-trivial lower bounds on the communication volume required to solve the MST problem. Let p denote the number of processors, n the number of nodes of the input graph, and m the number of edges of the input graph. We show that in the worst case a total of Ω(k·min(m, pn)) bits need to be transmitted in order to solve the MST problem, where k is the number of bits required to represent a single edge weight. This implies that if each message contains k bits, any BSP algorithm for finding an MST requires communication time Ω(g · min(m/p, n)), where g is the gap parameter of the BSP model. In addition, we present two algorithms whose running times match the lower bounds in different situations. Both algorithms perform linear work and use a number of super-steps independent of the input size. The first algorithm is simple but can employ at most m/n processors efficiently. Hence, it should be applied in situations where the input graph is relatively dense. The second algorithm is a randomized algorithm that performs linear work with high probability, provided that m ≥ n · log p. This is the first linear work BSP algorithm for finding an MST in sparse graphs.

关键词： parallel algorithms

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Massively parallel algorithms for b-Matching* 22

Massively Parallel Algorithms for b-Matching*

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34th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Ghaffari, Mohsen Grunau, Christoph Mitrovic, Slobodan Swiss Fed Inst Technol Zurich Switzerland Univ Calif Davis Davis CA USA

ISBN: (纸本)9781450391467

This paper presents an O (log log (d) over bar) round massively parallel algorithm for 1 +epsilon approximation of maximum weighted b-matchings, using near-linear memory per machine. Here (d) over bar denotes the average degree in the graph and epsilon is an arbitrarily small positive constant. Recall that b -matching is the natural and well-studied generalization of the matching problem where different vertices are allowed to have different numbers of incident edges in the matching. Concretely, each vertex v is given a positive integer budget b(v) and it can have up to b(v) incident edges in the matching. Previously, there were known algorithms with round complexity O (log log n), or O(log logn) where Delta denotes maximum degree, for 1 + epsilon approximation of weighted matching and for maximal matching [Czumaj et al., STOC'18, Ghaffari et al. PODC'18;Assadi et al. SODA'19;Behnezhad et al. FOCS'19;Gamlath et al. PODC'19]. But these algorithms do not extend to the more general b-matching problem.

关键词： matchings approximate b-matchings massively parallel computation MPC

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