Systems and Algorithms for Dynamic Graph Processing

Data generated from human and systems interactions could be naturally represented as graph data. Several emerging applications rely on graph data, such as the semantic web, social networks, bioinformatics, finance, and trading among others. These applications require graph querying capabilities which are often implemented in graph database management systems (GDBMS). Many GDBMSs have capabilities to evaluate one-time versions of recursive or subgraph queries over static graphs – graphs that do not change or a single snapshot of a changing graph. They generally do not support incrementally maintaining queries as graphs change. However, most applications that employ graphs are dynamic in nature resulting in graphs that change over time, also known as dynamic graphs. This thesis investigates how to build a generic and scalable incremental computation solution that is oblivious to graph workloads. It focuses on two fundamental computations performed by many applications: recursive queries and subgraph queries. Specifically, for subgraph queries, this thesis presents the first approach that (i) performs joins with worstcase optimal computation and communication costs; and (ii) maintains a total memory footprint almost linear in the number of input edges. For recursive queries, this thesis studies optimizations for using differential computation (DC). DC is a general incremental computation that can maintain the output of a recursive dataflow computation upon changes. However, it requires a prohibitively large amount of memory because it maintains differences that track changes in queries input/output. The thesis proposes a suite of optimizations that are based on reducing the number of these differences and recomputing them when necessary. The techniques and optimizations in this thesis, for subgraph and recursive computations, represent a proposal for how to build a state-of-the-art generic and scalable GDBMS for dynamic graph data management

GraphflowDB: Scalable Query Processing on Graph-Structured Relations

Finding patterns over graph-structured datasets is ubiquitous and integral to a wide range of analytical applications, e.g., recommendation and fraud detection. When expressed in the high-level query languages of database management systems (DBMSs), these patterns correspond to many-to-many join computations, which generate very large intermediate relations during query processing and degrade the performance of existing systems. This thesis argues that modern query processors need to adopt two novel techniques to be efficient on growing many-to-many joins: (i) worst-case optimal join algorithms; and (ii) factorized representations. Traditional query processors generate join plans that use binary joins, which in iteration take two relations, base or intermediate, to join and produce a new relation. The theory of worst-case optimal joins have shown that this style of join processing can be provably suboptimal and hence generate unnecessarily large intermediate results. This can be avoided on cyclic join queries if the join is performed in a multi-way fashion a join-attribute-at-a-time. As its first contribution, this thesis proposes the design and implementation of a query processor and optimizer that can generate plans that mix worst-case optimal joins, i.e., attribute-at-a-time joins and binary joins, i.e., table-at-a-time joins. In contrast to prior approaches with novel join optimizers that require solving hard computational problems, such as computing low-width hypertree decompositions of queries, our join optimizer is cost-based and uses a traditional dynamic programming approach with a new cost metric. On acyclic queries, or acyclic parts of queries, sometimes the generation of large intermediate results cannot be avoided. Yet, the theory of factorization has shown that often such intermediate results can be highly compressible if they contain multi-valued dependencies between join attributes. Factorization proposes two relation representation schemes, called f- and d-representations, to represent the large intermediate results generated under many-to-many joins in a compressed format. Existing proposals to adopt factorized representations require designing processing on fully materialized general tries and novel operators that operate on entire tries, which are not easy to adopt in existing systems. As a second contribution, we describe the implementation of a novel query processing approach we call factorized vector execution that adopts f-representations. Factorized vector execution extends the traditional vectorized query processors to use multiple blocks of vectors instead of a single block allowing us to factorize intermediate results and delay or even avoid Cartesian products. Importantly, our design ensures that every core operator in the system still performs computations on vectors. As a third contribution, we further describe how to extend our factorized vector execution model with novel operators to adopt d-representations, which extend f-representations with cached and reused sub-relations. Our design here is based on using nested hash tables that can point to sub-relations instead of copying them and on directed acyclic graph-based query plans. All of our techniques are implemented in the GraphflowDB system, which was developed throughout the years to facilitate the research in this thesis. We demonstrate that GraphflowDB’s query processor can outperform existing approaches and systems by orders of magnitude on both micro-benchmarks and end-to-end benchmarks. The designs proposed in this thesis adopt common-wisdom query processing techniques of pipelining, vector-based execution, and morsel-driven parallelism to ensure easy adoption in existing systems. We believe the design can serve as a blueprint for how to adopt these techniques in existing DBMSs to make them more efficient on workloads with many-to-many joins

DDSL: Efficient Subgraph Listing on Distributed and Dynamic Graphs

Subgraph listing is a fundamental problem in graph theory and has wide applications in areas like sociology, chemistry, and social networks. Modern graphs can usually be large-scale as well as highly dynamic, which challenges the efficiency of existing subgraph listing algorithms. Recent works have shown the benefits of partitioning and processing big graphs in a distributed system, however, there is only few work targets subgraph listing on dynamic graphs in a distributed environment. In this paper, we propose an efficient approach, called Distributed and Dynamic Subgraph Listing (DDSL), which can incrementally update the results instead of running from scratch. DDSL follows a general distributed join framework. In this framework, we use a Neighbor-Preserved storage for data graphs, which takes bounded extra space and supports dynamic updating. After that, we propose a comprehensive cost model to estimate the I/O cost of listing subgraphs. Then based on this cost model, we develop an algorithm to find the optimal join tree for a given pattern. To handle dynamic graphs, we propose an efficient left-deep join algorithm to incrementally update the join results. Extensive experiments are conducted on real-world datasets. The results show that DDSL outperforms existing methods in dealing with both static dynamic graphs in terms of the responding time

LSQB: A large-scale subgraph query benchmark

We introduce LSQB, a new large-scale subgraph query benchmark. LSQB tests the performance of database management systems on an important class of subgraph queries overlooked by existing benchmarks. Matching a labelled structural graph pattern, referred to as subgraph matching, is the focus of LSQB. In relational terms, the benchmark tests DBMSs' join performance as a choke-point since subgraph matching is equivalent to multi-way joins between base Vertex and base Edge tables on ID attributes. The benchmark focuses on read-heavy workloads by relying on global queries which have been ignored by prior benchmarks. Global queries, also referred to as unseeded queries, are a type of queries that are only constrained by labels on the query vertices and edges. LSQB contains a total of nine queries and leverages the LDBC social network data generator for scalability. The benchmark gained both academic and industrial interest and is used internally by 5+ different vendors

Edgeframe: Worst-case optimal joins for graph-pattern matching in spark

We describe the design and implementation of EdgeFrame: a graph-specialized Spark DataFrame that caches the edges of a graph in compressed form on all worker nodes of a cluster, and provides a fast and scalable Worst-Case-Optimal Join (WCOJ) that is especially useful for matching of complex and cyclical patterns in large graphs. Our choice to forego shuffle- or communication-based WCOJ is motivated by our analysis of the Shares algorithm for distributed WCOJ, that was proven communication-optimal, but which we show to quickly deteriorate to a full broadcast of all data already with moderately complex graph patterns. Our work shows that specializing WCOJ to a multi-way self-join, and leveraging compressed storage, provides a significant opportunity for better WCOJ performance. Finally, we investigate WCOJ parallelization and load-balancing strategies and show that fine-grained dynamic load-balancing with work-stealing is to be preferred, creating interesting insights and challenges for the future evolution of the Spark scheduler