Graphs, Matrices, and the GraphBLAS: Seven Good Reasons

The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istc- bigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.Comment: 10 pages; International Conference on Computational Science workshop on the Applications of Matrix Computational Methods in the Analysis of Modern Dat

Scalable Online Betweenness Centrality in Evolving Graphs

Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best known algorithm runs in O(nm) time. The problems of efficiency and scalability are exacerbated in a dynamic setting, where the input is an evolving graph seen edge by edge, and the goal is to keep the betweenness centrality up to date. In this paper we propose the first truly scalable algorithm for online computation of betweenness centrality of both vertices and edges in an evolving graph where new edges are added and existing edges are removed. Our algorithm is carefully engineered with out-of-core techniques and tailored for modern parallel stream processing engines that run on clusters of shared-nothing commodity hardware. Hence, it is amenable to real-world deployment. We experiment on graphs that are two orders of magnitude larger than previous studies. Our method is able to keep the betweenness centrality measures up to date online, i.e., the time to update the measures is smaller than the inter-arrival time between two consecutive updates.Comment: 15 pages, 9 Figures, accepted for publication in IEEE Transactions on Knowledge and Data Engineerin

Graph Algorithms on GPUs

This chapter introduces the topic of graph algorithms on GPUs. It starts by presenting and comparing the main important data structures and techniques applied for representing and analysing graphs on GPUs at the state of the art.It then presents the theory and an updated review of the most efficient implementations of graph algorithms for GPUs. In particular, the chapter focuses on graph traversal algorithms (breadth-first search), single-source shortest path(Djikstra, Bellman-Ford, delta stepping, hybrids), and all-pair shortest path (Floyd-Warshall). By the end of the chapter, load balancing and memory access techniques are discussed through an overview of their main issues and management techniques

Graph analytics on modern massively parallel systems

Graphs provide a very flexible abstraction for understanding and modeling complex systems in many fields such as physics, biology, neuroscience, engineering, and social science. Only in the last two decades, with the advent of Big Data era, supercomputers equipped by accelerators –i.e., Graphics Processing Unit (GPUs)–, advanced networking, and highly parallel file systems have been used to analyze graph properties such as reachability, diameter, connected components, centrality, and clustering coefficient. Today graphs of interest may be composed by millions, sometimes billions, of nodes and edges and exhibit a highly irregular structure. As a consequence, the design of efficient and scalable graph algorithms is an extraordinary challenge due to irregular communication and memory access patterns, high synchronization costs, and lack of data locality. In the present dissertation, we start off with a brief and gentle introduction for the reader to graph analytics and massively parallel systems. In particular, we present the intersection between graph analytics and parallel architectures in the current state-of-the-art and discuss the challenges encountered when solving such problems on large-scale graphs on these architectures (Chapter 1). In Chapter 2, some preliminary definitions and graph-theoretical notions are provided together with a description of the synthetic graphs used in the literature to model real-world networks. In Chapters 3-5, we present and tackle three different relevant problems in graph analysis: reachability (Chapter 3), Betweenness Centrality (Chapter 4), and clustering coefficient (Chapter 5). In detail, Chapter 3 tackles reachability problems by providing two scalable algorithms and implementations which efficiently solve st-connectivity problems on very large-scale graphs Chapter 4 considers the problem of identifying most relevant nodes in a network which plays a crucial role in several applications, including transportation and communication networks, social network analysis, and biological networks. In particular, we focus on a well-known centrality metrics, namely Betweenness Centrality (BC), and present two different distributed algorithms for the BC computation on unweighted and weighted graphs. For unweighted graphs, we present a new communication-efficient algorithm based on the combination of bi-dimensional (2D) decomposition and multi-level parallelism. Furthermore, new algorithms which exploit the underlying graph topology to reduce the time and space usage of betweenness centrality computations are described as well. Concerning weighted graphs, we provide a scalable algorithm based on an algebraic formulation of the problem. Finally, thorough comprehensive experimental results on synthetic and real- world large-scale graphs, we show that the proposed techniques are effective in practice and achieve significant speedups against state-of-the-art solutions. Chapter 5 considers clustering coefficients problem. Similarly to Betweenness Centrality, it is a fundamental tool in network analysis, as it specifically measures how nodes tend to cluster together in a network. In the chapter, we first extend caching techniques to Remote Memory Access (RMA) operations on distributed-memory system. The caching layer is mainly designed to avoid inter-node communications in order to achieve similar benefits for irregular applications as communication-avoiding algorithms. We also show how cached RMA is able to improve the performance of a new distributed asynchronous algorithm for the computation of local clustering coefficients. Finally, Chapter 6 contains a brief summary of the key contributions described in the dissertation and presents potential future directions of the work