From the Publisher: 
For this inexpensive paperback edition of a groundbreaking classic, the author has extensively rearranged, rewritten and enlarged the material. Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation Classical Theory; Fourier ApproximationModern Therory; Exponential Approximation.

Numerical Methods for Scientists and Engineers

In recent years, there has been tremendous interest in research that applies machine learning to database systems. Being one of the most complex components of a DBMS, query optimizers could benefit from adaptive policies that are learned systematically from the data and the query workload. Recent research has brought up novel ideas towards a learned query optimizer, however these ideas have not been evaluated on a commercial query processor or on large scale, real-world workloads. In this paper, we take the approach used by Marcus et al. in Bao and adapt it to SCOPE, a big data system used internally at Microsoft. Along the way, we solve multiple new challenges: we define how optimizer rules affect final query plans by introducing the concept of a rule signature, we devise a pipeline computing interesting rule configurations for recurring jobs, and we define a new learning problem allowing us to apply such interesting rule configurations to previously unseen jobs. We evaluate the efficacy of the approach on production workloads that include 150K daily jobs. Our results show that alternative rule configurations can generate plans with lower costs, and this can translate to runtime latency savings of 7-30% on average and up to 90% for a non trivial subset of the workload.

https://dl.acm.org/doi/pdf/10.1145/3448016.3457568

Steering Query Optimizers: A Practical Take on Big Data Workloads

This work deals with redesigning business process models, e.g., in BPMN, based on cost-based optimization techniques that were initially proposed for data analytics workflows. More specifically, it discusses execution cost and cycle time improvements through treating business processes in the same way as data-centric workflows. The presented solutions are cost-based, i.e., they employ quantitative metadata and cost models. The advantage of this approach is that business processes can benefit from recent advances in data-intensive workflow optimization similarly to the manner they nowadays benefit from additional data analytics areas, e.g., in the area of process mining. Concrete use cases are presented that are capable of demonstrating that even in small, more conservative cases, the benefits are significant. The contribution of this work is to show how to automatically optimize the model structure of a given process in terms of the ordering of tasks and how to perform resource allocation under contradicting objectives. Finally, the work identifies open issues in developing end-to-end business process redesign solutions with regards to the case studies considered.

On Knowledge Transfer from Cost-Based Optimization of Data-Centric Workflows to Business Process Redesign

Client-side SPARQL query processing enables evaluating queries over RDF datasets published on the Web without producing high loads on the data providers’ servers. Triple Pattern Fragment (TPF) servers provide means to publish highly available RDF data on the Web and clients to evaluate SPARQL queries over them have been proposed. For clients to devise efficient query plans that minimize both the number of requests submitted to the server as well as the overall execution time, it is key to accurately estimate join cardinalities to appropriately place physical join operators. However, collecting accurate and fine-grained statistics from remote sources is a challenging task, and clients typically rely on the metadata provided by the TPF server. Addressing this shortcoming, we propose CROP, a cost- and robust-based query optimizer to devise efficient plans combining both cost and robustness of query plans. The idea of robustness is determining the impact of join cardinality estimation errors on the cost of a query plan and to avoid plans where this impact is very high. In our experimental study, we show that our concept of robustness complements the cost model and improves the efficiency of query plans. Additionally, we show that our approach outperforms existing TPF clients in terms of overall runtime and number of requests.

Cost- and Robustness-Based Query Optimization for Linked Data Fragments

Robust query processing with strong performance guarantees is an extremely desirable objective in the design of industrial-strength database engines. However, it has proved to be a largely intractable and elusive challenge in spite of sustained efforts spanning several decades. The good news is that in recent times, there have been a host of exciting technical advances, at different levels in the database architecture, that collectively promise to materially address this problem. In this tutorial, we will present these novel research approaches, characterize their strengths and limitations, and enumerate open technical problems that remain to be solved to make robust query processing a contemporary reality.

/pdf/robust-query-processing-mission-possible-1qrghxc207.pdf

Robust query processing: mission possible

The quality of query execution plans in database systems determines how fast a query can be executed. It has been shown that conventional query optimization still selects sub-optimal or even bad execution plans, due to errors in the cardinality estimation. Although cardinality estimation errors are an evident problem, they are in general not considered in the selection of query execution plans. In this paper, we present three novel metrics for the robustness of relational query execution plans w.r.t. cardinality estimation errors. We also present a novel plan selection strategy that takes both, estimated cost and estimated robustness into account, when choosing a plan for execution. Finally, we share the results of our experimental comparison between robust and conventional plan selection on real world and synthetic benchmarks, showing a speedup of at most factor 3.49.

/pdf/robustness-metrics-for-relational-query-execution-plans-50end8sfia.pdf

Robustness metrics for relational query execution plans

Enterprises increasingly move their databases into the cloud. As a result, database-as-a-service providers are challenged to meet the performance guarantees assured in service-level agreements (SLAs) while keeping hardware costs as low as possible. Being cost-effective is particularly crucial for cloud databases where the provisioned amount of DRAM dominates the hardware costs. A way to decrease the memory footprint is to leverage access skew in the workload by moving rarely accessed cold data to cheaper storage layers and retaining only frequently accessed hot data in main memory. In this paper, we present SAHARA, an advisor that proposes a table partitioning for column stores with minimal memory footprint while still adhering to all performance SLAs. SAHARA collects lightweight workload statistics, classifies data as hot and cold, and calculates optimal or near-optimal range partitioning layouts with low optimization time using a novel cost model. We integrated SAHARA into a commercial cloud database and show in our experiments for real-world and synthetic benchmarks a memory footprint reduction of 2.5 × while still fulfilling all performance SLAs provided by the customer or advertised by the DBaaS provider.

SAHARA: Memory Footprint Reduction of Cloud Databases with Automated Table Partitioning

Precise, Compact, and Fast Data Access Counters for Automated Physical Database Design.

Memory Footprint Reduction of Cloud Databases with Automated Physical Database Design

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Robustness metrics for relational query execution plans

SAHARA: Memory Footprint Reduction of Cloud Databases with Automated Table Partitioning

Precise, Compact, and Fast Data Access Counters for Automated Physical Database Design.

Memory Footprint Reduction of Cloud Databases with Automated Physical Database Design