Scalable data parallel graph algorithms from generation to management

Scalable Data-Parallel graph algorithms from generation to management Sadegh Nobari (B.Eng.(Hons.),IUST) (Ph.D.,NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF COMPUTER SCIENCE SCHOOL OF COMPUTING NATIONAL UNIVERSITY OF SINGAPORE 2012 Declaration I hereby declare that this thesis is my original work and it has been written by me in its entirety I have duly acknowledged all the sources of information which have been used in the thesis This thesis has also not been submitted for any degree in any university previously Sadegh Nobari 23 July 2012 i Acknowledgements Ph.D was a wonderful extraordinary one time in life experience I would like to say thanks To my parents (Zeynab and Nader) and my only brother (Ghasem), through their sacrifice my opportunities were possible To my advisors, Professor St´ phane Bressan e Professors Anastasia Ailamaki, Panagiotis Karras, Panos Kalnis, Nikos Mamoulis and Yannis Velegrakis for patiently supporting me To my committee, ă Professors Tan Tiow Seng, Tan Kian-Lee, M Tamer Ozsu and Leong Hon Wai for gladly suffering my impenetrable prose and helping me to better communicate ii To my friends, Xuesong Lu, Song Yi, Tang Ruiming, Antoine Veillard, Quoc Trung Tran, Cao Thanh Tung, Ehsan Kazemi, Siarhei Bykau, Mohammad Oliya, Behzad Nemat Pajouh, Thomas Heinis, Clemens Lay, Reza Sherkat and for accompanying me To my groups, people in Database research and Embedded System labs of NUS, DIAS of EPFL, dbTrento of University of Trento and Dennis Shasha’s group of NYU for accepting me To my wife Mozhdeh, for redefining my senses Best Wishes, Dr Sadegh Nobari With a quarter-century of life experience 2012 iii Abstract J J Sylvester, in 1878, in an article on chemistry and algebra in Nature, called a mathematical structure to model connections between objects, ”graph” More than a century later, the versatility of graphs as a data model is demonstrated by the long list of applications in mathematics, science, engineering and the humanities Cormen, Leiserson, Rivest, and Stein describe the role of graphs and graph algorithms in computer science as follows in their popular textbook: ”graphs are a pervasive data structure in computer science, and algorithms working with them are fundamental to the field.” Graphs are natural data structures for modern applications Social network data are typically represented as graphs, semantic web is based on RDF formalism that is a graph model, software models and program dependence in software engineering represented via graphs In many cases these are very large and dynamic graphs The convergence of applications managing large graphs and the availability of cheap parallel processing hardware caused a renewed interest in managing very large graphs over parallel systems In this dissertation, we design scalable and practical graph algorithms for a selected set of large graph generation and management problems In particular, we provide par- i allel solutions for graph generation with both random and real-world graph models Afterward, we propose techniques for processing large graphs in parallel, specifically for computing the Minimum Spanning Forest and the Shortest Path between vertices Chapter focuses on the generation of very large graphs The nave algorithm for generating eros graphs does not scale to large graphs In this chapter we take a systematic approach to the development of the PPreZER algorithm by proposing a series of seven algorithms The results of our study depict that our fine tuned algorithm, PPreZER, for generating random graph data can be executed on a typical GPU on average 19 times faster than its fastest sequential version on the CPU Chapter moves beyond random graphs and considers the generation of real-world graphs This chapter considers the spatial datasets and the generation of graphs by taking the spatial join of the elements in the two datasets We propose an algorithm (called HiDOP) to perform this spatial join operation efficiently Consequently we design a data parallel algorithm inspired from HiDOP algorithm Chapters and cover the data management part of the thesis Two graph algorithms, a.k.a graph queries, are studied: Minimum Spanning Forest (Chapter 5) and All-Pairs Shortest Path (Chapter 6) In Chapter 5, PMA, a novel data parallel algorithm this is inspired from Bor˙ vka’s and Prims MSF algorithm is proposed PMA experimentally u shows to be superior over the state of the art MSF algorithms Chapter introduces a threshold Lto the problem definition of all-pairs shortest path such that only the paths that have weight less than Lare found, the problem is called L-APSP This threshold is advantageous when only close connections are of interest, like in large social networks A large number of APSP algorithms are studied and for each a counterpart L-APSP algorithm is designed and a parallel version algorithm that exploits GPU is proposed Finally, this dissertation has led to the proposal of four scalable data-parallel algorithms for graph data processing ii Table of Contents Acknowledgements Abstract Table of Contents List of Figures List of Tables List of Algorithms Introduction 1.1 Graph 1.2 Parallel processing 1.3 Contributions 1.4 Graph data generation 1.4.1 Generating random graphs Application Existing algorithms Proposed algorithm 1.4.2 Generating real-world graphs Application Existing algorithms Proposed algorithm 1.5 Graph data management 1.5.1 Finding Minimum Spanning Forest Application Existing algorithms iii ii i viii xii xiii xv 1 6 7 8 9 10 10 1.6 Proposed algorithm 1.5.2 Finding Shortest Path Application Existing algorithms Proposed algorithm Overview Parallel processing on Graphics Processing Unit (GPU) 2.1 Many and Multi core architectures 2.2 GPU Architecture 2.3 The CUDA and BrookGPU programming frameworks 2.4 SIMT: Single Instruction, Multiple Threads 2.5 Parallel Thread Execution (PTX) 2.6 GPU Memory hierarchy 2.7 GPU Optimizations 2.8 GPU empirical analysis 2.9 Programming the GPU 2.9.1 Parallel Pseudo-Random Number Generator 2.9.2 Parallel Prefix Sum 2.9.3 Parallel Stream Compaction 2.10 chapter summary Scalable Random Graph Generation 3.1 Introduction 3.2 Related Work 3.3 Baseline algorithm 3.4 Sequential algorithms 3.4.1 Skipping Edges 3.4.2 ZER 3.4.3 PreLogZER 3.4.4 PreZER 3.5 Parallel algorithms 3.5.1 PER 3.5.2 PZER 3.5.3 PPreZER 3.6 Performance Evaluation 3.6.1 Setup 3.6.2 Results Overall Comparison iv 10 11 12 13 13 14 15 15 16 16 17 21 22 22 25 27 27 29 30 30 33 33 36 38 40 40 42 43 44 45 45 47 50 51 51 51 51 3.7 Speedup Assessment Comparison among Parallel algorithms Parallelism Speedup Size Scalability Performance Tuning 3.6.3 Discussion Chapter Summary Scalable Real-world graph generation 4.1 Introduction 4.2 Related Work 4.2.1 In-Memory Approaches 4.2.2 On-disk Approaches Both Datasets Indexed One Dataset Indexed Unindexed 4.3 Motivation 4.3.1 Touch Detection 4.3.2 Motivation Examples 4.3.3 Motivation Experiments 4.4 HiDOP: Hierarchical Data Oriented Partitioning 4.4.1 Problem Definition 4.4.2 HiDOP Ideas 4.4.3 Algorithm Overview 4.4.4 Tree Building Phase 4.4.5 Assignment Phase 4.4.6 Probing Phase 4.4.7 Proof of Correctness 4.5 Implementation 4.5.1 Partitioning 4.5.2 Design Parameters Tree Parameters Local Join Parameters Join Order 4.6 Parallel algorithms 4.7 Experimental Evaluation 4.7.1 Setup 4.7.2 Experimental Methodology 4.7.3 Loading the Data v 53 54 55 56 57 58 59 63 63 66 66 67 67 67 68 70 71 72 73 75 75 76 76 78 80 82 83 84 84 85 85 86 87 87 90 90 91 92 4.7.4 4.8 Varying Dataset B Small Datasets Large Datasets 4.7.5 Varying Epsilon 4.7.6 Neuroscience Datasets 4.7.7 Parallel HiDOP experiments Overall Comparison Speedup Assessment Chapter Summary Scalable Parallel Minimum Spanning Forest Computation 5.1 Introduction 5.2 Related Work 5.2.1 Sequential algorithms Bor˙ vka u Kruskal Reverse-Delete Prim 5.2.2 Parallel algorithms 5.3 DPMST: Bor˙ vka based Data Parallel MST algorithm u 5.3.1 Implementation on GPU 5.4 Motivation for scalability 5.5 PMA: Scalable Parallel MSF algorithm 5.5.1 Partial Prim 5.5.2 Unification step 5.5.3 Proof of Correctness 5.5.4 Complexity Analysis 5.6 PMA implementation 5.6.1 Partial Prim implementation MinPMA algorithm SortPMA algorithm HybridPMA algorithm 5.6.2 Unification implementation 5.6.3 Implementation notes 5.7 Experiments 5.7.1 DPMST performance evaluation Experimental Setup Experimental Results 5.7.2 PMA performance evaluation vi 93 93 94 96 96 99 99 100 101 103 103 106 106 106 107 108 108 108 110 112 113 114 114 115 117 118 119 119 120 121 121 122 123 123 124 124 124 127 sampling these gigantic graphs in order to discover the properties of the whole graph given the properties of the sampled sub graphs The goal of processing the sampled graphs is to quickly find properties of huge dynamic graphs like social networks 7.4.2 Long term goals Parallel graph processing We are interested to similarly data parallelize the algorithms for the 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generation This thesis first studies the algorithms for generating graphs Graphs may be generated from a random process, i.e random graphs, or from modeling a real-world data, ... narrow our attention to graph data generators and graph data managements We first study the algorithms for generating random graphs [138] in chapter and for generating real-world graphs [139] in chapter