Query Maintenance Under Batch Changes with Small-Depth Circuits

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.

Authors

• Samir Datta
• Asif Khan 0009
• Anish Mukherjee 0001
• Felix Tschirbs
• Nils Vortmeier
• Thomas Zeume

Keywords

• Dynamic complexity theory
• parallel computation
• dynamic algorithms