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arXiv · 2407.20031

Query maintenance under batch changes with small-depth circuits

Samir Datta·Asif Khan·Anish Mukherjee·Felix Tschirbs·Nils Vortmeier·Thomas Zeume
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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, Thomas Zeume. 2024-07-29. Query maintenance under batch changes with small-depth circuits. https://arxiv.org/abs/2407.20031

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