arXiv subjects

Albert Kim

Publications and source records attributed to Albert Kim.

8 recordsLinked to original sources

arXiv2024

Optimizing Disjunctive Queries with Tagged Execution

Despite decades of research into query optimization, optimizing queries with disjunctive predicate expressions remains a challenge. Solutions employed by existing systems (if any) are often simplistic and lead to much redundant work being performed by the execution engine. To address these problems, we propose a novel form of query execution called tagged execution. Tagged execution groups tuples into subrelations based on which predicates in the query they satisfy (or don't satisfy) and tags them with that information. These tags then provide additional context for query operators to take advantage of during runtime, allowing them to eliminate much of the redundant work performed by traditional engines and realize predicate pushdown optimizations for disjunctive predicates. However, tagged execution brings its own challenges, and the question of what tags to create is a nontrivial one. Careless creation of tags can lead to an exponential blowup in the tag space, with the overhead outweighing the benefits. To address this issue, we present a technique called tag generalization to minimize the space of tags. We implemented the tagged execution model with tag generalization in our system Basilisk, and our evaluation shows an average 2.7x speedup in runtime over the traditional execution model with up to a 19x speedup in certain situations.

cs.DB↗

arXiv2023

On the proportion of irreducible polynomials in unicritically generated semigroups

Let $p$ be a prime number and let $S=\{x^p+c_1,\dots,x^p+c_r\}$ be a finite set of unicritical polynomials for some $c_1,\dots,c_r\in\mathbb{Z}$. Moreover, assume that $S$ contains at least one irreducible polynomial over $\mathbb{Q}$. Then we construct a large, explicit subset of irreducible polynomials within the semigroup generated by $S$ under composition; in fact, we show that this subset has positive asymptotic density within the full semigroup when we count polynomials by degree. In addition, when $p=2$ or $3$ we construct an infinite family of semigroups that break the local-global principle for irreducibility. To do this, we use a mix of algebraic and arithmetic techniques and results, including Runge's method, the elliptic curve Chabauty method, and Fermat's Last Theorem.

math.NT↗

arXiv2020

Optimizing Query Predicates with Disjunctions for Column-Oriented Engines

Database research has always given limited attention to optimizing predicates with disjunctions. What little past work there is, has mostly focused on optimizations for traditional row-oriented databases. However, a key difference between how row-oriented and column-oriented engines evaluate predicates is that while row-oriented engines apply predicates to a single tuple at a time, column-oriented engines apply predicates to sets of tuples, adding another dimension to the problem. As such, row-oriented engines focus only on the best order to apply predicates in to "short-circuit" the overall predicate expression, but column-oriented engines must additionally decide on the input sets of tuples for each predicate application. This is important, since smaller inputs lead to faster runtimes, and nontrivial, since the results of earlier predicates can be used to reduce the inputs to later predicates and predicates may be combined via disjunctions in the predicate expression. In this work, we formally analyze the predicate evaluation problem for column-oriented engines and present BestD/Update, the first ever polynomial-time, provably optimal algorithms to deduce the minimum input sets for each predicate application. BestD/Update's optimality is guaranteed under a wide range of cost models, representing different real-world scenarios. Furthermore, when combined with the predicate ordering algorithm Hanani, BestD/Update reduce into EvalPred, a simple O(n log^2 n) algorithm, which we recommend for practical use and optimal for all predicate expressions of nested depth 2 or less. Our evaluation shows, thanks to its optimality and polynomial planning time, EvalPred outperforms not implementing any disjunction optimizations and exiting optimal algorithms by up to 2.6x and 28x respectively for synthetic workloads and by up to 1.3x and 100x respectively for queries from TPC-H and the CH-benchmark.

cs.DB↗

arXiv2017

SilkMoth: An Efficient Method for Finding Related Sets with Maximum Matching Constraints

Determining if two sets are related - that is, if they have similar values or if one set contains the other - is an important problem with many applications in data cleaning, data integration, and information retrieval. A particularly popular metric that has been proposed is to measure the relatedness of two sets by treating the elements as vertices of a bipartite graph and calculating the score of the maximum matching pairing between elements. Compared to other metrics which require exact matchings between elements, this metric uses a similarity function to compare elements between the two sets, making it robust to small dissimilarities in elements and more useful for real-world, dirty data. Unfortunately, the metric suffers from expensive computational cost, taking O(n^3) time, where n is the number of elements in sets, for each set-to-set comparison. Thus for applications which try to search for all pairings of related sets in a brute-force manner, the runtime becomes unacceptably large. To address this challenge, we developed SilkMoth, a system capable of rapidly discovering related set pairs in collections of sets. Internally, SilkMoth creates a signature for each set, with the property that any other set which is related must match the signature. SilkMoth then uses these signatures to prune the search space, so only sets which match the signatures are left as candidates. Finally, SilkMoth applies the maximum matching metric on remaining candidates to verify which of these candidates are truly related sets. Thus, a contribution of this paper is the characterization of the space of signatures which enable this property. We show that selecting the optimal signature in this space is NP-complete, and based on insights from the characterization of the space, we propose two novel filters which help to prune the candidates further before verification.

cs.DB↗

arXiv2016

Optimally Leveraging Density and Locality to Support LIMIT Queries

Existing database systems are not optimized for queries with a LIMIT clause---operating instead in an all-or-nothing manner. In this paper, we propose a fast LIMIT query evaluation engine, called NeedleTail, aimed at letting analysts browse a small sample of the query results on large datasets as quickly as possible, independent of the overall size of the result set. NeedleTail introduces density maps, a lightweight in-memory indexing structure, and a set of efficient algorithms (with desirable theoretical guarantees) to quickly locate promising blocks, trading off locality and density. In settings where the samples are used to compute aggregates, we extend techniques from survey sampling to mitigate the bias in our samples. Our experimental results demonstrate that NeedleTail returns results 4x faster on HDDs and 9x faster on SSDs on average, while occupying up to 23x less memory than existing techniques.

cs.DB↗

arXiv2016

Effortless Data Exploration with zenvisage: An Expressive and Interactive Visual Analytics System

Data visualization is by far the most commonly used mechanism to explore data, especially by novice data analysts and data scientists. And yet, current visual analytics tools are rather limited in their ability to guide data scientists to interesting or desired visualizations: the process of visual data exploration remains cumbersome and time-consuming. We propose zenvisage, a platform for effortlessly visualizing interesting patterns, trends, or insights from large datasets. We describe zenvisage's general purpose visual query language, ZQL ("zee-quel") for specifying the desired visual trend, pattern, or insight - ZQL draws from use-cases in a variety of domains, including biology, mechanical engineering, climate science, and commerce. We formalize the expressiveness of ZQL via a visual exploration algebra, and demonstrate that ZQL is at least as expressive as that algebra. While analysts are free to use ZQL directly, we also expose ZQL via a visual specification interface that we describe in this paper. We then describe our architecture and optimizations, preliminary experiments in supporting and optimizing for ZQL queries in our initial zenvisage prototype, and a user study to evaluate whether data scientists are able to effectively use zenvisage for real applications.

cs.DB↗

arXiv2014

Rapid Sampling for Visualizations with Ordering Guarantees

Visualizations are frequently used as a means to understand trends and gather insights from datasets, but often take a long time to generate. In this paper, we focus on the problem of rapidly generating approximate visualizations while preserving crucial visual proper- ties of interest to analysts. Our primary focus will be on sampling algorithms that preserve the visual property of ordering; our techniques will also apply to some other visual properties. For instance, our algorithms can be used to generate an approximate visualization of a bar chart very rapidly, where the comparisons between any two bars are correct. We formally show that our sampling algorithms are generally applicable and provably optimal in theory, in that they do not take more samples than necessary to generate the visualizations with ordering guarantees. They also work well in practice, correctly ordering output groups while taking orders of magnitude fewer samples and much less time than conventional sampling schemes.

cs.DB↗

arXiv1994

Graded Unification: A Framework for Interactive Processing

An extension to classical unification, called {\em graded unification} is presented. It is capable of combining contradictory information. An interactive processing paradigm and parser based on this new operator are also presented.

cmp-lg↗