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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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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.

References

  1. Eric Allender, Lisa Hellerstein, Paul McCabe, Toniann Pitassi, and Michael E. Saks. Minimizing disjunctive normal form formulas and AC^0 circuits given a truth table. SIAM J. Comput., 38(1):63-84, 2008. URL: https://doi.org/10.1137/060664537.
  2. David A. Mix Barrington, Peter Kadau, Klaus-Jörn Lange, and Pierre McKenzie. On the complexity of some problems on groups input as multiplication tables. J. Comput. Syst. Sci., 63(2):186-200, 2001. URL: https://doi.org/10.1006/JCSS.2001.1764.
  3. Hans L. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput., 25(6):1305-1317, 1996. URL: https://doi.org/10.1137/S0097539793251219.
  4. Stephen A. Cook. Path systems and language recognition. In Patrick C. Fischer, Robert Fabian, Jeffrey D. Ullman, and Richard M. Karp, editors, Proceedings of the 2nd Annual ACM Symposium on Theory of Computing, May 4-6, 1970, Northampton, Massachusetts, USA, pages 70-72. ACM, 1970. URL: https://doi.org/10.1145/800161.805151.
  5. Bruno Courcelle. The monadic second-order logic of graphs. I. recognizable sets of finite graphs. Inf. Comput., 85(1):12-75, 1990. URL: https://doi.org/10.1016/0890-5401(90)90043-H.
  6. Samir Datta, Raghav Kulkarni, Anish Mukherjee, Thomas Schwentick, and Thomas Zeume. Reachability is in DynFO. J. ACM, 65(5):33:1-33:24, 2018. URL: https://doi.org/10.1145/3212685.
  7. Samir Datta, Pankaj Kumar, Anish Mukherjee, Anuj Tawari, Nils Vortmeier, and Thomas Zeume. Dynamic complexity of reachability: How many changes can we handle? In Artur Czumaj, Anuj Dawar, and Emanuela Merelli, editors, 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference), volume 168 of LIPIcs, pages 122:1-122:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ICALP.2020.122.
  8. Samir Datta, Anish Mukherjee, Thomas Schwentick, Nils Vortmeier, and Thomas Zeume. A strategy for dynamic programs: Start over and muddle through. Logical Methods in Computer Science, 15(2), 2019. URL: https://doi.org/10.23638/LMCS-15(2:12)2019.
  9. Samir Datta, Anish Mukherjee, Nils Vortmeier, and Thomas Zeume. Reachability and distances under multiple changes. In Ioannis Chatzigiannakis, Christos Kaklamanis, Dániel Marx, and Donald Sannella, editors, 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, July 9-13, 2018, Prague, Czech Republic, volume 107 of LIPIcs, pages 120:1-120:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.ICALP.2018.120.
  10. Guozhu Dong and Jianwen Su. First-order incremental evaluation of datalog queries. In Database Programming Languages (DBPL-4), Proceedings of the Fourth International Workshop on Database Programming Languages - Object Models and Languages, pages 295-308, 1993. Google Scholar
  11. Guozhu Dong and Jianwen Su. Incremental and decremental evaluation of transitive closure by first-order queries. Inf. Comput., 120(1):101-106, 1995. URL: https://doi.org/10.1006/inco.1995.1102.
  12. Guozhu Dong and Jianwen Su. Arity bounds in first-order incremental evaluation and definition of polynomial time database queries. J. Comput. Syst. Sci., 57(3):289-308, 1998. URL: https://doi.org/10.1006/jcss.1998.1565.
  13. Michael Elberfeld, Andreas Jakoby, and Till Tantau. Logspace versions of the theorems of Bodlaender and Courcelle. In 51th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2010, October 23-26, 2010, Las Vegas, Nevada, USA, pages 143-152. IEEE Computer Society, 2010. URL: https://doi.org/10.1109/FOCS.2010.21.
  14. Kousha Etessami. Dynamic tree isomorphism via first-order updates. In PODS, pages 235-243, 1998. URL: https://doi.org/10.1145/275487.275514, db/conf/pods/Etessami98.html.
  15. Wouter Gelade, Marcel Marquardt, and Thomas Schwentick. The dynamic complexity of formal languages. ACM Trans. Comput. Log., 13(3):19:1-19:36, 2012. URL: https://doi.org/10.1145/2287718.2287719.
  16. Andrew V. Goldberg and Serge A. Plotkin. Parallel (Δ + 1)-coloring of constant-degree graphs. Information Processing Letters, 25(4):241-245, 1987. URL: https://doi.org/10.1016/0020-0190(87)90169-4.
  17. Erich Grädel and Sebastian Siebertz. Dynamic definability. In Alin Deutsch, editor, 15th International Conference on Database Theory, ICDT '12, Berlin, Germany, March 26-29, 2012, pages 236-248. ACM, 2012. URL: https://doi.org/10.1145/2274576.2274601.
  18. William Hesse, Eric Allender, and David A. Mix Barrington. Uniform constant-depth threshold circuits for division and iterated multiplication. J. Comput. Syst. Sci., 65(4):695-716, 2002. URL: https://doi.org/10.1016/S0022-0000(02)00025-9.
  19. Neil Immerman. Descriptive complexity. Graduate texts in computer science. Springer, 1999. URL: https://doi.org/10.1007/978-1-4612-0539-5.
  20. Stasys Jukna. Boolean function complexity: advances and frontiers, volume 27. Springer Science & Business Media, 2012. URL: https://doi.org/10.1007/978-3-642-24508-4.
  21. Pablo Muñoz, Nils Vortmeier, and Thomas Zeume. Dynamic graph queries. In Wim Martens and Thomas Zeume, editors, 19th International Conference on Database Theory, ICDT 2016, Bordeaux, France, March 15-18, 2016, volume 48 of LIPIcs, pages 14:1-14:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. URL: https://doi.org/10.4230/LIPICS.ICDT.2016.14.
  22. Chaoyi Pang, Guozhu Dong, and Kotagiri Ramamohanarao. Incremental maintenance of shortest distance and transitive closure in first-order logic and SQL. ACM Trans. Database Syst., 30(3):698-721, 2005. URL: https://doi.org/10.1145/1093382.1093384.
  23. Sushant Patnaik and Neil Immerman. Dyn-FO: A parallel, dynamic complexity class. J. Comput. Syst. Sci., 55(2):199-209, 1997. URL: https://doi.org/10.1006/jcss.1997.1520.
  24. Felix Tschirbs, Nils Vortmeier, and Thomas Zeume. Dynamic complexity of regular languages: Big changes, small work. In Bartek Klin and Elaine Pimentel, editors, 31st EACSL Annual Conference on Computer Science Logic, CSL 2023, February 13-16, 2023, Warsaw, Poland, volume 252 of LIPIcs, pages 35:1-35:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPICS.CSL.2023.35.
  25. Nils Vortmeier. Dynamic expressibility under complex changes. PhD thesis, TU Dortmund University, Germany, 2019. URL: https://doi.org/10.17877/DE290R-20434.
  26. Nils Vortmeier and Thomas Zeume. Dynamic complexity of parity exists queries. Log. Methods Comput. Sci., 17(4), 2021. URL: https://doi.org/10.46298/LMCS-17(4:9)2021.
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