Any-k: Anytime Top-k Tree Pattern Retrieval in Labeled Graphs

Many problems in areas as diverse as recommendation systems, social network analysis, semantic search, and distributed root cause analysis can be modeled as pattern search on labeled graphs (also called "heterogeneous information networks" or HINs). Given a large graph and a query pattern with node and edge label constraints, a fundamental challenge is to nd the top-k matches ac- cording to a ranking function over edge and node weights. For users, it is di cult to select value k . We therefore propose the novel notion of an any-k ranking algorithm: for a given time budget, re- turn as many of the top-ranked results as possible. Then, given additional time, produce the next lower-ranked results quickly as well. It can be stopped anytime, but may have to continues until all results are returned. This paper focuses on acyclic patterns over arbitrary labeled graphs. We are interested in practical algorithms that effectively exploit (1) properties of heterogeneous networks, in particular selective constraints on labels, and (2) that the users often explore only a fraction of the top-ranked results. Our solution, KARPET, carefully integrates aggressive pruning that leverages the acyclic nature of the query, and incremental guided search. It enables us to prove strong non-trivial time and space guarantees, which is generally considered very hard for this type of graph search problem. Through experimental studies we show that KARPET achieves running times in the order of milliseconds for tree patterns on large networks with millions of nodes and edges.Comment: To appear in WWW 201

Incremental Processing and Optimization of Update Streams

Over the recent years, we have seen an increasing number of applications in networking, sensor networks, cloud computing, and environmental monitoring, which monitor, plan, control, and make decisions over data streams from multiple sources. We are interested in extending traditional stream processing techniques to meet the new challenges of these applications. Generally, in order to support genuine continuous query optimization and processing over data streams, we need to systematically understand how to address incremental optimization and processing of update streams for a rich class of queries commonly used in the applications. Our general thesis is that efficient incremental processing and re-optimization of update streams can be achieved by various incremental view maintenance techniques if we cast the problems as incremental view maintenance problems over data streams. We focus on two incremental processing of update streams challenges currently not addressed in existing work on stream query processing: incremental processing of transitive closure queries over data streams, and incremental re-optimization of queries. In addition to addressing these specific challenges, we also develop a working prototype system Aspen, which serves as an end-to-end stream processing system that has been deployed as the foundation for a case study of our SmartCIS application. We validate our solutions both analytically and empirically on top of our prototype system Aspen, over a variety of benchmark workloads such as TPC-H and LinearRoad Benchmarks

Adding Logical Operators to Tree Pattern Queries on Graph-Structured Data

As data are increasingly modeled as graphs for expressing complex relationships, the tree pattern query on graph-structured data becomes an important type of queries in real-world applications. Most practical query languages, such as XQuery and SPARQL, support logical expressions using logical-AND/OR/NOT operators to define structural constraints of tree patterns. In this paper, (1) we propose generalized tree pattern queries (GTPQs) over graph-structured data, which fully support propositional logic of structural constraints. (2) We make a thorough study of fundamental problems including satisfiability, containment and minimization, and analyze the computational complexity and the decision procedures of these problems. (3) We propose a compact graph representation of intermediate results and a pruning approach to reduce the size of intermediate results and the number of join operations -- two factors that often impair the efficiency of traditional algorithms for evaluating tree pattern queries. (4) We present an efficient algorithm for evaluating GTPQs using 3-hop as the underlying reachability index. (5) Experiments on both real-life and synthetic data sets demonstrate the effectiveness and efficiency of our algorithm, from several times to orders of magnitude faster than state-of-the-art algorithms in terms of evaluation time, even for traditional tree pattern queries with only conjunctive operations.Comment: 16 page

Using materialized views for answering graph pattern queries

Discovering patterns in graphs by evaluating graph pattern queries involving direct (edge-to-edge mapping) and reachability (edge-to-path mapping) relationships under homomorphisms on data graphs has been extensively studied. Previous studies have aimed to reduce the evaluation time of graph pattern queries due to the potentially numerous matches on large data graphs. In this work, the concept of the summary graph is developed to improve the evaluation of tree pattern queries and graph pattern queries. The summary graph first filters out candidate matches which violate certain reachability constraints, and then finds local matches of query edges. This reduces redundancy in the representation of the query results and allows for computation sharing during the generation of these results. Methods using materialized graph pattern views are developed to improve the efficiency of graph pattern query evaluation. A view is materialized as a summary graph, which compactly records all the homomorphisms of the view to the data graph. View usability is characterized in terms of query edge coverage to provide necessary and sufficient conditions for answering queries using views, and algorithms are developed for determining view usability and for summary graph construction. Experimental evaluation shows that the methods using summary graphs and its related concepts outperform previous state-of-the-art approaches. It also demonstrates that the view materialization method outperforms, by several orders of magnitude, a state-of-the-art approach which does not use materialized views, and substantially improves upon its scalability

Algorithms for Efficient Top-Down Join Enumeration

For a DBMS that provides support for a declarative query language like SQL, the query optimizer is a crucial piece of software. The declarative nature of a query allows it to be translated into many equivalent evaluation plans. The process of choosing a suitable plan from all alternatives is known as query optimization. The basis of this choice are a cost model and statistics over the data. Essential for the costs of a plan is the execution order of join operations in its operator tree, since the runtime of plans with different join orders can vary by several orders of magnitude. An exhaustive search for an optimal solution over all possible operator trees is computationally infeasible. To decrease complexity, the search space must be restricted. Therefore, a well-accepted heuristic is applied: All possible bushy join trees are considered, while cross products are excluded from the search. There are two efficient approaches to identify the best plan: bottom-up and top-down join enumeration. But only the top-down approach allows for branch-and-bound pruning, which can improve compile time by several orders of magnitude, while still preserving optimality. Hence, this thesis focuses on the top-down join enumeration. In the first part, we present two efficient graph-partitioning algorithms suitable for top-down join enumeration. However, as we will see, there are two severe limitations: The proposed algorithms can handle only (1) simple (binary) join predicates and (2) inner joins. Therefore, the second part adopts one of the proposed partitioning strategies to overcome those limitations. Furthermore, we propose a more generic partitioning framework that enables every graph-partitioning algorithm to handle join predicates involving more than two relations, and outer joins as well as other non-inner joins. As we will see, our framework is more efficient than the adopted graph-partitioning algorithm. The third part of this thesis discusses the two branch-and-bound pruning strategies that can be found in the literature. We present seven advancements to the combined strategy that improve pruning (1) in terms of effectiveness, (2) in terms of robustness and (3), most importantly, avoid the worst-case behavior otherwise observed. Different experiments evaluate the performance improvements of our proposed methods. We use the TPC-H, TPC-DS and SQLite test suite benchmarks to evaluate our joined contributions

Robust and adaptive query processing in hybrid transactional/analytical database systems

The quality of query execution plans in database systems determines how fast a query can be processed. Conventional query optimization may still select sub-optimal or even bad query execution plans, due to errors in the cardinality estimation. In this work, we address limitations and unsolved problems of Robust and Adaptive Query Processing, with the goal of improving the detection and compensation of sub-optimal query execution plans. We demonstrate that existing heuristics cannot sufficiently characterize the intermediate result cardinalities, for which a given query execution plan remains optimal, and present an algorithm to calculate precise optimality ranges. The compensation of sub-optimal query execution plans is a complementary problem. We describe metrics to quantify the robustness of query execution plans with respect to cardinality estimations errors. In queries with cardinality estimation errors, our corresponding robust plan selection strategy chooses query execution plans, which are up to 3.49x faster, compared to the estimated cheapest plans. Furthermore, we present an adaptive query processor to compensate sub-optimal query execution plans. It collects true cardinalities of intermediate results at query execution time to re-optimize the currently running query. We show that the overall effort for re-optimizations and plan switches is similar to the initial optimization. Our adaptive query processor can execute queries up to 5.19x faster, compared to a conventional query processor.Die Qualität von Anfrageausführungsplänen in Datenbank Systemen bestimmt, wie schnell eine Anfrage verarbeitet werden kann. Aufgrund von Fehlern in der Kardinalitätsschätzung können konventionelle Anfrageoptimierer immer noch sub-optimale oder sogar schlechte Anfrageausführungsplänen auswählen. In dieser Arbeit behandeln wir Einschränkungen und ungelöste Probleme robuster und adaptiver Anfrageverarbeitung, um die Erkennung und den Ausgleich sub-optimaler Anfrageausführungspläne zu verbessern. Wir zeigen, dass bestehende Heuristiken nicht entscheiden können, für welche Kardinalitäten ein Anfrageausführungsplan optimal ist, und stellen einen Algorithmus vor, der präzise Optimalitätsbereiche berechnen kann. Der Ausgleich von sub-optimalen Anfrageausführungsplänen ist ein ergänzendes Problem. Wir beschreiben Metriken, welche die Robustheit von Anfrageausführungsplänen gegenüber Fehlern in der Kardinalitätsschätzung quantifizieren können. Unsere robuste Planauswahlstrategie, die auf Robustheitsmetriken aufbaut, kann Pläne finden, die bei Fehlern in der Kardinalitätsschätzung bis zu 3.49x schneller sind als die geschätzt günstigsten Pläne. Des Weiteren stellen wir einen adaptiven Anfrageverarbeiter vor, der sub-optimale Anfrageausführungspläne ausgleichen kann. Er erfasst die wahren Kardinalitäten von Zwischenergebnissen während der Anfrageausführung, um damit die aktuell laufende Anfrage zu re-optimieren. Wir zeigen, dass der gesamte Aufwand für Re-Optimierungen und Planänderungen einer initialen Optimierung entspricht. Unser adaptiver Anfrageverarbeiter kann Anfragen bis zu 5.19x schneller ausführen als ein konventioneller Anfrageverarbeiter