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Repairing Databases over Metric Spaces with Coincidence Constraints

Authors Youri Kaminsky , Benny Kimelfeld , Ester Livshits , Felix Naumann , David Wajc

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Author Details

Youri Kaminsky
  • Hasso Plattner Institute, University of Potsdam, Germany
Benny Kimelfeld
  • Technion, Haifa, Israel
Ester Livshits
  • Technion, Haifa, Israel
Felix Naumann
  • Hasso Plattner Institute, University of Potsdam, Germany
David Wajc
  • Technion, Haifa, Israel

Funding

  • Kimelfeld, Benny: Israel Science Foundation grant 768/19, German Research Foundation grant KI 2348/1-1.
  • Wajc, David: Taub Family Foundation "Leader in Science and Technology" fellowship, Israel Science Foundation grant 3200/24.

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Youri Kaminsky, Benny Kimelfeld, Ester Livshits, Felix Naumann, and David Wajc. Repairing Databases over Metric Spaces with Coincidence Constraints. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICDT.2025.14

Abstract

Datasets often contain values that naturally reside in a metric space: numbers, strings, geographical locations, machine-learned embeddings in a vector space, and so on. We study the computational complexity of repairing inconsistent databases that violate integrity constraints, where the database values belong to an underlying metric space. The goal is to update the database values to retain consistency while minimizing the total distance between the original values and the repaired ones. We consider what we refer to as coincidence constraints, which include unary key constraints, inclusion constraints, foreign keys, and generally any restriction on the relationship between the numbers of cells of different labels (attributes) coinciding in a single value, for a fixed attribute set. 

We begin by showing that the problem is APX-hard for general metric spaces. We then present an algorithm solving the problem optimally for tree metrics, which generalize both the line metric (i.e., where repaired values are numbers) and the discrete metric (i.e., where we simply count the number of changed values). Combining our algorithm for tree metrics and a classic result on probabilistic tree embeddings, we design a (high probability) logarithmic-ratio approximation for general metrics. We also study the variant of the problem where we limit the allowed change of each individual value. In this variant, it is already NP-complete to decide the existence of any legal repair for a general metric, and we present a polynomial-time repairing algorithm for the case of a line metric.

Subject Classification

ACM Subject Classification
  • Information systems → Data management systems
Keywords
  • Database repairs
  • metric spaces
  • coincidence constraints
  • inclusion constraints
  • foreign-key constraints

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