Efficient Subgraph Matching on Billion Node Graphs

The ability to handle large scale graph data is crucial to an increasing number of applications. Much work has been dedicated to supporting basic graph operations such as subgraph matching, reachability, regular expression matching, etc. In many cases, graph indices are employed to speed up query processing. Typically, most indices require either super-linear indexing time or super-linear indexing space. Unfortunately, for very large graphs, super-linear approaches are almost always infeasible. In this paper, we study the problem of subgraph matching on billion-node graphs. We present a novel algorithm that supports efficient subgraph matching for graphs deployed on a distributed memory store. Instead of relying on super-linear indices, we use efficient graph exploration and massive parallel computing for query processing. Our experimental results demonstrate the feasibility of performing subgraph matching on web-scale graph data.Comment: VLDB201

A survey of parallel execution strategies for transitive closure and logic programs

An important feature of database technology of the nineties is the use of parallelism for speeding up the execution of complex queries. This technology is being tested in several experimental database architectures and a few commercial systems for conventional select-project-join queries. In particular, hash-based fragmentation is used to distribute data to disks under the control of different processors in order to perform selections and joins in parallel. With the development of new query languages, and in particular with the definition of transitive closure queries and of more general logic programming queries, the new dimension of recursion has been added to query processing. Recursive queries are complex; at the same time, their regular structure is particularly suited for parallel execution, and parallelism may give a high efficiency gain. We survey the approaches to parallel execution of recursive queries that have been presented in the recent literature. We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused on optimization of more general Datalog queries. Though the subareas seem radically different because of the approach and formalism used, they have many common features. This is not surprising, because most typical Datalog queries can be solved by means of the transitive closure of simple algebraic expressions. We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs. We then review sequential methods for evaluating transitive closure, distinguishing iterative and direct methods. We address the parallelization of these methods, by discussing various forms of parallelization. Data fragmentation plays an important role in obtaining parallel execution; we describe hash-based and semantic fragmentation. Finally, we consider Datalog queries, and present general methods for parallel rule execution; we recognize the similarities between these methods and the methods reviewed previously, when the former are applied to linear Datalog queries. We also provide a quantitative analysis that shows the impact of the initial data distribution on the performance of methods

NOUS: Construction and Querying of Dynamic Knowledge Graphs

The ability to construct domain specific knowledge graphs (KG) and perform question-answering or hypothesis generation is a transformative capability. Despite their value, automated construction of knowledge graphs remains an expensive technical challenge that is beyond the reach for most enterprises and academic institutions. We propose an end-to-end framework for developing custom knowledge graph driven analytics for arbitrary application domains. The uniqueness of our system lies A) in its combination of curated KGs along with knowledge extracted from unstructured text, B) support for advanced trending and explanatory questions on a dynamic KG, and C) the ability to answer queries where the answer is embedded across multiple data sources.Comment: Codebase: https://github.com/streaming-graphs/NOU

Communication Patterns for Randomized Algorithms

Examples of large scale networks include the Internet, peer-to-peer networks, parallel computing systems, cloud computing systems, sensor networks, and social networks. Efficient dissemination of information in large networks such as these is a funda- mental problem. In many scenarios the gathering of information by a centralised controller can be impractical. When designing and analysing distributed algorithms we must consider the limitations imposed by the heterogeneity of devices in the networks. Devices may have limited computational ability or space. This makes randomised algorithms attractive solutions. Randomised algorithms can often be simpler and easier to implement than their deterministic counterparts. This thesis analyses the effect of communication patterns on the performance of distributed randomised algorithms. We study randomized algorithms with application to three different areas. Firstly, we study a generalization of the balls-into-bins game. Balls into bins games have been used to analyse randomised load balancing. Under the Greedy[d] allocation scheme each ball queries the load of d random bins and is then allocated to the least loaded of them. We consider an infinite, parallel setting where expectedly λn balls are allocated in parallel according to the Greedy[d] allocation scheme in to n bins and subsequently each non-empty bin removes a ball. Our results show that for d = 1,2, the Greedy[d] allocation scheme is self-stabilizing and that in any round the maximum system load for high arrival rates is exponentially smaller for d = 2 compared to d = 1 (w.h.p). Secondly, we introduce protocols that solve the plurality consensus problem on arbitrary graphs for arbitrarily small bias. Typically, protocols depend heavily on the employed communication mechanism. Our protocols are based on an interest- ing relationship between plurality consensus and distributed load balancing. This relationship allows us to design protocols that are both time and space efficient and generalize the state of the art for a large range of problem parameters. Finally, we investigate the effect of restricting the communication of the classical PULL algorithm for randomised rumour spreading. Rumour spreading (broadcast) is a fundamental task in distributed computing. Under the classical PULL algo- rithm, a node with the rumour that receives multiple requests is able to respond to all of them in a given round. Our model restricts nodes such that they can re- spond to at most one request per round. Our results show that the restricted PULL algorithm is optimal for several graph classes such as complete graphs, expanders, random graphs and several Cayley graphs

Capturing Topology in Graph Pattern Matching

Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be conducted in cubic-time. However, they fall short of capturing the topology of data graphs, i.e., graphs may have a structure drastically different from pattern graphs they match, and the matches found are often too large to understand and analyze. To rectify these problems, this paper proposes a notion of strong simulation, a revision of graph simulation, for graph pattern matching. (1) We identify a set of criteria for preserving the topology of graphs matched. We show that strong simulation preserves the topology of data graphs and finds a bounded number of matches. (2) We show that strong simulation retains the same complexity as earlier extensions of simulation, by providing a cubic-time algorithm for computing strong simulation. (3) We present the locality property of strong simulation, which allows us to effectively conduct pattern matching on distributed graphs. (4) We experimentally verify the effectiveness and efficiency of these algorithms, using real-life data and synthetic data.Comment: VLDB201