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Query Maintenance Under Batch Changes with Small-Depth Circuits

Authors Samir Datta , Asif Khan, Anish Mukherjee , Felix Tschirbs, Nils Vortmeier , Thomas Zeume

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LIPIcs.MFCS.2024.46.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and databases
  • Theory of computation → Complexity theory and logic
Keywords
  • Dynamic complexity theory
  • parallel computation
  • dynamic algorithms

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Abstract

Which dynamic queries can be maintained efficiently? For constant-size changes, it is known that constant-depth circuits or, equivalently, first-order updates suffice for maintaining many important queries, among them reachability, tree isomorphism, and the word problem for context-free languages. In other words, these queries are in the dynamic complexity class DynFO. We show that most of the existing results for constant-size changes can be recovered for batch changes of polylogarithmic size if one allows circuits of depth 𝒪(log log n) or, equivalently, first-order updates that are iterated 𝒪(log log n) times.

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Samir Datta, Asif Khan, Anish Mukherjee, Felix Tschirbs, Nils Vortmeier, and Thomas Zeume. Query Maintenance Under Batch Changes with Small-Depth Circuits. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.46

Author Details

Samir Datta
  • Chennai Mathematical Institute & UMI ReLaX, Chennai, India
Asif Khan
  • Chennai Mathematical Institute, India
Anish Mukherjee
  • University of Warwick, Coventry, UK
Felix Tschirbs
  • Ruhr University Bochum, Germany
Nils Vortmeier
  • Ruhr University Bochum, Germany
Thomas Zeume
  • Ruhr University Bochum, Germany

Funding

  • Datta, Samir: Partially funded by a grant from Infosys foundation.
  • Khan, Asif: Partially funded by a grant from Infosys foundation.
  • Mukherjee, Anish: Research was supported in part by the Centre for Discrete Mathematics and its Applications (DIMAP) and by EPSRC award EP/V01305X/1.
  • Tschirbs, Felix: Supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant 532727578.
  • Vortmeier, Nils: Supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant 532727578.
  • Zeume, Thomas: Supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant 532727578.

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