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

Hardware-conscious query processing for the many-core era

Die optimale Nutzung von moderner Hardware zur Beschleunigung von Datenbank-Anfragen ist keine triviale Aufgabe. Viele DBMS als auch DSMS der letzten Jahrzehnte basieren auf Sachverhalten, die heute kaum noch Gültigkeit besitzen. Ein Beispiel hierfür sind heutige Server-Systeme, deren Hauptspeichergröße im Bereich mehrerer Terabytes liegen kann und somit den Weg für Hauptspeicherdatenbanken geebnet haben. Einer der größeren letzten Hardware Trends geht hin zu Prozessoren mit einer hohen Anzahl von Kernen, den sogenannten Manycore CPUs. Diese erlauben hohe Parallelitätsgrade für Programme durch Multithreading sowie Vektorisierung (SIMD), was die Anforderungen an die Speicher-Bandbreite allerdings deutlich erhöht. Der sogenannte High-Bandwidth Memory (HBM) versucht diese Lücke zu schließen, kann aber ebenso wie Many-core CPUs jeglichen Performance-Vorteil negieren, wenn dieser leichtfertig eingesetzt wird. Diese Arbeit stellt die Many-core CPU-Architektur zusammen mit HBM vor, um Datenbank sowie Datenstrom-Anfragen zu beschleunigen. Es wird gezeigt, dass ein hardwarenahes Kostenmodell zusammen mit einem Kalibrierungsansatz die Performance verschiedener Anfrageoperatoren verlässlich vorhersagen kann. Dies ermöglicht sowohl eine adaptive Partitionierungs und Merge-Strategie für die Parallelisierung von Datenstrom-Anfragen als auch eine ideale Konfiguration von Join-Operationen auf einem DBMS. Nichtsdestotrotz ist nicht jede Operation und Anwendung für die Nutzung einer Many-core CPU und HBM geeignet. Datenstrom-Anfragen sind oft auch an niedrige Latenz und schnelle Antwortzeiten gebunden, welche von höherer Speicher-Bandbreite kaum profitieren können. Hinzu kommen üblicherweise niedrigere Taktraten durch die hohe Kernzahl der CPUs, sowie Nachteile für geteilte Datenstrukturen, wie das Herstellen von Cache-Kohärenz und das Synchronisieren von parallelen Thread-Zugriffen. Basierend auf den Ergebnissen dieser Arbeit lässt sich ableiten, welche parallelen Datenstrukturen sich für die Verwendung von HBM besonders eignen. Des Weiteren werden verschiedene Techniken zur Parallelisierung und Synchronisierung von Datenstrukturen vorgestellt, deren Effizienz anhand eines Mehrwege-Datenstrom-Joins demonstriert wird.Exploiting the opportunities given by modern hardware for accelerating query processing speed is no trivial task. Many DBMS and also DSMS from past decades are based on fundamentals that have changed over time, e.g., servers of today with terabytes of main memory capacity allow complete avoidance of spilling data to disk, which has prepared the ground some time ago for main memory databases. One of the recent trends in hardware are many-core processors with hundreds of logical cores on a single CPU, providing an intense degree of parallelism through multithreading as well as vectorized instructions (SIMD). Their demand for memory bandwidth has led to the further development of high-bandwidth memory (HBM) to overcome the memory wall. However, many-core CPUs as well as HBM have many pitfalls that can nullify any performance gain with ease. In this work, we explore the many-core architecture along with HBM for database and data stream query processing. We demonstrate that a hardware-conscious cost model with a calibration approach allows reliable performance prediction of various query operations. Based on that information, we can, therefore, come to an adaptive partitioning and merging strategy for stream query parallelization as well as finding an ideal configuration of parameters for one of the most common tasks in the history of DBMS, join processing. However, not all operations and applications can exploit a many-core processor or HBM, though. Stream queries optimized for low latency and quick individual responses usually do not benefit well from more bandwidth and suffer from penalties like low clock frequencies of many-core CPUs as well. Shared data structures between cores also lead to problems with cache coherence as well as high contention. Based on our insights, we give a rule of thumb which data structures are suitable to parallelize with focus on HBM usage. In addition, different parallelization schemas and synchronization techniques are evaluated, based on the example of a multiway stream join operation

Sketching Algorithms for Sparse Dictionary Learning: PTAS and Turnstile Streaming

Sketching algorithms have recently proven to be a powerful approach both for designing low-space streaming algorithms as well as fast polynomial time approximation schemes (PTAS). In this work, we develop new techniques to extend the applicability of sketching-based approaches to the sparse dictionary learning and the Euclidean $k$-means clustering problems. In particular, we initiate the study of the challenging setting where the dictionary/clustering assignment for each of the $n$ input points must be output, which has surprisingly received little attention in prior work. On the fast algorithms front, we obtain a new approach for designing PTAS's for the $k$-means clustering problem, which generalizes to the first PTAS for the sparse dictionary learning problem. On the streaming algorithms front, we obtain new upper bounds and lower bounds for dictionary learning and $k$-means clustering. In particular, given a design matrix $\mathbf A\in\mathbb R^{n\times d}$ in a turnstile stream, we show an $\tilde O(nr/\epsilon^2 + dk/\epsilon)$ space upper bound for $r$-sparse dictionary learning of size $k$, an $\tilde O(n/\epsilon^2 + dk/\epsilon)$ space upper bound for $k$-means clustering, as well as an $\tilde O(n)$ space upper bound for $k$-means clustering on random order row insertion streams with a natural "bounded sensitivity" assumption. On the lower bounds side, we obtain a general $\tilde\Omega(n/\epsilon + dk/\epsilon)$ lower bound for $k$-means clustering, as well as an $\tilde\Omega(n/\epsilon^2)$ lower bound for algorithms which can estimate the cost of a single fixed set of candidate centers.Comment: To appear in NeurIPS 202

Extending dynamic-programming-based plan generators: beyond pure enumeration

The query optimizer plays an important role in a database management system supporting a declarative query language, such as SQL. One of its central components is the plan generator, which is responsible for determining the optimal join order of a query. Plan generators based on dynamic programming have been known for several decades. However, some significant progress in this field has only been made recently. This includes the emergence of highly efficient enumeration algorithms and the ability to optimize a wide range of queries by supporting complex join predicates. This thesis builds upon the recent advancements by providing a framework for extending the aforementioned algorithms. To this end, a modular design is proposed that allows for the exchange of individual parts of the plan generator, thus enabling the implementor to add new features at will. This is demonstrated by taking the example of two previously unsolved problems, namely the correct and complete reordering of different types of join operators as well as the efficient reordering of join operators and grouping operators

Artificial Intelligence for the design of symmetric cryptographic primitives

Algorithms and the Foundations of Software technolog

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

28th Annual Symposium on Combinatorial Pattern Matching : CPM 2017, July 4-6, 2017, Warsaw, Poland

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