Graph coloring algorithms for multi-core and massively multithreaded architectures

Çatalyürek, Ümit V.; Feo, John; Gebremedhin, Assefaw H.; Halappanavar, Mahantesh; Pothen, Alex

doi:10.1016/j.parco.2012.07.001

Cited by 65 publications

(46 citation statements)

References 29 publications

(51 reference statements)

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“…The real-world graphs came from the Large Network Dataset Collection provided by Stanford's SNAP project [40]. The synthetic graphs consist of the adversarial graphs described in Section 4 and a set of graphs from three classes: constant degree, 3D grid, and "recursive matrix" (rMat) [14,17]. The adversarial graphs -clique-chain-400 and path-10M -are described in Figure 4 with ∆ = 400 and Theorem 8 with |V | = 10, 000, 000, respectively.…”

Section: Methodsmentioning

confidence: 99%

“…Catalyurek et al [14] present the algorithm ITERATIVE, which first speculatively colors a graph G and then fixes coloring conflicts, that is, corrects the coloring where two adjacent vertices are assigned the same color. The process of fixing conflicting colors can introduce new conflicts, though the authors observe empirically that comparatively few iterations suffice to find a valid coloring.…”

Section: Related Workmentioning

confidence: 99%

“…Thanks to Aydın Buluç of Lawrence Berkeley Laboratory for helping us in our search for collections of large sparse graphs. Thanks to Mahantesh Halappanavar of Pacific Northwest National Laboratory for providing us with the code for ITERATIVE [14]. Thanks to Assefaw Gebremedhin for input regarding the publicly available graph-coloring library COLPACK [28].…”

Section: Acknowledgmentsmentioning

confidence: 99%

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Ordering heuristics for parallel graph coloring

Hasenplaugh¹,

Kaler²,

Schardl³

et al. 2014

Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures

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This paper introduces the largest-log-degree-first (LLF) and smallest-log-degree-last (SLL) ordering heuristics for parallel greedy graph-coloring algorithms, which are inspired by the largest-degree-first (LF) and smallest-degree-last (SL) serial heuristics, respectively. We show that although LF and SL, in practice, generate colorings with relatively small numbers of colors, they are vulnerable to adversarial inputs for which any parallelization yields a poor parallel speedup. In contrast, LLF and SLL allow for provably good speedups on arbitrary inputs while, in practice, producing colorings of competitive quality to their serial analogs.We applied LLF and SLL to the parallel greedy coloring algorithm introduced by Jones and Plassmann, referred to here as JP. Jones and Plassman analyze the variant of JP that processes the vertices of a graph in a random order, and show that on an O(1)-degree graph G = (V, E), this JP-R variant has an expected parallel running time of O(lgV / lg lgV ) in a PRAM model. We improve this bound to show, using work-span analysis, that JP-R, augmented to handle arbitrary-degree graphs, colors a graph G = (V, E) with degree ∆ using Θ(V + E) work and O(lgV + lg ∆ · min{ √ E, ∆ + lg ∆ lgV / lg lgV }) expected span. We prove that JP-LLF and JP-SLL-JP using the LLF and SLL heuristics, respectivelyexecute with the same asymptotic work as JP-R and only logarithmically more span while producing higher-quality colorings than JP-R in practice.We engineered an efficient implementation of JP for modern shared-memory multicore computers and evaluated its performance on a machine with 12 Intel Core-i7 (Nehalem) processor cores. Our implementation of JP-LLF achieves a geometric-mean speedup of 7.83 on eight real-world graphs and a geometric-mean speedup of 8.08 on ten synthetic graphs, while our implementation using SLL achieves a geometric-mean speedup of 5.36 on these real-world graphs and a geometric-mean speedup of 7.02 on these synthetic graphs. Furthermore, on one processor, JP-LLF is slightly faster than a well-engineered serial greedy algorithm using LF, and likewise, JP-SLL is slightly faster than the greedy algorithm using SL.

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Section: Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Acknowledgmentsmentioning

confidence: 99%

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Ordering heuristics for parallel graph coloring

Hasenplaugh¹,

Kaler²,

Schardl³

et al. 2014

Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures

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“…A commonly used heuristic is the greedy heuristic [2] summarised in Algorithm 3, which depends, firstly, on the ordering in which the vertices are visited and, secondly, on how a colour is chosen from amongst those not forbidden. Hasenplaugh et.…”

Section: Colouring Algorithmsmentioning

confidence: 99%

Analysis of the semi-synchronous approach to large-scale parallel community finding

Duriakova

Hurley

Ajwani³

et al. 2014

Proceedings of the Second ACM Conference on Online Social Networks

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Community-finding in graphs is the process of identifying highly cohesive vertex subsets. Recently the vertex-centric approach has been found effective for scalable graph processing and is implemented in systems such as GraphLab and Pregel. In the vertex-centric approach, the analysis is decomposed into a set of local computations at each vertex of the graph, with results propagated to neighbours along the vertex's edges. Many community finding algorithms are amenable to this approach as they are based on the optimisation of an objective through a process of iterative local update (ILU), in which vertices are successively moved to the community of one of their neighbours in order to achieve the highest local gain in the quality of the objective. The sequential processing of such iterative algorithms generally benefits from an asynchronous approach, where a vertex update uses the most recent state as generated by the previous update of vertices in its neighbourhood. When vertices are distributed over a parallel machine, the asynchronous approach can encounter race conditions that impact on its performance and destroy the consistency of the results. Alternatively, a semi-synchronous approach ensures that only non-conflicting vertices are updated simultaneously. In this paper we study the semi-synchronous approach to ILU algorithms for community finding on social networks. Because of the heavy-tailed vertex distribution, the order in which vertex updates are applied in asynchronous ILU can greatly impact both convergence time and quality of the found communities. We study the impact of ordering on the distributed label propagation and modularity maximisation algorithms implemented on a shared-memory multicore architecture. We demonstrate that the semi-synchronous ILU approach is competitive in time and quality with the asynchronous approach, while allowing the analyst to maintain consistent control over update ordering. Thus, our implementation results in a more robust and predictable performance and provides control over the order in which the node Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. labels are updated, which is crucial to obtaining the correct trade-off between running time and quality of communities on many graph classes.

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“…We provided efficient implementation of our algorithm on shared memory architectures [8,9]. We evaluated the performance of the shared--memory algorithm on novel Intel MIC architecture [10].…”

Section: Parallel Graph Coloringmentioning

confidence: 99%

SciDAC Institute: Combinatorial Scientific Computing and Petascale Simulations (CSCAPES) (Final Report)

Çatalyürek¹

2014

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Graph coloring algorithms for multi-core and massively multithreaded architectures

Cited by 65 publications

References 29 publications

Ordering heuristics for parallel graph coloring

Ordering heuristics for parallel graph coloring

Analysis of the semi-synchronous approach to large-scale parallel community finding

SciDAC Institute: Combinatorial Scientific Computing and Petascale Simulations (CSCAPES) (Final Report)

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