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Answering UCQs under Updates and in the Presence of Integrity Constraints

Authors Christoph Berkholz, Jens Keppeler, Nicole Schweikardt

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Christoph Berkholz
Jens Keppeler
Nicole Schweikardt

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Christoph Berkholz, Jens Keppeler, and Nicole Schweikardt. Answering UCQs under Updates and in the Presence of Integrity Constraints. In 21st International Conference on Database Theory (ICDT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 98, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ICDT.2018.8

Abstract

We investigate the query evaluation problem for fixed queries over
fully dynamic databases where tuples can be inserted or deleted.
The task is to design a dynamic data structure that can immediately
report the new result of a fixed query after every database update.
We consider unions of conjunctive queries (UCQs) and focus on the query evaluation tasks testing (decide whether an input tuple belongs to the query result), enumeration (enumerate, without repetition,
all tuples in the query result), and counting (output the number of tuples in the query result).

We identify three increasingly restrictive classes of UCQs which we
call t-hierarchical, q-hierarchical, and exhaustively q-hierarchical UCQs.
Our main results provide the following dichotomies:
If the query's homomorphic core is t-hierarchical (q-hierarchical,
exhaustively q-hierarchical), then the testing (enumeration, counting)
problem can be solved with constant update time and constant testing time (delay, counting time). Otherwise, it cannot be solved with sublinear update time and sublinear testing time (delay, counting time), unless the OV-conjecture and/or the OMv-conjecture fails. 

We also study the complexity of query evaluation in the dynamic setting in the presence of integrity constraints, and we obtain similar dichotomy results for the special case of small domain constraints (i.e., constraints which state that 
all values in a particular column of a relation belong to a fixed domain of constant size).

Subject Classification

Keywords
  • dynamic query evaluation
  • union of conjunctive queries
  • constant-delay enumeration
  • counting problem
  • testing

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