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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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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.

Cite As Get BibTex

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

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.

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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References

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