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Fast parallel algorithms for Enumeration of Simple, Temporal, and Hop-constrained Cycles

ACM TRANSACTIONS ON parallel COMPUTING 2023年第3期10卷 1-35页

作者： Blanusa, Jovan Atasu, Kubilay Ienne, Paolo IBM Res Europe Zurich Saumerstr 4 CH-8803 Ruschlikon Switzerland Ecole Polytech Fed Lausanne Sch Comp & Commun Sci Route Cantonale CH-1015 Lausanne Switzerland Ecole Polytech Fed Lausanne Sch Comp & Commun Sci Lausanne Switzerland

Cycles are one of the fundamental subgraph patterns and being able to enumerate them in graphs enables important applications in a wide variety of fields, including finance, biology, chemistry, and network science. However, to enable cycle enumeration in real-world applications, efficient parallel algorithms are required. In this work, we propose scalable parallelisation of state-of-the-art sequential algorithms for enumerating simple, temporal, and hop-constrained cycles. First, we focus on the simple cycle enumeration problem and parallelise the algorithms by Johnson and by Read and Tarjan in a fine-grained manner. We theoretically show that our resulting fine-grained parallel algorithms are scalable, with the fine-grained parallel ReadTarjan algorithm being strongly scalable. In contrast, we show that straightforward coarse-grained parallel versions of these simple cycle enumeration algorithms that exploit edge- or vertex-level parallelism are not scalable. Next, we adapt our fine-grained approach to enable the enumeration of cycles under time-window, temporal, and hop constraints. Our evaluation on a cluster with 256 CPU cores that can execute up to 1,024 simultaneous threads demonstrates a near-linear scalability of our fine-grained parallel algorithms when enumerating cycles under the aforementioned constraints. On the same cluster, our fine-grained parallel algorithms achieve, on average, one order of magnitude speedup compared to the respective coarse-grained parallel versions of the state-of-the-art algorithms for cycle enumeration. The performance gap between the fine-grained and the coarse-grained parallel algorithms increases as we use more CPU cores.

关键词： Cycle enumeration parallel graph algorithms graph pattern mining

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Finding the k shortest paths in parallel

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ALGORITHMICA 2000年第2期28卷 242-254页

作者： Ruppert, E Brown Univ Dept Comp Sci Providence RI 02912 USA

A concurrent-read exclusive-write PRAM algorithm is developed to find the k shortest paths between pairs of vertices in an edge-weighted directed graph. Repetitions of vertices along the paths are allowed. The algorithm computes an implicit representation of the k shortest paths to a given destination vertex from every vertex of a graph with n vertices and in edges, using O (m + nk log(2) k) work and O (log(3) k log* k + log n(log log k + log* n)) time, assuming that a shortest path tree rooted at the destination is pre-computed. The paths themselves can be extracted from the implicit representation in O(log k + log n) time, and O(n log n + L) work, where L is the total length of the output.

关键词： parallel graph algorithms data structures shortest paths

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A Practical parallel Algorithm for Diameter Approximation of Massive Weighted graphs 30

A Practical Parallel Algorithm for Diameter Approximation of...

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30th IEEE International parallel and Distributed Processing Symposium (IPDPS)

作者： Ceccarello, Matteo Pietracaprina, Andrea Pucci, Geppino Upfal, Eli Univ Padua Dept Informat Engn Padua Italy Brown Univ Dept Comp Sci Providence RI USA

ISBN: (纸本)9781509021406

We present a space and time efficient practical parallel algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. The core of the algorithm is a weighted graph decomposition strategy generating disjoint clusters of bounded weighted radius. Theoretically, our algorithm uses linear space and yields a polylogarithmic approximation guarantee;moreover, for important practical classes of graphs, it runs in a number of rounds asymptotically smaller than those required by the natural approximation provided by the state-of-the-art.-stepping SSSP algorithm, which is its only practical linear-space competitor in the aforementioned computational scenario. We complement our theoretical findings with an extensive experimental analysis on large benchmark graphs, which demonstrates that our algorithm attains substantial improvements on a number of key performance indicators with respect to the aforementioned competitor, while featuring a similar approximation ratio (a small constant less than 1.4, as opposed to the polylogarithmic theoretical bound).

关键词： graph Analytics parallel graph algorithms Weighted graph Decomposition Weighted Diameter Approximation MapReduce

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Log(graph): A Near-Optimal High-Performance graph Representation 18

Log(Graph): A Near-Optimal High-Performance Graph Representa...

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27th IEEE/ACM/IFIP International Conference on parallel Architectures and Compilation Techniques (PACT)

作者： Besta, Maciej Stanojevic, Dimitri Zivic, Tijana Singh, Jagpreet Hoerold, Maurice Hoefler, Torsten Swiss Fed Inst Technol Dept Comp Sci Zurich Switzerland

ISBN: (纸本)9781450359863

Today's graphs used in domains such as machine learning or social network analysis may contain hundreds of billions of edges. Yet, they are not necessarily stored efficiently, and standard graph representations such as adjacency lists waste a significant number of bits while graph compression schemes such as Webgraph often require time-consuming decompression. To address this, we propose Log(graph): a graph representation that combines high compression ratios with very low-overhead decompression to enable cheaper and faster graph processing. The key idea is to encode a graph so that the parts of the representation approach or match the respective storage lower bounds. We call our approach "graph logarithmization" because these bounds are usually logarithmic. Our high-performance Log(graph) implementation based on modern bitwise operations and state-of-the-art succinct data structures achieves high compression ratios as well as performance. For example, compared to the tuned graph Algorithm Processing Benchmark Suite (GAPBS), it reduces graph sizes by 20-35% while matching GAPBS' performance or even delivering speedups due to reducing amounts of transferred data. It approaches the compression ratio of the established Webgraph compression library while enabling speedups of up to more than 2x. Log(graph) can improve the design of various graph processing engines or libraries on single NUMA nodes as well as distributed-memory systems.

关键词： graph compression graph representation graph layout parallel graph algorithms ILP succinct data structures

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Optimizing large-scale graph analysis on multithreaded, multicore platforms

Optimizing large-scale graph analysis on multithreaded, mult...

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26th IEEE International parallel and Distributed Processing Symposium (IPDPS) / Workshop on High Performance Data Intensive Computing

作者： Cong, Guojing Makarychev, Konstantin IBM Corp TJ Watson Res Ctr Yorktown Hts NY 10598 USA

ISBN: (纸本)9780769546759

The erratic memory access pattern of graph algorithms makes it hard to optimize on cache-based architectures. While multithreading hides memory latency, it is unclear how hardware threads combined with caches impact the performance of typical graph workload. As modern architectures strike different balances between caching and multithreading, it remains an open question whether the benefit of optimizing locality behavior outweighs the cost. We study parallel graph algorithms on two different multi-threaded, multi-core platforms, that is, IBM Power7 and Sun Niagara2. Our experiments first demonstrate their performance advantage over prior architectures. We find nonetheless the number of hardware threads in either platform is not sufficient to fully mask memory latency. Our cache-friendly scheduling of memory accesses improves performance by up to 2.6 times on Power7 and prior cache-based architectures, yet the same technique significantly degrades performance on Niagara2. Software prefetching and manipulating the storage of the input to improve spatial locality improve performance by up to 2.1 times and 1.3 times on both platforms. Our study reveals interesting interplay between architecture and algorithm.

关键词： Multi-threading parallel graph algorithms Software Prefetch Traversal

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Fast Approximate Distance Queries in Unweighted graphs Using Bounded Asynchrony 1

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29th International Workshop on Languages and Compilers for parallel Computing (LCPC)

作者： Fidel, Adam Sabido, Francisco Coral Riedel, Colton Amato, Nancy M. Rauchwerger, Lawrence Texas A&M Univ Dept Comp Sci & Engn Parasol Lab College Stn TX 77843 USA

ISBN: (数字)9783319527093

ISBN: (纸本)9783319527093;9783319527086

We introduce a new parallel algorithm for approximate breadth-first ordering of an unweighted graph by using bounded asynchrony to parametrically control both the performance and error of the algorithm. This work is based on the k-level asynchronous (KLA) paradigm that trades expensive global synchronizations in the level-synchronous model for local synchronizations in the asynchronous model, which may result in redundant work. Instead of correcting errors introduced by asynchrony and redoing work as in KLA, in this work we control the amount of work that is redone and thus the amount of error allowed, leading to higher performance at the expense of a loss of precision. Results of an implementation of this algorithm are presented on up to 32,768 cores, showing 2.27x improvement over the exact KLA algorithm and 3.8x improvement over the level-synchronous version with minimal error on several graph inputs.

关键词： parallel graph algorithms Breadth-first search Distance query Approximate algorithms Asynchronous Distributed memory

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NetworKit: A tool suite for large-scale complex network analysis

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NETWORK SCIENCE 2016年第4期4卷 508-530页

作者： Staudt, Christian L. Sazonovs, Aleksejs Meyerhenke, Henning Karlsruhe Inst Technol Inst Theoret Informat D-76131 Karlsruhe Germany Wellcome Trust Sanger Inst Wellcome Genome Campus Cambridge CB10 1SA England

We introduce NetworKit, an open-source software package for analyzing the structure of large complex networks. Appropriate algorithmic solutions are required to handle increasingly common large graph data sets containing up to billions of connections. We describe the methodology applied to develop scalable solutions to network analysis problems, including techniques like parallelization, heuristics for computationally expensive problems, efficient data structures, and modular software architecture. Our goal for the software is to package results of our algorithm engineering efforts and put them into the hands of domain experts. NetworKit is implemented as a hybrid combining the kernels written in C++ with a Python frontend, enabling integration into the Python ecosystem of tested tools for data analysis and scientific computing. The package provides a wide range of functionality (including common and novel analytics algorithms and graph generators) and does so via a convenient interface. In an experimental comparison with related software, NetworKit shows the best performance on a range of typical analysis tasks.

关键词： complex networks network analysis network science parallel graph algorithms data analysis software

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Expressing graph algorithms Using Generalized Active Messages 13

Expressing Graph Algorithms Using Generalized Active Message...

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18th ACM SIGPLAN Symposium on Principles and Practice of parallel Programming

作者： Edmonds, Nick Willcock, Jeremiah Lumsdaine, Andrew Indiana Univ Bloomington IN 47405 USA

ISBN: (纸本)9781450319225

Recently, graph computation has emerged as an important class of high-performance computing application whose characteristics differ markedly from those of traditional, compute-bound, kernels. Libraries such as BLAS, LAPACK, and others have been successful in codifying best practices in numerical computing. The data-driven nature of graph applications necessitates a more complex application stack incorporating runtime optimization. In this paper, we present a method of phrasing graph algorithms as collections of asynchronous, concurrently executing, concise code fragments which may be invoked both locally and in remote address spaces. A runtime layer performs a number of dynamic optimizations, including message coalescing, message combining, and software routing. Practical implementations and performance results are provided for a number of representative algorithms.

关键词： parallel graph algorithms Active Messages parallel Programming Models

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Distributed, Shared-Memory parallel Triangle Counting 18

Distributed, Shared-Memory Parallel Triangle Counting

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5th Platform for Advanced Scientific Computing Conference (PASC)

作者： Kanewala, Thejaka Amila Zalewski, Marcin Lumsdaine, Andrew Indiana Univ Sch Informat Comp & Engn Bloomington IN 47405 USA Pacific Northwest Natl Lab Seattle WA USA Univ Washington Seattle WA 98195 USA

ISBN: (纸本)9781450358910

Triangles are the most basic non-trivial subgraphs. Triangle counting is used in a number of different applications, including social network mining, cyber security, and spam detection. In general, triangle counting algorithms are readily parallelizable, but when implemented in distributed, shared-memory, their performance is poor due to high communication, imbalance of work, and the difficulty of exploiting locality available in shared memory. In this paper, we discuss four different (but related) triangle counting algorithms and how their performance can be improved in distributed, shared-memory by reducing in-node load imbalance, improving cache utilization, minimizing network overhead, and minimizing algorithmic work. We generalize the four different triangle counting algorithms into a common framework and show that for all four algorithms the in-node load imbalance can be minimized while utilizing caches by partitioning work into blocks of vertices, the network overhead can be minimized by aggregation of blocks of work, and algorithm work can be reduced by partitioning vertex neighbors by degree. We experimentally evaluate the weak and the strong scaling performance of the proposed algorithms with two types of synthetic graph inputs and three real-world graph inputs. We also compare the performance of our implementations with the distributed, shared-memory triangle counting algorithms available in Powergraph-graphLab and show that our proposed algorithms outperform those algorithms, both in terms of space and time.

关键词： triangle counting distributed shared-memory graph algorithms parallel graph algorithms

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parallel-external computation of the cycle structure of invertible cryptographic functions

Parallel-external computation of the cycle structure of inve...

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15th Euromicro International Conference on parallel, Distributed and Network-Based Processing

作者： Beckmann, Andreas Keller, Jorg Univ Halle Wittenberg Inst Informat D-06099 Halle Saale Germany Fernuniv VLSI LG Parallelitat D-58084 Hagen Germany

ISBN: (纸本)9780769527840

We present an algorithm to compute the cycle structure of large directed graphs where each node has exactly one outgoing edge. Such graphs appear as state diagrams of finite state machines such as pseudo-random number generators in cryptography. The size of the graphs necessitates that the adjacency list is kept on hard disks. Our algorithm uses multiple processing units, so that a parallel storage system has to be employed to store the graph. We present experimental resultsfor randomly chosen graphs, andfor the graph of the A5/1 generator used in GSM mobile phones.

关键词： parallel storage systems parallel graph algorithms cryptography

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