In a dynamic data structure problem we wish to maintain an encoding of some data in memory, in such a way that we may efficiently carry out a sequence of queries and updates to the data. A long-standing open problem in this area is to prove an unconditional polynomial lower bound of a trade-off between the update time and the query time of an adaptive dynamic data structure computing some explicit function. Ko and Weinstein provided such lower bound for a restricted class of semi-adaptive data structures, which compute the Disjointness function. There, the data are subsets x₁,… ,x_k and y of {1,… ,n}, the updates can modify y (by inserting and removing elements), and the queries are an index i ∈ {1,… ,k} (query i should answer whether x_i and y are disjoint, i.e., it should compute the Disjointness function applied to (x_i, y)). The semi-adaptiveness places a restriction in how the data structure can be accessed in order to answer a query. We generalize the lower bound of Ko and Weinstein to work not just for the Disjointness, but for any function having high complexity under the smooth corruption bound.
@InProceedings{dvorak_et_al:LIPIcs.FSTTCS.2020.20, author = {Dvo\v{r}\'{a}k, Pavel and Loff, Bruno}, title = {{Lower Bounds for Semi-adaptive Data Structures via Corruption}}, booktitle = {40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)}, pages = {20:1--20:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-174-0}, ISSN = {1868-8969}, year = {2020}, volume = {182}, editor = {Saxena, Nitin and Simon, Sunil}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.20}, URN = {urn:nbn:de:0030-drops-132617}, doi = {10.4230/LIPIcs.FSTTCS.2020.20}, annote = {Keywords: semi-adaptive dynamic data structure, polynomial lower bound, corruption bound, information theory} }
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