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Optimal parallel algorithms in the Binary-Forking Model 20

Optimal Parallel Algorithms in the Binary-Forking Model

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

作者： Blelloch, Guy E. Fineman, Jeremy T. Gu, Yan Sun, Yihan Carnegie Mellon Univ Pittsburgh PA 15213 USA Georgetown Univ Washington DC 20057 USA Univ Calif Riverside Riverside CA 92521 USA

ISBN: (纸本)9781450369350

In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference. In the binary-forking model, tasks can only fork into two child tasks, but can do so recursively and asynchronously. The tasks share memory, supporting reads, writes and test-and-sets. Costs are measured in terms of work (total number of instructions), and span (longest dependence chain). The binary-forking model is meant to capture both algorithm performance and algorithm-design considerations on many existing multithreaded languages, which are also asynchronous and rely on binary forks either explicitly or under the covers. In contrast to the widely studied PRAM model, it does not assume arbitrary-way forks nor synchronous operations, both of which are hard to implement in modern hardware. While optimal PRAM algorithms are known for the problems studied herein, it turns out that arbitrary-way forking and strict synchronization are powerful, if unrealistic, capabilities. Natural simulations of these PRAM algorithms in the binary-forking model (i.e., implementations in existing parallel languages) incur an Omega(logn) overhead in span. This paper explores techniques for designing optimal algorithms when limited to binary forking and assuming asynchrony. All algorithms described in this paper are the first algorithms with optimal work and span in the binary-forking model. Most of the algorithms are simple. Many are randomized.

关键词： list ranking RMQ list contraction tree contraction intersection binary forking set-set operation range minimum query semisort parallel computational model tree merging fork-join union difference sorting

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architectures and algorithms for millisecond-scale molecular dynamics simulations of proteins 41

Architectures and algorithms for millisecond-scale molecular...

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2008 - 41st annual IEEE/acm International symposium on Microarchitecture, MICRO-41

作者： Shaw, David E. Columbia's Medical School United States

ISBN: (纸本)9781424428366

The ability to perform long, accurate molecular dynamics (MD) simulations involving proteins and other biological macromolecules could in principle lead to important scientific advances and provide a powerful new tool for drug discovery. A wide range of biologically interesting phenomena, however, occur over time scales on the order of a millisecond - several orders of magnitude beyond the duration of the longest current MD simulations. Our research group is currently building a specialized, massively parallel machine, called Anton, which should soon be capable of executing millisecond-scale MD simulations of proteins at an atomic level of detail. Anton's highly accelerated execution of such simulations is attributable in large part to specialized logic for the high-speed calculation of pairwise interactions between particles and/or gridpoints separated by no more than some specified cutoff radius. In particular, each of Anton's 512 ASICs, which are implemented using 90-nm technology, includes a "high-throughput interaction subsystem" incorporating 32 highly specialized pipelines running at 800 MHz. During every cycle, each of these pipelines produces a pairwise-interaction result that would require approximately 50 arithmetic operations to calculate on a general-purpose processor. Novel algorithms and architectural features are used to greatly reduce the requirements for inter- and intra-chip communication, allowing Anton to feed these pipelines and collect their results at a speed sufficient to take advantage of the machine's computational power. The ASIC also includes a "flexible subsystem" based on eight programmable "geometry cores," each containing eight arithmetic pipelines. This talk will provide an overview of our work on parallel algorithms and machine architectures for high-speed MD simulation, with special attention to the respective roles of specialized vs. general-purpose hardware, and to the techniques used to minimize communication at various levels

关键词： Molecular dynamics

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Near Optimal parallel algorithms for Dynamic DFS in Undirected Graphs 17

Near Optimal Parallel Algorithms for Dynamic DFS in Undirect...

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29th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Khan, Shahbaz IIT Kanpur Dept CSE Kanpur 208016 Uttar Pradesh India

ISBN: (纸本)9781450345934

Depth first search (DFS) tree is a fundamental data structure for solving various graph problems. The classical algorithm [37] for building a DFS tree requires O(m + n) time for a given undirected graph G having n vertices and m edges. Recently, Baswana et al. [5] presented a simple algorithm for updating the DFS tree of an undirected graph after an edge/vertex update in (O) over tilde (n)(1) time. However, their algorithm is strictly sequential. We present an algorithm achieving similar bounds that can be easily adopted to the parallel environment. In the parallel environment, a DFS tree can be computed from scratch using O(m) processors in expected (O) over tilde (1) time [2] on an EREW PRAM, whereas the best deterministic algorithm takes (O) over tilde (root n) time [2, 17] on a CRCW PRAM. Our algorithm can be used to develop optimal time (upto poly log n factors) deterministic parallel algorithms for maintaining fully dynamic DFS and fault tolerant DFS of an undirected graph. (1) parallel Fully Dynamic DFS: Given any arbitrary online sequence of vertex or edge updates, we can maintain a DFS tree of an undirected graph in (O) over tilde (1) time per update using m processors on an EREW PRAM. (2) parallel Fault tolerant DFS: An undirected graph can be preprocessed to build a data structure of size O(m), such that for any set of k updates (where k is constant) in the graph, a DFS tree of the updated graph can be computed in (O) over tilde (1) time using n processors on an EREW PRAM. For constant k, this is also work optimal (upto poly log n factors). Moreover, our fully dynamic DFS algorithm provides, in a seamless manner, nearly optimal (upto poly log n factors) algorithms for maintaining a DFS tree in the semi-streaming environment and a restricted distributed model. These are the first parallel, semi-streaming and distributed algorithms for maintaining a DFS tree in the dynamic setting.

关键词： parallel dynamic DFS graph algorithm streaming distributed

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Provably Efficient Scheduling of Cache-oblivious Wavefront algorithms 17

Provably Efficient Scheduling of Cache-oblivious Wavefront A...

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29th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Chowdhury, Rezaul Ganapathi, Pramod Tang, Yuan Tithi, Jesmin Jahan SUNY Stony Brook Stony Brook NY 11790 USA Fudan Univ Shanghai Key Lab Intelligent Informat Proc State Key Lab Comp Arch ICT Sch Comp SciSch SoftwareCAS Shanghai Peoples R China Intel Corp Santa Clara CA USA

ISBN: (纸本)9781450345934

Iterative wavefront algorithms for evaluating dynamic programming recurrences exploit optimal parallelism but show poor cache performance. Tiled-iterative wavefront algorithms achieve optimal cache complexity and high parallelism but are cache-aware and hence are not portable and not cache-adaptive. On the other hand, standard cache-oblivious recursive divide-and-conquer algorithms have optimal serial cache complexity but often have low parallelism due to artificial dependencies among subtasks. Recen tly, we introduced cache-oblivious recursive wavefront (COW) algorithms, which do not have any artificial dependencies, but they are too complicated to develop, analyze, implement, and generalize. Though COW algorithms are based on fork-join primitives, they extensively use atomic operations for ensuring correctness, and as a result, performance guarantees (i.e., parallel running time and parallel cache complexity) provided by state-of-the-art schedulers (e.g., the randomized work-stealing scheduler) for programs with fork-join primitives do not apply. Also, extensive use of atomic locks may result in high overhead in implementation. In this paper, we show how to systematically transform standard cache-oblivious recursive divide-and-conquer algorithms into recursive wavefront algorithms to achieve optimal parallel cache complexity and high parallelism under state-of-the-art schedulers for fork-join programs. Unlike COW algorithms these new algorithms do not use atomic operations. Instead, they use closed-form formulas to compute the time when each divide-and-conquer function must be launched in order to achieve high parallelism without losing cache performance. The resulting implementations are arguably much simpler than implementations of known COW algorithms. We present theoretical analyses and experimental performance and scalability results showing a superiority of these new algorithms over existing algorithms.

关键词： wavefront cache-oblivious parallel recursive divide-and-conquer dynamic programming parallelism

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Brief announcement: An implementation report for parallel triangular decompositions

Brief announcement: An implementation report for parallel tr...

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SPAA 2006: 18th annual acm symposium on parallelism in algorithms and architectures

作者： Maza, Marc Moreno Xie, Yuzhen London Ont. Canada

ISBN: (纸本)1595934529

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 process. Our 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 parallelization. In [4] an algorithm, called Triade, for TRIAngular DEcompositions, provides a good management of the intermediate computa

关键词： Computational geometry

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A Novel Computational Model for GPUs with Application to I/O Optimal Sorting algorithms 28

A Novel Computational Model for GPUs with Application to I/O...

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28th IEEE International parallel & Distributed Processing symposium Workshops (IPDPSW)

作者： Koike, Atsushi Sadakane, Kunihiko Natl Inst Informat Principles Informat Res Div Tokyo Japan Grad Univ Adv Studies Dept Informat Tokyo Japan

ISBN: (纸本)9781479941162

We propose a novel computational model for GPU. Known parallel computational models such as the PRAM model are not appropriate for evaluating GPU algorithms. Our model, called AGPU, abstracts the essence of current GPU architectures such as global and shared memory, memory coalescing and bank conflicts. We can therefore evaluate asymptotic behavior of GPU algorithms more accurately than known models and we can develop algorithms that are efficient on many real architectures. As a showcase, we first analyze known comparison-based sorting algorithms using the AGPU model and show that they are not I/O optimal, that is, the number of global memory accesses is more than necessary. Then we propose a new algorithm which uses an asymptotically optimal number of global memory accesses and whose time complexity is also nearly optimal.

关键词： GPU GPGPU parallel computational models sorting algorithms

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Scheduling Strategies for Optimistic parallel Execution of Irregular Programs 08

Scheduling Strategies for Optimistic Parallel Execution of I...

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20th acm symposium on parallelism in algorithms and architectures

作者： Kulkarni, Milind Carribault, Patrick Pingali, Keshav Ramanarayanan, Ganesh Walter, Bruce Bala, Kavita Chew, L. Paul Univ Texas Austin Austin TX 78712 USA Cornell Univ Ithaca NY USA

ISBN: (纸本)9781595939739

Recent application studies have shown that many irregular applications have a generalized data parallelism that manifests itself as iterative computations over worklists of different kinds. In general, there are complex dependencies between iterations. These dependencies cannot be elucidated statically because they depend on the inputs to the program;thus, optimistic parallel execution is the only tractable approach to parallelizing these applications. We have built a system called Galois that supports this style of parallel execution. Its main features are (i) set iterators for expressing worklist-based data parallelism, and (ii) a runtime system that performs optimistic parallelization of these iterators, detecting conflicts and rolling back computations as needed. Our work builds on the Galois system, and it addresses the problem of scheduling iterations of set iterators on multiple cores. The policy used by the base Galois system is to assign an iteration to a core whenever it needs work to do, but we show in this paper that this policy is not optimal for many applications. We also argue that OpenMP-style DO-ALL loop scheduling directives such as chunked and guided self-scheduling are too simplistic for irregular programs. These difficulties led us to develop a general scheduling framework for irregular problems;OpenMP-style scheduling strategies are special cases of this general approach. We also provide hooks into our framework, allowing the programmer to leverage application knowledge to further tune a schedule for a particular application. To evaluate this framework, we implemented it as an extension of the Galois system. We then tested the system using five real-world, irregular, data-parallel applications. Our results show that (i) the optimal scheduling policy can be different for different applications and often leverages application-specific knowledge and (ii) implementing these schedules in the Galois system is relatively straightforward.

关键词： Optimistic parallelism Irregular Programs Scheduling

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parallel graph contraction 89

Parallel graph contraction

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Phillips, Cynthia A. Laboratory for Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States

ISBN: (纸本)089791323X

This paper shows how n-node, e-edge graphs can be contracted in a manner similar to the parallel tree contraction algorithm due to Miller and Reif. We give an O((n + e)/lgn)-processor deterministic algorithm that contracts a graph in O(lg 2 n) time in the EREW PRAM model. We also give art O(n/lg n)-processor randomized algorithm that with high probability can contract a bounded-degree graph in O(lg n+lg 2 γ) time, where γ is the maximum genus of any connected component of the graph. (The algorithm can be made to run in deterministic O(lg n lg∗ n + lg 2 γ) time using known techniques.) This algorithm does not require a priori knowledge of the genus of the graph to be contracted. The contraction algorithm for boundeddegree graphs can be used directly to solve the problem of region labeling in vision systems, i.e., determining the connected components of bounded-degree planar graphs in O(lgn) time, thus improving the best previous bound of O(lg 2 n). © 1989 acm.

关键词： Trees (mathematics)

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parallel Approximate Undirected Shortest Paths via Low Hop Emulators 2020

Parallel Approximate Undirected Shortest Paths via Low Hop E...

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52nd annual acm SIGACT symposium on Theory of Computing (STOC)

作者： Andoni, Alexandr Stein, Clifford Zhong, Peilin Columbia Univ New York NY 10027 USA

ISBN: (纸本)9781450369794

We present a (1 + epsilon) -approximate parallel algorithm for computing shortest paths in undirected graphs, achieving poly(log n) depth and mpoly(log n) work for n-nodes m-edges graphs. Although sequential algorithms with (nearly) optimal running time have been known for several decades, near-optimal parallel algorithms have turned out to be a much tougher challenge. For (1 + epsilon) -approximation, all prior algorithms with poly(log n) depth perform at least Omega(mn(c)) work for some constant c > 0. Improving this long-standing upper bound obtained by Cohen (STOC'94) has been open for 25 years. We develop several new tools of independent interest. One of them is a new notion beyond hopsets - low hop emulator - a poly(log n)-approximate emulator graph in which every shortest path has at most O(log log n) hops (edges). Direct applications of the low hop emulators are parallel algorithms for poly(log n)-approximate single source shortest path (SSSP), Bourgain's embedding, metric tree embedding, and low diameter decomposition, all with poly(log n) depth and mpoly(log n) work. To boost the approximation ratio to (1 + epsilon), we introduce compressible preconditioners and apply it inside Sherman's framework (SODA'17) to solve the more general problem of uncapacitated minimum cost flow (a.k.a., transshipment problem). Our algorithm computes a (1 + epsilon)-approximate uncapacitated minimum cost flow in poly(log n) depth using mpoly(log n) work. As a consequence, it also improves the state-of-the-art sequential running time from m . 2(O(root log n)) to mpoly(log n).

关键词： parallel algorithms shortest paths minimum cost flow low hop emulators

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Bipartite Perfect Matching Is in Quasi-NC 16

Bipartite Perfect Matching Is in Quasi-NC

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48th annual acm SIGACT symposium on Theory of Computing (STOC)

作者： Fenner, Stephen Gurjar, Rohit Thierauf, Thomas Univ South Carolina Columbia SC 29208 USA Aalen Univ Aalen Germany

ISBN: (纸本)9781450341325

We show that the bipartite perfect matching problem is in quasi-NC2. That is, it has uniform circuits of quasi polynomial size n(O(log n)) and O(log(2) n) depth. Previously, only an exponential upper bound was known on the size of such circuits with poly-logarithmic depth. We obtain our result by an almost complete derandomization of the famous Isolation Lemma when applied to yield an efficient randomized parallel algorithm for the bipartite perfect matching problem.

关键词： Graph Matching parallel complexity Derandomization quasi-NC

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