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.
@InProceedings{datta_et_al:LIPIcs.MFCS.2024.46, author = {Datta, Samir and Khan, Asif and Mukherjee, Anish and Tschirbs, Felix and Vortmeier, Nils and Zeume, Thomas}, title = {{Query Maintenance Under Batch Changes with Small-Depth Circuits}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {46:1--46:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-335-5}, ISSN = {1868-8969}, year = {2024}, volume = {306}, editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.46}, URN = {urn:nbn:de:0030-drops-206027}, doi = {10.4230/LIPIcs.MFCS.2024.46}, annote = {Keywords: Dynamic complexity theory, parallel computation, dynamic algorithms} }
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