arXiv subjects

Wolfgang Gatterbauer

Publications and source records attributed to Wolfgang Gatterbauer.

At least 19 recordsLinked to original sources

arXiv2026

An Extended Tutorial and Vocabulary for Relational Language Design in an Era of AI-Assisted Query Generation

Relational query languages have been studied and used for more than 50 years, with SQL dominant in practice. Today, queries are increasingly generated by machines and read by humans. At the same time, the landscape also includes dataframe, pipeline, logical, functional, graph, and relational programming notations. These developments invite two related questions beyond expressive power: which relational structures do languages make explicit, and how well can notation support users in reading and revising queries? This 3-hour tutorial extends an earlier SIGMOD'26 tutorial in three directions: recursive and path queries (connecting relational and graph query languages), nested relational data, and relational languages for problems beyond PTIME. Rather than beginning from formal definitions, we start from example queries and compare how different languages express the same intent. To compare recurring structure across notations, we use Abstract Relational Calculus (ARC) and Relational Diagrams as reference representations. From these examples, we develop a vocabulary for relational language design, including information need, query mapping, relational pattern structure, relational pattern denotation, and semantic conventions. Participants will leave with a framework for comparing existing and future relational languages, a precise vocabulary for articulating design trade-offs, and a concrete set of examples connecting classical database languages with alternative proposals.

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arXiv2026

How to Train Your Filter: Should You Learn, Stack or Adapt?

Filters are ubiquitous in computer science, enabling space-efficient approximate membership testing. Since Bloom filters were introduced in 1970, decades of work improved their space efficiency and performance. Recently, three new paradigms have emerged offering orders-of-magnitude improvements in false positive rates (FPRs) by using information beyond the input set: (1) learned filters train a model to distinguish (non)members, (2) stacked filters use negative workload samples to build cascading layers, and (3) adaptive filters update internal representation in response to false positive feedback. Yet each paradigm targets specific use cases, introduces complex configuration tuning, and has been evaluated in isolation. This results in unclear trade-offs and a gap in understanding how these approaches compare and when each is most appropriate. This paper presents the first comprehensive evaluation of learned, stacked, and adaptive filters across real-world datasets and query workloads. Our results reveal critical trade-offs: (1) Learned filters achieve up to 10^2 times lower FPRs but exhibit high variance and lack robustness under skewed or dynamic workloads. Critically, model inference overhead leads to up to 10^4 times slower query latencies than stacked or adaptive filters. (2) Stacked filters reliably achieve up to 10^3 times lower FPRs on skewed workloads but require workload knowledge. (3) Adaptive filters are robust across settings, achieving up to 10^3 times lower FPRs under adversarial queries without workload assumptions. Based on our analysis, learned filters suit stable workloads where input features enable effective model training and space constraints are paramount, stacked filters excel when reliable query distributions are known, and adaptive filters are most generalizable, providing robust theoretically bound guarantees even in dynamic or adversarial environments.

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arXiv2026

Database Views as Explanations for Relational Deep Learning

In recent years, there has been significant progress in the development of deep learning models over relational databases, including architectures based on heterogeneous graph neural networks (hetero-GNNs) and heterogeneous graph transformers. In effect, such architectures state how the database records and links (e.g., foreign-key references) translate into a large, complex numerical expression, involving numerous learnable parameters. This complexity makes it hard to explain, in human-understandable terms, how a model uses the available data to arrive at a given prediction. We present a novel framework for explaining machine-learning models over relational databases, where explanations are view definitions that highlight focused parts of the database that mostly contribute to the model's prediction. We establish such global abductive explanations by adapting the classic notion of determinacy by Nash, Segoufin, and Vianu (2010). In addition to tuning the tradeoff between determinacy and conciseness, the framework allows controlling the level of granularity by adopting different fragments of view definitions, such as ones highlighting whole columns, foreign keys between tables, relevant groups of tuples, and so on. We investigate the realization of the framework in the case of hetero-GNNs, and develop a model-specific approach via the notion of learnable masks. For comparison, we propose model-agnostic heuristic baselines and show that our approach is both more efficient and achieves better explanation quality in most cases. Our extensive empirical evaluation on the RelBench collection across diverse domains and record-level tasks demonstrates both the usefulness of our explanations and the efficiency of their generation.

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arXiv2026

The Importance of Parameters in Ranking Functions

How important is the weight of a given column in determining the ranking of tuples in a table? To address such an explanation question about a ranking function, we investigate the computation of SHAP scores for column weights, adopting a recent framework by Grohe et al.[ICDT'24]. The exact definition of this score depends on three key components: (1) the ranking function in use, (2) an effect function that quantifies the impact of using alternative weights on the ranking, and (3) an underlying weight distribution. We analyze the computational complexity of different instantiations of this framework for a range of fundamental ranking and effect functions, focusing on probabilistically independent finite distributions for individual columns. For the ranking functions, we examine lexicographic orders and score-based orders defined by the summation, minimum, and maximum functions. For the effect functions, we consider global, top-k, and local perspectives: global measures quantify the divergence between the perturbed and original rankings, top-k measures inspect the change in the set of top-k answers, and local measures capture the impact on an individual tuple of interest. Although all cases admit an additive fully polynomial-time randomized approximation scheme (FPRAS), we establish the complexity of exact computation, identifying which cases are solvable in polynomial time and which are #P-hard. We further show that all complexity results, lower bounds and upper bounds, extend to a related task of computing the Shapley value of whole columns (regardless of their weight).

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arXiv2025

Database Research needs an Abstract Relational Query Language

For decades, SQL has been the default language for composing queries, but it is increasingly used as an artifact to be read and verified rather than authored. With Large Language Models (LLMs), queries are increasingly machine-generated, while humans read, validate, and debug them. This shift turns relational query languages into interfaces for back-and-forth communication about intent, which will lead to a rethinking of relational language design, and more broadly, relational interface design. We argue that this rethinking needs support from an Abstract Relational Query Language (ARQL): a semantics-first reference metalanguage that separates query intent from user-facing syntax and makes underlying relational patterns explicit and comparable across user-facing languages. An ARQL separates a query into (i) a relational core (the compositional structure that determines intent), (ii) modalities (alternative representations of that core tailored to different audiences), and (iii) conventions (orthogonal environment-level semantic parameters under which the core is interpreted, e.g., set vs. bag semantics, or treatment of null values). Usability for humans or machines then depends less on choosing a particular language and more on choosing an appropriate modality. Comparing languages becomes a question of which relational patterns they support and what conventions they choose. We introduce Abstract Relational Calculus (ARC), a strict generalization of Tuple Relational Calculus (TRC), as a concrete instance of ARQL. ARC comes in three modalities: (i) a comprehension-style textual notation, (ii) an Abstract Language Tree (ALT) for machine reasoning about meaning, and (iii) a diagrammatic hierarchical graph (higraph) representation for humans. ARC provides the missing vocabulary and acts as a Rosetta Stone for relational querying.

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arXiv2025

Resilience for Regular Path Queries: Towards a Complexity Classification

The resilience problem for a query and an input set or bag database is to compute the minimum number of facts to remove from the database to make the query false. In this paper, we study how to compute the resilience of Regular Path Queries (RPQs) over graph databases. Our goal is to characterize the regular languages L for which it is tractable to compute the resilience of the existentially-quantified RPQ built from L. We show that computing the resilience in this sense is tractable (even in combined complexity) for all RPQs defined from so-called local languages. By contrast, we show hardness in data complexity for RPQs defined from the following language classes (after reducing the languages to eliminate redundant words): all finite languages featuring a word containing a repeated letter, and all languages featuring a specific kind of counterexample to being local (which we call four-legged languages). The latter include in particular all languages that are not star-free. Our results also imply hardness for all non-local languages with a so-called neutral letter. We last show tractability for some classes of non-local languages, namely the so-called bipartite chain languages and one-dangling languages, and highlight some remaining obstacles towards a full dichotomy.

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arXiv2025

Is Integer Linear Programming All You Need for Deletion Propagation? A Unified and Practical Approach for Generalized Deletion Propagation

Deletion Propagation (DP) refers to a family of database problems rooted in the classical view-update problem: how to propagate intended deletions in a view (query output) back to the source database while satisfying constraints and minimizing side effects. Although studied for over 40 years, DP variants, their complexities, and practical algorithms have been typically explored in isolation. This work presents a unified and generalized framework for DP with several key benefits: (1) It unifies and generalizes all previously known DP variants, effectively subsuming them within a broader class of problems, including new, well-motivated variants. (2) It comes with a practical and general-purpose algorithm that is ``coarse-grained instance-optimal'': it runs in PTIME for all known PTIME cases and can automatically exploit structural regularities in the data, i.e. it does not rely on hints about such regularities as part of the input. (3) It is complete: our framework handles all known DP variants in all settings (including those involving self-joins, unions, and bag semantics), and allows us to provide new complexity results. (4) It is easy to implement and, in many cases, outperforms prior variant-specific solutions, sometimes by orders of magnitude. We provide the first experimental results for several DP variants previously studied only in theory.

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arXiv2025

Ranked Enumeration for Database Queries

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. In addition to their practical usefulness, these techniques complement a long line of theoretical research on unranked enumeration, where answers are also returned incrementally, but with no explicit ordering requirement. For a broad class of ranking functions with certain monotonicity properties, including lexicographic orders and sum-based rankings, the ordering requirement surprisingly does not increase the asymptotic time or space complexity, apart from logarithmic factors. A key insight is the connection between ranked enumeration for database queries and the fundamental task of computing the kth-shortest path in a graph. Although this connection is important for grounding the problem in the literature, it can obfuscate the simplicity of the algorithm. In this article, we adopt a pragmatic approach and present a slightly simplified version of the algorithm without the shortest-path interpretation. We believe that this will benefit practitioners looking to implement and optimize any-k approaches.

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arXiv2024

A Principled Solution to the Disjunction Problem of Diagrammatic Query Representations

Finding unambiguous diagrammatic representations for first-order logical formulas and relational queries with arbitrarily nested disjunctions has been a surprisingly long-standing unsolved problem. We refer to this problem as the disjunction problem (of diagrammatic query representations). This work solves the disjunction problem. Our solution unifies, generalizes, and overcomes the shortcomings of prior approaches for disjunctions. It extends the recently proposed Relational Diagrams and is identical for disjunction-free queries. However, it can preserve the relational patterns and the safety for all well-formed Tuple Relational Calculus (TRC) queries, even with arbitrary disjunctions. Additionally, its size is proportional to the original TRC query and can thus be exponentially more succinct than Relational Diagrams.

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arXiv2024

Towards Agentic Schema Refinement

Large enterprise databases can be complex and messy, obscuring the data semantics needed for analytical tasks. We propose a semantic layer in-between the database and the user as a set of small and easy-to-interpret database views, effectively acting as a refined version of the schema. To discover these views, we introduce a multi-agent Large Language Model (LLM) simulation where LLM agents collaborate to iteratively define and refine views with minimal input. Our approach paves the way for LLM-powered exploration of unwieldy databases.

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arXiv2024

Minimally Factorizing the Provenance of Self-join Free Conjunctive Queries

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 $Σ^p_2$-complete, we show that the problem is NP-C in our case. Additionally, we identify a large category 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.

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arXiv2024

A Comprehensive Tutorial on over 100 Years of Diagrammatic Representations of Logical Statements and Relational Queries

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 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 key visual metaphors developed for diagrammatic representations of logical statements and relational expressions, across both the relational database and the much older diagrammatic reasoning communities. We 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 investigations into diagrammatic languages, and organize the landscape by mapping the visual alphabets of diagrammatic representation systems to the syntax and semantics of Relational Algebra (RA) and Relational Calculus (RC). Tutorial website: https://northeastern-datalab.github.io/diagrammatic-representation-tutorial/

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arXiv2024

On The Reasonable Effectiveness of Relational Diagrams: Explaining Relational Query Patterns and the Pattern Expressiveness of Relational Languages

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.

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arXiv2023

HITSnDIFFs: From Truth Discovery to Ability Discovery by Recovering Matrices with the Consecutive Ones Property

We analyze a general problem in a crowd-sourced setting where one user asks a question (also called item) and other users return answers (also called labels) for this question. Different from existing crowd sourcing work which focuses on finding the most appropriate label for the question (the "truth"), our problem is to determine a ranking of the users based on their ability to answer questions. We call this problem "ability discovery" to emphasize the connection to and duality with the more well-studied problem of "truth discovery". To model items and their labels in a principled way, we draw upon Item Response Theory (IRT) which is the widely accepted theory behind standardized tests such as SAT and GRE. We start from an idealized setting where the relative performance of users is consistent across items and better users choose better fitting labels for each item. We posit that a principled algorithmic solution to our more general problem should solve this ideal setting correctly and observe that the response matrices in this setting obey the Consecutive Ones Property (C1P). While C1P is well understood algorithmically with various discrete algorithms, we devise a novel variant of the HITS algorithm which we call "HITSNDIFFS" (or HND), and prove that it can recover the ideal C1P-permutation in case it exists. Unlike fast combinatorial algorithms for finding the consecutive ones permutation (if it exists), HND also returns an ordering when such a permutation does not exist. Thus it provides a principled heuristic for our problem that is guaranteed to return the correct answer in the ideal setting. Our experiments show that HND produces user rankings with robustly high accuracy compared to state-of-the-art truth discovery methods. We also show that our novel variant of HITS scales better in the number of users than ABH, the only prior spectral C1P reconstruction algorithm.

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arXiv2023

A Unified Approach for Resilience and Causal Responsibility with Integer Linear Programming (ILP) and LP Relaxations

Resilience is one of the key algorithmic problems underlying various forms of reverse data management (such as view maintenance, deletion propagation, and various interventions for fairness): What is the minimal number of tuples to delete from a database in order to remove all answers from a query? A long-open question is determining those conjunctive queries (CQs) for which this problem can be solved in guaranteed PTIME. We shed new light on this and the related problem of causal responsibility by proposing a unified Integer Linear Programming (ILP) formulation. It is unified in that it can solve both prior studied restrictions (e.g., self-join-free CQs under set semantics that allow a PTIME solution) and new cases (e.g., all CQs under set or bag semantics It is also unified in that all queries and all instances are treated with the same approach, and the algorithm is guaranteed to terminate in PTIME for the easy cases. We prove that, for all easy self-join-free CQs, the Linear Programming (LP) relaxation of our encoding is identical to the ILP solution and thus standard ILP solvers are guaranteed to return the solution in PTIME. Our approach opens up the door to new variants and new fine-grained analysis: 1) It also works under bag semantics and we give the first dichotomy result for bags semantics in the problem space. 2) We give a more fine-grained analysis of the complexity of causal responsibility. 3) We recover easy instances for generally hard queries, such as instances with read-once provenance and instances that become easy because of Functional Dependencies in the data. 4) We solve an open conjecture from PODS 2020. 5) Experiments confirm that our results indeed predict the asymptotic running times, and that our universal ILP encoding is at times even faster to solve for the PTIME cases than a prior proposed dedicated flow algorithm.

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arXiv2023

Any-k Algorithms for Enumerating Ranked Answers to Conjunctive Queries

We study ranked enumeration for Conjunctive Queries (CQs) where the answers are ordered by a given ranking function (e.g., an ORDER BY clause in SQL). We develop "any-k" algorithms, which, without knowing the number k of desired answers, push down the ranking into joins by carefully ordering the computation of intermediate tuples and avoiding materialization of join answers until they are needed. For this to be possible, the ranking function needs to obey a particular type of monotonicity. Supported ranking functions include the common sum-of-weights, where answers are compared by the sum of input-tuple weights, as well as any commutative selective dioid. Our results extend a well-known unranked-enumeration dichotomy, which states that only free-connex CQs are tractable (under certain hardness hypotheses and for CQs without self-joins). For this class of queries and with n denoting the size of the input, the data complexity of our ranked enumeration approach for the time to the kth CQ answer is O(n+klogk), which is only a logarithmic factor slower than the O(n+k) unranked-enumeration guarantee. A core insight of our work is that ranked enumeration for CQs is closely related to Dynamic Programming and the fundamental task of path enumeration in a weighted DAG. We uncover a previously unknown tradeoff: one any-k algorithm has lower complexity when the number of returned answers is small, the other when their number is large. This tradeoff is eliminated under a stricter monotonicity property that we define and exploit for a novel algorithm that asymptotically dominates all previously known alternatives, including Eppstein's algorithm for sum-of-weights path enumeration. We empirically demonstrate the findings of our theoretical analysis in an experimental study that highlights the superiority of our approach over the join-then-rank approach that existing database systems follow.

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arXiv2023

A Tutorial on Visual Representations of Relational Queries

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 key visual 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).

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arXiv2023

Towards Unbiased Exploration in Partial Label Learning

We consider learning a probabilistic classifier from partially-labelled supervision (inputs denoted with multiple possibilities) using standard neural architectures with a softmax as the final layer. We identify a bias phenomenon that can arise from the softmax layer in even simple architectures that prevents proper exploration of alternative options, making the dynamics of gradient descent overly sensitive to initialisation. We introduce a novel loss function that allows for unbiased exploration within the space of alternative outputs. We give a theoretical justification for our loss function, and provide an extensive evaluation of its impact on synthetic data, on standard partially labelled benchmarks and on a contributed novel benchmark related to an existing rule learning challenge.

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