HPC techniques for large scale data analysis

In the present work we apply High-Performance Computing techniques to two Big Data problems. The frst one deals with the analysis of large graphs by using a parallel distributed architecture, whereas the second one consists in the design and implementation of a scalable solution for fast indexing and searching of large datasets of heterogeneous documents

Fully polynomial FPT algorithms for some classes of bounded clique-width graphs

Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More recently, hardness results for problems in P were achieved using reasonable complexity theoretic assumptions such as: Strong Exponential Time Hypothesis (SETH), 3SUM and All-Pairs Shortest-Paths (APSP). According to these assumptions, many graph theoretic problems do not admit truly subquadratic algorithms, nor even truly subcubic algorithms (Williams and Williams, FOCS 2010 and Abboud, Grandoni, Williams, SODA 2015). A central technique used to tackle the difficulty of the above mentioned problems is fixed-parameter algorithms for polynomial-time problems with polynomial dependency in the fixed parameter (P-FPT). This technique was introduced by Abboud, Williams and Wang in SODA 2016 and continued by Husfeldt (IPEC 2016) and Fomin et al. (SODA 2017), using the treewidth as a parameter. Applying this technique to clique-width, another important graph parameter, remained to be done. In this paper we study several graph theoretic problems for which hardness results exist such as cycle problems (triangle detection, triangle counting, girth, diameter), distance problems (diameter, eccentricities, Gromov hyperbolicity, betweenness centrality) and maximum matching. We provide hardness results and fully polynomial FPT algorithms, using clique-width and some of its upper-bounds as parameters (split-width, modular-width and $P\_4$-sparseness). We believe that our most important result is an ${\cal O}(k^4 \cdot n + m)$-time algorithm for computing a maximum matching where $k$ is either the modular-width or the $P\_4$-sparseness. The latter generalizes many algorithms that have been introduced so far for specific subclasses such as cographs, $P\_4$-lite graphs, $P\_4$-extendible graphs and $P\_4$-tidy graphs. Our algorithms are based on preprocessing methods using modular decomposition, split decomposition and primeval decomposition. Thus they can also be generalized to some graph classes with unbounded clique-width

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

Performance Characterization of High-Level Programming Models for GPU Graph Analytics

We identify several factors that are critical to high-performance GPU graph analytics: efficient building block operators, synchronization and data movement, workload distribution and load balancing, and memory access patterns. We analyze the impact of these critical factors through three GPU graph analytic frameworks, Gunrock, MapGraph, and VertexAPI2. We also examine their effect on different workloads: four common graph primitives from multiple graph application domains, evaluated through real-world and synthetic graphs. We show that efficient building block operators enable more powerful operations for fast information propagation and result in fewer device kernel invocations, less data movement, and fewer global synchronizations, and thus are key focus areas for efficient large-scale graph analytics on the GPU

Epidemics on dynamic networks

In many populations, the patterns of potentially infectious contacts are transients that can be described as a network with dynamic links. The relative timescales of link and contagion dynamics and the characteristics that drive their tempos can lead to important differences to the static case. Here, we propose some essential nomenclature for their analysis, and then review the relevant literature. We describe recent advances in they apply to infection processes, considering all of the methods used to record, measure and analyse them, and their implications for disease transmission. Finally, we outline some key challenges and opportunities in the field. Keywords: Social network analysis, Disease models, Network metrics, Network dat

Algorithmes polynomiaux paramétrés pour des classes de graphes de largeur de clique bornée

Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More recently, hardness results for problems in P were achieved using reasonable complexity theoretic assumptions such as: Strong Exponential Time Hypothesis (SETH), 3SUM and All-Pairs Shortest-Paths (APSP). According to these assumptions, many graph theoretic problems do not admit truly subquadratic algorithms, nor even truly subcubic algorithms (Williams and Williams, FOCS 2010 and Abboud, Grandoni, Williams, SODA 2015). A central technique used to tackle the difficulty of the above mentioned problems is fixed-parameter algorithms for polynomial-time problems with polynomial dependency in the fixed parameter (P-FPT). This technique was introduced by Abboud, Williams and Wang in SODA 2016 and continued by Husfeldt (IPEC 2016) and Fomin et al. (SODA 2017), using the treewidth as a parameter. Applying this technique to clique-width, another important graph parameter, remained to be done. In this paper we study several graph theoretic problems for which hardness results exist such as cycle problems (triangle detection, triangle counting, girth, diameter), distance problems (diameter, eccentricities, Gromov hyperbolicity, betweenness centrality) and maximum matching. We provide hardness results and fully polynomial FPT algorithms, using clique-width and some of its upper-bounds as parameters (split-width, modular-width and $P_4$-sparseness). We believe that our most important result is an ${\cal O}(k^4 \cdot n + m)$-time algorithm for computing a maximum matching where $k$ is either the modular-width or the $P_4$-sparseness. The latter generalizes many algorithms that have been introduced so far for specific subclasses such as cographs, $P_4$-lite graphs, $P_4$-extendible graphs and $P_4$-tidy graphs. Our algorithms are based on preprocessing methods using modular decomposition, split decomposition and primeval decomposition. Thus they can also be generalized to some graph classes with unbounded clique-width

Graph Processing in Main-Memory Column Stores

Evermore, novel and traditional business applications leverage the advantages of a graph data model, such as the offered schema flexibility and an explicit representation of relationships between entities. As a consequence, companies are confronted with the challenge of storing, manipulating, and querying terabytes of graph data for enterprise-critical applications. Although these business applications operate on graph-structured data, they still require direct access to the relational data and typically rely on an RDBMS to keep a single source of truth and access. Existing solutions performing graph operations on business-critical data either use a combination of SQL and application logic or employ a graph data management system. For the first approach, relying solely on SQL results in poor execution performance caused by the functional mismatch between typical graph operations and the relational algebra. To the worse, graph algorithms expose a tremendous variety in structure and functionality caused by their often domain-specific implementations and therefore can be hardly integrated into a database management system other than with custom coding. Since the majority of these enterprise-critical applications exclusively run on relational DBMSs, employing a specialized system for storing and processing graph data is typically not sensible. Besides the maintenance overhead for keeping the systems in sync, combining graph and relational operations is hard to realize as it requires data transfer across system boundaries. A basic ingredient of graph queries and algorithms are traversal operations and are a fundamental component of any database management system that aims at storing, manipulating, and querying graph data. Well-established graph traversal algorithms are standalone implementations relying on optimized data structures. The integration of graph traversals as an operator into a database management system requires a tight integration into the existing database environment and a development of new components, such as a graph topology-aware optimizer and accompanying graph statistics, graph-specific secondary index structures to speedup traversals, and an accompanying graph query language. In this thesis, we introduce and describe GRAPHITE, a hybrid graph-relational data management system. GRAPHITE is a performance-oriented graph data management system as part of an RDBMS allowing to seamlessly combine processing of graph data with relational data in the same system. We propose a columnar storage representation for graph data to leverage the already existing and mature data management and query processing infrastructure of relational database management systems. At the core of GRAPHITE we propose an execution engine solely based on set operations and graph traversals. Our design is driven by the observation that different graph topologies expose different algorithmic requirements to the design of a graph traversal operator. We derive two graph traversal implementations targeting the most common graph topologies and demonstrate how graph-specific statistics can be leveraged to select the optimal physical traversal operator. To accelerate graph traversals, we devise a set of graph-specific, updateable secondary index structures to improve the performance of vertex neighborhood expansion. Finally, we introduce a domain-specific language with an intuitive programming model to extend graph traversals with custom application logic at runtime. We use the LLVM compiler framework to generate efficient code that tightly integrates the user-specified application logic with our highly optimized built-in graph traversal operators. Our experimental evaluation shows that GRAPHITE can outperform native graph management systems by several orders of magnitude while providing all the features of an RDBMS, such as transaction support, backup and recovery, security and user management, effectively providing a promising alternative to specialized graph management systems that lack many of these features and require expensive data replication and maintenance processes