This article targets the Incremental View Maintenance (IVM) of sophisticated analytics (such as statistical models, machine learning programs, and graph algorithms) expressed as linear algebra programs. We present LAGO, a unified framework for linear algebra that automatically synthesizes efficient incremental trigger programs, thereby freeing the user from error-prone manual derivations, performance tuning, and low-level implementation details. The key technique underlying our framework is abstract interpretation, which is used to infer various properties of analytical programs. These properties give the reasoning power required for the automatic synthesis of efficient incremental triggers. We evaluate the effectiveness of our framework on a wide range of applications from regression models to graph computations.

We address the problem of load balancing for parallel joins.We show that the distribution of input data received and the output data produced by worker machines are both important for performance. As a result, previous work, which optimizes either for input or output, stands ineffective for load balancing. To that end, we propose a multi-stage load-balancing algorithm which considers the properties of both input and output data through sampling of the original join matrix. To do this efficiently, we propose a novel category of equi-weight histograms. To build them, we exploit state-of-the-art computational geometry algorithms for rectangle tiling. To our knowledge, we are the first to employ tiling algorithms for join load-balancing. In addition, we propose a novel, join-specialized tiling algorithm that has drastically lower time and space complexity than existing algorithms. Experiments show that our scheme outperforms state-of-the-art techniques by up to a factor of 15.

Squall is a scalable online query engine that runs complex analytics in a cluster using skew-resilient, adaptive operators. Squall builds on state-of-the-art partitioning schemes and local algorithms, including some of our own. This paper presents the overview of Squall, including some novel join operators. The paper also presents lessons learned over the five years of working on this system, and outlines the plan for the proposed system demonstration.

Many analytics tasks and machine learning problems can be naturally expressed by iterative linear algebra programs. In this paper, we study the incremental view maintenance problem for such complex analytical queries. We develop a framework, called LINVIEW, for capturing deltas of linear algebra programs and understanding their computational cost. Linear algebra operations tend to cause an avalanche effect where even very local changes to the input matrices spread out and infect all of the intermediate results and the final view, causing incremental view maintenance to lose its performance benefit over re-evaluation. We develop techniques based on matrix factorizations to contain such epidemics of change. As a consequence, our techniques make incremental view maintenance of linear algebra practical and usually substantially cheaper than re-evaluation. We show, both analytically and experimentally, the usefulness of these techniques when applied to standard analytics tasks. Our evaluation demonstrates the efficiency of LINVIEW in generating parallel incremental programs that outperform re-evaluation techniques by more than an order of magnitude.

Mining frequent subgraphs is an important operation on graphs; it is defined as finding all subgraphs that appear frequently in a database according to a given frequency threshold. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs, or protein-protein interactions in bioinformatics, are modeled as a single large graph. In this paper we present GraMi, a novel framework for frequent subgraph mining in a single large graph. GraMi undertakes a novel approach that only finds the minimal set of instances to satisfy the frequency threshold and avoids the costly enumeration of all instances required by previous approaches. We accompany our approach with a heuristic and optimizations that significantly improve performance. Additionally, we present an extension of GraMi that mines frequent patterns. Compared to subgraphs, patterns offer a more powerful version of matching that captures transitive interactions between graph nodes (like friend of a friend) which are very common in modern applications. Finally, we present CGraMi, a version supporting structural and semantic constraints, and AGraMi, an approximate version producing results with no false positives. Our experiments on real data demonstrate that our framework is up to 2 orders of magnitude faster and discovers more interesting patterns than existing approaches.

Scalable join processing in a parallel shared-nothing environment requires a partitioning policy that evenly distributes the processing load while minimizing the size of state maintained and number of messages communicated. Previous research proposes static partitioning schemes that require statistics beforehand. In an online or streaming environment in which no statistics about the workload are known, traditional static approaches perform poorly. This paper presents a novel parallel online dataflow join operator that supports arbitrary join predicates. The proposed operator continuously adjusts itself to the data dynamics through adaptive dataflow routing and state repartitioning. The operator is resilient to data skew, maintains high throughput rates, avoids blocking behavior during state repartitioning, takes an eventual consistency approach for maintaining its local state, and behaves strongly consistently as a black-box dataflow operator. We prove that the operator ensures a constant competitive ratio 3:75 in data distribution optimality and that the cost of processing an input tuple is amortized constant, taking into account adaptivity costs. Our evaluation demonstrates that our operator outperforms the state-of-the-art static partitioning schemes in resource utilization, throughput, and execution time.