High-Performance Parallel Graph Coloring with Strong Guarantees on Work, Depth, and Quality

Besta, Maciej; Carigiet, Armon; Janda, Kacper; Vonarburg-Shmaria, Zur; Gianinazzi, Lukas; Hoefler, Torsten

doi:10.1109/sc41405.2020.00103

Cited by 21 publications

(27 citation statements)

References 137 publications

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“…We compared to Blanco et al's [7] implementations as well, which we found to also be slower than pkt and pkt-opt-cpu, and arb-nucleus-decomp achieves 2.45-21.36x speedups over their best implementation. 6 We also found that Che et al's implementations outperform the reported numbers from a recent parallel (2, 3) nucleus decomposition implementation by Conte et al [17].…”

Section: Performancementioning

confidence: 51%

“…An 𝑎-orientation of an undirected graph is a total ordering on the vertices such that when edges in the graph are directed from vertices lower in the ordering to vertices higher in the ordering, the outdegree of each vertex is bounded by 𝑎. Shi et al provide parallel work-efficient algorithms to obtain an 𝑂 (𝛼)-orientation, namely the parallel Barenboim-Elkin algorithm which takes 𝑂 (𝑚) work and 𝑂 (log 2 𝑛) span, and the parallel Goodrich-Pszona algorithm which takes 𝑂 (𝑚) work and 𝑂 (log 2 𝑛) span w.h.p. Besta et al [6] present a parallel 𝑂 (𝛼)-orientation algorithm that takes 𝑂 (𝑚) work and 𝑂 (log 2 𝑛) span.…”

Section: Preliminariesmentioning

confidence: 99%

“…For pkt-opt-cpu, we consider the reordering option that gives the fastest overall running time for each graph 6. Blanco et al's implementation requires the maximum 𝑘-truss number to be provided as an input, which we did in these experiments.…”

mentioning

confidence: 99%

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Theoretically and Practically Efficient Parallel Nucleus Decomposition

Shi

Dhulipala

Shun

2021

Preprint

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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.

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Section: Performancementioning

confidence: 51%

Section: Preliminariesmentioning

confidence: 99%

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Theoretically and Practically Efficient Parallel Nucleus Decomposition

Shi

Dhulipala

Shun

2021

Preprint

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“…In GMS, we rst consider the abovementioned degree ordering. We also provide two algorithms for the degeneracy ordering [54] (exact and approximate), which was shown to improve the performance of maximal clique listing or graph coloring [15,29,51,117].…”

Section: Graphmentioning

confidence: 99%

“…Moreover, we alleviate the fact that the default DGR is not easily parallelizable and takes O(n) iterations even in a parallel setting. For this, GMS delivers a modular implementation of a recent (2+ )-approximate degeneracy order [15] (ADG), which has O(log n) iterations for any > 0. Deriving ADG is in Algorithm 3.…”

Section: High-performance and Simplicitymentioning

confidence: 99%

GraphMineSuite

et al. 2021

Self Cite

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We propose GraphMineSuite (GMS): the first benchmarking suite for graph mining that facilitates evaluating and constructing high-performance graph mining algorithms. First, GMS comes with a benchmark specification based on extensive literature review, prescribing representative problems, algorithms, and datasets. Second, GMS offers a carefully designed software platform for seamless testing of different fine-grained elements of graph mining algorithms, such as graph representations or algorithm subroutines. The platform includes parallel implementations of more than 40 considered baselines, and it facilitates developing complex and fast mining algorithms. High modularity is possible by harnessing set algebra operations such as set intersection and difference, which enables breaking complex graph mining algorithms into simple building blocks that can be separately experimented with. GMS is supported with a broad concurrency analysis for portability in performance insights, and a novel performance metric to assess the throughput of graph mining algorithms, enabling more insightful evaluation. As use cases, we harness GMS to rapidly redesign and accelerate state-of-the-art baselines of core graph mining problems: degeneracy reordering (by >2X), maximal clique listing (by >9×), k -clique listing (by up to 1.1×), and subgraph isomorphism (by 2.5×), also obtaining better theoretical performance bounds.

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High-performance and balanced parallel graph coloring on multicore platforms

et al. 2022

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Graph coloring is widely used to parallelize scientific applications by identifying subsets of independent tasks that can be executed simultaneously. Graph coloring assigns colors the vertices of a graph, such that no adjacent vertices have the same color. The number of colors used corresponds to the number of parallel steps in a real-world end-application. Therefore, the total runtime of the graph coloring kernel adds to the overall parallel overhead of the real-world end-application, whereas the number of the vertices of each color class determines the number of the independent concurrent tasks of each parallel step, thus affecting the amount of parallelism and hardware resource utilization in the execution of the real-world end-application. In this work, we propose a high-performance graph coloring algorithm, named ColorTM, that leverages Hardware Transactional Memory (HTM) to detect coloring inconsistencies between adjacent vertices. ColorTM detects and resolves coloring inconsistencies between adjacent vertices with an eager approach to minimize data access costs, and implements a speculative synchronization scheme to minimize synchronization costs and increase parallelism. We extend our proposed algorithmic design to propose a balanced graph coloring algorithm, named BalColorTM, with which all color classes include almost the same number of vertices to achieve high parallelism and resource utilization in the execution of the real-world end-applications. We evaluate ColorTM and BalColorTM using a wide variety of large real-world graphs with diverse characteristics. ColorTM and BalColorTM improve performance by 12.98$$\times$$ × and 1.78$$\times$$ × on average using 56 parallel threads compared to prior state-of-the-art approaches. Moreover, we study the impact of our proposed graph coloring algorithmic designs on a popular end-application, i.e., Community Detection, and demonstrate the ColorTM and BalColorTM can provide high-performance improvements in real-world end-applications across various input data given.

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High-Performance Parallel Graph Coloring with Strong Guarantees on Work, Depth, and Quality

Cited by 21 publications

References 137 publications

Theoretically and Practically Efficient Parallel Nucleus Decomposition

Theoretically and Practically Efficient Parallel Nucleus Decomposition

GraphMineSuite

High-performance and balanced parallel graph coloring on multicore platforms

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