Query maintenance under batch changes with small-depth circuits
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909272676237312 |
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| author | Datta, Samir Khan, Asif Mukherjee, Anish Tschirbs, Felix Vortmeier, Nils Zeume, Thomas |
| author_facet | Datta, Samir Khan, Asif Mukherjee, Anish Tschirbs, Felix Vortmeier, Nils Zeume, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Query maintenance under batch changes with small-depth circuits Datta, Samir Khan, Asif Mukherjee, Anish Tschirbs, Felix Vortmeier, Nils Zeume, Thomas Logic in Computer Science Computational Complexity 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. |
| title | Query maintenance under batch changes with small-depth circuits |
| topic | Logic in Computer Science Computational Complexity |
| url | https://arxiv.org/abs/2407.20031 |