Parallel, Portable Algorithms for Distance-2 Maximal Independent Set and Graph Coarsening.
Abstract not provided.
Kelley, Brian↗
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ConnectIt: a framework for static and incremental parallel graph connectivity algorithms
Connected components is a fundamental kernel in graph applications. The fastest existing multicore algorithms for solving graph connectivity are based on some form of edge sampling and/or linking and compressing trees. However, many combinations of these design choices have been left unexplored. In this paper, we design the ConnectIt framework, which provides different sampling strategies as well as various tree linking and compression schemes. ConnectIt enables us to obtain several hundred new variants of connectivity algorithms, most of which extend to computing spanning forest. In addition to static graphs, we also extend ConnectIt to support mixes of insertions and connectivity queries in the concurrent setting. We present an experimental evaluation of ConnectIt on a 72-core machine, which we believe is the most comprehensive evaluation of parallel connectivity algorithms to date. Compared to a collection of state-of-the-art static multicore algorithms, we obtain an average speedup of 12.4x (2.36x average speedup over the fastest existing implementation for each graph). Using ConnectIt, we are able to compute connectivity on the largest publicly-available graph (with over 3.5 billion vertices and 128 billion edges) in under 10 seconds using a 72-core machine, providing a 3.1x speedup over the fastest existing connectivity result for this graph, in any computational setting. For our incremental algorithms, we show that our algorithms can ingest graph updates at up to several billion edges per second. To guide the user in selecting the best variants in ConnectIt for different situations, we provide a detailed analysis of the different strategies. Finally, we show how the techniques in ConnectIt can be used to speed up two important graph applications: approximate minimum spanning forest and SCAN clustering.
Computer Science↗
TriC: Distributed-memory Triangle Counting by Exploiting the Graph Structure
Graph analytics has emerged as an important tool in the analysis of large scale data from diverse application domains such as social networks, cyber security and bioinformatics. Counting the number of triangles in a graph is a fundamental kernel with several applications such as detecting the community structure of a graph or in identifying important vertices in a graph. The ubiquity of massive datasets is driving the need to scale graph analytics on parallel systems. However, numerous challenges exist in efficiently parallelizing graph algorithms, especially on distributed-memory systems. Irregular memory accesses and communication patterns, low computation to communication ratios, and the need for frequent synchronization are some of the leading challenges. In this paper, we present TriC, our distributed-memory implementation of triangle counting in graphs using the Message Passing Interface (MPI), as a submission to the 2020 GraphChallenge competition. Using a set of synthetic and real-world inputs from the challenge, we demonstrate a speedup of up to 90x relative to previous work on 32 processor-cores of a NERSC Cori node. We also provide details from distributed runs with up to8192 processes along with strong scaling results. The observations presented in this work provide an understanding of the system-level bottlenecks at scale that specifically impact sparse-irregular workloads and will therefore benefit other efforts to parallelize graph algorithms.
Halappanavar, Mahantesh↗
Parallel graph coloring algorithms for distributed GPU environments
Not Available
Bogle, Ian (ORCID:0000000165918785)↗
Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs
This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).
hypergraph algorithms, graph algorithms, parallel ↗
Distributed Memory Parallel Algorithms for Massive Graphs
Explore the source record for details and available documents.
Alam, Maksudul↗
DyG-DPCD: A Distributed Parallel Community Detection Algorithm for Large-Scale Dynamic Graphs
Dynamic (Temporal) graphs capture the valuable evolution of real-world systems, from the continuously evolving patterns of social interactions and genetic pathways to the dynamic fluctuations of economic forces. Detecting communities for such evolving networks poses unique challenges. Detecting and analyzing the evolution of communities within dynamic graphs unlocks valuable insights into the underlying structural and temporal patterns of real-world systems. However, the sheer volume of modern graph data and the inherent complexity of the temporal dimension pose significant challenges to scalable community detection algorithms. Addressing this gap, our work explores the limited landscape of scalable distributed-memory parallel methods specifically designed for dynamic network community detection. We propose a novel parallel algorithm, DyG-DPCD (Dynamic Graph Distributed Parallel Community Detection), to detect communities in dynamic networks using the Message Passing Interface (MPI) framework. We present a vertex-centric approach, allowing us to detect communities through local optimization. Furthermore, we enhance our baseline algorithm by incorporating three heuristics, which improve the algorithm’s performance significantly while maintaining the quality of the solutions. We demonstrate the efficiency of our algorithm by experimenting on several real-world large-scale networks with hundreds of millions of edges spanning diverse domains. Notably, DyG-DPCD achieves speedups between 25× and 30× for large networks that we experimented on using NERSC compute nodes. In conclusion, our algorithm outperforms the STINGER parallel re-agglomeration algorithm by 30×.
97 MATHEMATICS AND COMPUTING↗
Picasso: Memory-Efficient Graph Coloring Using Palettes With Applications in Quantum Computing
A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and a parallel implementation of the proposed algorithm. We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.
artificial intelligence, quantum computing↗
Towards scaling community detection on distributed-memory heterogeneous systems
Distributed multi-GPU systems pose significant challenges and opportunities for efficient execution of parallel applications. Graph algorithms are generally characterized by irregular memory accesses, low computation to communication ratios, and load balancing problems that are especially hard to address on multi-GPU systems. Graph community detection is an important problem in the emerging domain of graph analytics with numerous applications. In this paper, we present our ongoing work on distributed-memory multi-GPU implementation for graph community detection. Our work parallelizes the widely used (albeit serial) Louvain method on distributed multi-GPU platforms. Supported by an extensive set of experiments on a multi-GPU enabled supercomputer (OLCF Summit) and a single compute node (Nvidia DGX-2®), we demonstrate competitive performance to existing distributed-memory CPU-based implementation, and up to 6.5 better results than Nvidia RAPIDS® CUGRAPH. To the best of our knowledge, this work represents the first effort for community detection on distributed multi-GPU systems. Our approach and related findings can be extended to numerous other iterative graph algorithms on multi-GPU systems.
97 MATHEMATICS AND COMPUTING↗
Triangle Counting with Cyclic Distributions
Triangles are the simplest non-trivial subgraphs and triangle counting is used in a number of different applications. The order in which vertices are processed in triangle counting strongly effects the amount of work that needs to be done (and thus the overall performance). Ordering vertices by degree has been shown to be one particularly effective ordering approach. However, for graphs with skewed degree distributions (such as power-law graphs), ordering by degree effects the distribution of work; parallelization must account for this distribution in order to balance work among workers. In this paper we provide an in- depth analysis of the ramifications of degree-based ordering on parallel triangle counting. We present approach for partitioning work in triangle counting, based on cyclic distribution and some surprisingly simple C++ implementations. Experimental results demonstrate the effectiveness of our approach, particularly for power-law (and social network) graphs.
Graph algorithms, parallel algorithms↗
Portable Parallel Algorithms and Frameworks for Exascale Graph Analytics
Graphs (or networks) are a tool used to model the interactions among various entities. Efficiently processing large graphs has recently attracted significant attention due to the applications of graphs in various domains, such as biology, chemistry, and cyber-security. Analyzing the structure and properties of these graphs is an important component of many scientific computing pipelines. With the explosion in the volume of data, graphs have become very large and can contain hundreds of billions of vertices and trillions of edges. Therefore, it is crucial to develop high-performance methods to enable graph analysis to be done quickly and energy-efficiently. Furthermore, these solutions should be highly parallel in order to take advantage of modern parallel machines. However, designing efficient solutions is not enough. With the wide variety of computing environments available, each with different programmability and performance characteristics, it is necessary to develop solutions that are portable in terms of both performance (i.e., provide theoretical guarantees) and programmability (i.e., provide high level abstractions).
97 MATHEMATICS AND COMPUTING↗
SPARTA: High-Level Synthesis of Parallel Multi-Threaded Accelerators
This article presents a methodology for the Synthesis of PARallel multi-Threaded Accelerators (SPARTA) from OpenMP annotated C/C++ specifications. SPARTA extends an open-source HLS tool, enabling the generation of accelerators that provide latency tolerance for irregular memory accesses through multithreading, support fine-grained memory-level parallelism through a hot-potato deflection-based network-on-chip (NoC), support synchronization constructs, and can instantiate memory-side caches. Our approach is based on a custom runtime OpenMP library, providing flexibility and extensibility. Experimental results show high scalability when synthesizing irregular graph kernels. The accelerators generated with our approach are, on average, 2.29x faster than state-of-the-art HLS methodologies.
Design automation↗
GreediRIS: Scalable influence maximization using distributed streaming maximum cover
Not Available
97 MATHEMATICS AND COMPUTING↗
Trust: Triangle Counting Reloaded on GPUs
Triangle counting is a building block for a wide range of graph applications. Here, traditional wisdom suggests that i) hashing is not suitable for triangle counting, ii) edge-centric triangle counting beats vertex-centric design, and iii) communication-free and workload balanced graph partitioning is a grand challenge for triangle counting. On the contrary, we advocate that i) hashing can help the key operations for scalable triangle counting on Graphics Processing Units (GPUs), i.e., list intersection and graph partitioning, ii) vertex-centric option reduces both hash table construction cost and memory consumption, which is limited on GPUs. In addition, iii) we exploit graph and workload collaborative, and hash-based 2D partitioning to scale vertex-centric triangle counting over 1,000 GPUs with sustained scalability. In this work, we present TRUST, which performs triangle counting with the hash operation and vertex-centric paradigm. To the best of our knowledge, TRUST is the first work that achieves over one trillion Traversed Edges Per Second (TEPS) rate for triangle counting.
97 MATHEMATICS AND COMPUTING↗
Experience of Migrating a Parallel Graph Coloring Program from CUDA to SYCL
We describe the experience of converting a CUDA implementation of a parallel graph coloring algorithm to SYCL. The goals are for our work to be useful to application and compiler developers by providing a detailed description of migration paths between CUDA and SYCL. We will describe how CUDA functions are mapped to SYCL functions. Evaluating the CUDA and SYCL implementations of the algorithm shows that the performance of SYCL and CUDA kernels are comparable over the test graph set on NVIDIA P100 and V100 GPUs. The SYCL program also allows for performance evaluation with the OpenCL and Level Zero interfaces and power profiling on an Intel GPU computing platform.
97 MATHEMATICS AND COMPUTING↗
A dataflow analysis tool for parallel processing of algorithms
A graph-theoretic design process and software tool is presented for selecting a multiprocessing scheduling solution for a class of computational problems. The problems of interest are those that can be described using a dataflow graph and are intended to be executed repetitively on a set of identical parallel processors. Typical applications include signal processing and control law problems. Graph analysis techniques are introduced and shown to effectively determine performance bounds, scheduling constraints, and resource requirements. The software tool is shown to facilitate the application of the design process to a given problem.
Jones, Robert L., III↗
Theoretically and practically efficient parallel nucleus decomposition
This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves a work complexity matching the best sequential algorithm while also having low depth (parallel running time), which significantly improves upon the only existing parallel nucleus decomposition algorithm (Sariyüce et al. , PVLDB 2018). The key to the theoretical efficiency of our algorithm is a new lemma that bounds the amount of work done when peeling cliques from the graph, combined with the use of a theoretically-efficient parallel algorithms for clique listing and bucketing. We introduce several new practical optimizations, including a new multi-level hash table structure to store information on cliques space-efficiently and a technique for traversing this structure cache-efficiently. On a 30-core machine with two-way hyper-threading on real-world graphs, we achieve up to a 55x speedup over the state-of-the-art parallel nucleus decomposition algorithm by Sariyüce et al. , and up to a 40x self-relative parallel speedup. We are able to efficiently compute larger nucleus decompositions than prior work on several million-scale graphs for the first time.
Computer Science↗
Fast shared-memory streaming multilevel graph partitioning
In this report we show that a fast parallel graph partitioner can benefit many applications by reducing data transfers. The online methods for partitioning graphs have to be fast and they often rely on simple one-pass streaming algorithms, while the offline methods for partitioning graphs contain more involved algorithms and the most successful methods in this category belong to the multilevel approaches. In this work, we assess the feasibility of using streaming graph partitioning algorithms within the multilevel framework. Our end goal is to come up with a fast parallel offline multilevel partitioner that can produce competitive cutsize quality. We rely on a simple but fast and flexible streaming algorithm throughout the entire multilevel framework. This streaming algorithm serves multiple purposes in the partitioning process: a clustering algorithm in the coarsening, an effective algorithm for the initial partitioning, and a fast refinement algorithm in the uncoarsening. Its simple nature also lends itself easily for parallelization. The experiments on various graphs show that our approach is on the average up to 5.1x faster than the multi-threaded MeTiS, which comes at the expense of only 2x worse cutsize.
97 MATHEMATICS AND COMPUTING↗