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Ranked enumeration is a query-answering paradigm where the query answers are returned incrementally in order of importance (instead of returning all answers at once). Importance is defined by a ranking function that can be specific to the application, but typically involves either a lexicographic order (e.g., ORDER BY R.A, S.B in SQL) or a weighted sum of attributes (e.g., ORDER BY 3*R.A + 2*S.B). Recent work has introduced any-k algorithms for (multi-way) join queries, which push ranking into joins and avoid materializing intermediate results until necessary. The top-ranked answers are returned asymptotically faster than the common join-then-rank approach of database systems, resulting in orders-of-magnitude speedup in practice. 

We consider the problem of finding the minimal-size factorization of the provenance of self-join-free conjunctive queries, i.e.,we want to find a formula that minimizes the number of variable repetitions. This problem is equivalent to solving the fundamental Boolean formula factorization problem for the restricted setting of the provenance formulas of self-join free queries. While general Boolean formula minimization is Σ^p₂-complete, we show that the problem is NP-Complete in our case. Additionally, we identify a large class of queries that can be solved in PTIME, expanding beyond the previously known tractable cases of read-once formulas and hierarchical queries.

We describe connections between factorizations, Variable Elimination Orders (VEOs), and minimal query plans. We leverage these insights to create an Integer Linear Program (ILP) that can solve the minimal factorization problem exactly. We also propose a Max-Flow Min-Cut (MFMC) based algorithm that gives an efficient approximate solution. Importantly, we show that both the Linear Programming (LP) relaxation of our ILP, and our MFMC-based algorithm are always correct for all currently known PTIME cases. Thus, we present two unified algorithms (ILP and MFMC) that can both recover all known PTIME cases in PTIME, yet also solve NP-Complete cases either exactly (ILP) or approximately (MFMC), as desired.

 

Comparing relational languages by their logical expressiveness is well understood. Less well understood is how to compare relational languages by their ability to represent relational query patterns. Indeed, what are query patterns other than a certain way of writing a query? And how can query patterns be defined across procedural and declarative languages, irrespective of their syntax? To the best of our knowledge, we provide the first semantic definition of relational query patterns by using a variant of structure-preserving mappings between the relational tables of queries. This formalism allows us to analyze the relative pattern expressiveness of relational language fragments and create a hierarchy of languages with equal logical expressiveness yet different pattern expressiveness. Notably, for the non-disjunctive language fragment, we show that relational calculus can express a larger class of patterns than the basic operators of relational algebra. Our language-independent definition of query patterns opens novel paths for assisting database users. For example, these patterns could be leveraged to create visual query representations that faithfully represent query patterns, speed up interpretation, and provide visual feedback during query editing. As a concrete example, we propose Relational Diagrams, a complete and sound diagrammatic representation of safe relational calculus that is provably (i) unambiguous, (ii) relationally complete, and (iii) able to represent all query patterns for unions of non-disjunctive queries. Among all diagrammatic representations for relational queries that we are aware of, ours is the only one with these three properties. Furthermore, our anonymously preregistered user study shows that Relational Diagrams allow users to recognize patterns meaningfully faster and more accurately than SQL. 

What is a minimal set of tuples to delete from a database in order to eliminate all query answers? This problem is called the resilience of a query and is one of the key algorithmic problems underlying various forms of reverse data management, such as view maintenance, deletion propagation and causal responsibility. A long-open question is determining the conjunctive queries (CQs) for which resilience can be solved in PTIME.

We shed new light on this problem by proposing a unified Integer Linear Programming (ILP) formulation. It is unified in that it can solve both previously studied restrictions (e.g., self-join-free CQs under set semantics that allow a PTIME solution) and new cases (all CQs under set or bag semantics). It is also unified in that all queries and all database instances are treated with the same approach, yet the algorithm is guaranteed to terminate in PTIME for all known PTIME cases. In particular, we prove that for all known easy cases, the optimal solution to our ILP is identical to a simpler Linear Programming (LP) relaxation, which implies that standard ILP solvers return the optimal solution to the original ILP in PTIME.

Our approach allows us to explore new variants and obtain new complexity results. 1) It works under bag semantics, for which we give the first dichotomy results in the problem space. 2) We extend our approach to the related problem of causal responsibility and give a more fine-grained analysis of its complexity. 3) We recover easy instances for generally hard queries, including instances with read-once provenance and instances that become easy because of Functional Dependencies in the data. 4) We solve an open conjecture about a unified hardness criterion from PODS 2020 and prove the hardness of several queries of previously unknown complexity. 5) Experiments confirm that our findings accurately predict the asymptotic running times, and that our universal ILP is at times even quicker than a previously proposed dedicated flow algorithm.

 

Query formulation is increasingly performed by systems that need to guess a user's intent (e.g. via spoken word interfaces). But how can a user know that the computational agent is returning answers to the right query? More generally, given that relational queries can become pretty complicated,how can we help users understand existing relational queries, whether human-generated or automatically generated? Now seems the right moment to revisit a topic that predates the birth of the relational model: developing visual metaphors that help users understand relational queries.

This lecture-style tutorial surveys the keyvisual metaphors developed for visual representations of relational expressions.We will survey the history and state-of-the art of relationally-complete diagrammatic representations of relational queries, discuss the key visual metaphors developed in over a century of investigating diagrammatic languages, and organize the landscape by mapping their used visual alphabets to the syntax and semantics of Relational Algebra (RA) and Relational Calculus (RC).

 

Modern data lakes are heterogeneous in the vocabulary that is used to describe data. We study a problem of disambiguation in data lakes:How can we determine if a data value occurring more than once in the lake has different meanings and is therefore a homograph?While word and entity disambiguation have been well studied in computational linguistics, data management, and data science, we show that data lakes provide a new opportunity for disambiguation of data values, because tables implicitly define a massive network of interconnected values. We introduceDomainNet, which efficiently represents this network, and investigate to what extent it can be used to disambiguate values without requiring any supervision.

DomainNetleverages network-centrality measures on a bipartite graph whose nodes represent data values and attributes to determine if a value is a homograph. A thorough experimental evaluation demonstrates that state-of-the-art techniques in domain discovery cannot be re-purposed to compete with our method. Specifically, using a domain discovery method to identify homographs achieves an F1-score of 0.38 versus 0.69 forDomainNet, which separates homographs well from data values that have a unique meaning. On a real data lake, our top-100 precision is 93%. Given a homograph, we also present a novel method for determining the number of meanings of the homograph and for assigning its data lake attributes to a meaning. We show the influence of homographs on two downstream tasks: entity-matching and domain discovery.

 

We study the question of when we can provide direct access to the k-th answer to a Conjunctive Query (CQ) according to a specified order over the answers in time logarithmic in the size of the database, following a preprocessing step that constructs a data structure in time quasilinear in database size. Specifically, we embark on the challenge of identifying the tractable answer orderings , that is, those orders that allow for such complexity guarantees. To better understand the computational challenge at hand, we also investigate the more modest task of providing access to only a single answer (i.e., finding the answer at a given position), a task that we refer to as the selection problem , and ask when it can be performed in quasilinear time. We also explore the question of when selection is indeed easier than ranked direct access. We begin with lexicographic orders . For each of the two problems, we give a decidable characterization (under conventional complexity assumptions) of the class of tractable lexicographic orders for every CQ without self-joins. We then continue to the more general orders by the sum of attribute weights and establish the corresponding decidable characterizations, for each of the two problems, of the tractable CQs without self-joins. Finally, we explore the question of when the satisfaction of Functional Dependencies (FDs) can be utilized for tractability and establish the corresponding generalizations of our characterizations for every set of unary FDs.