2026-07-21T20:25:01Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16358 2024-03-06T10:57:16Z ddc:004 open_access

Finding Monotone Patterns in Sublinear Time, Adaptively Ben-Eliezer, Omri Letzter, Shoham Waingarten, Erik property testing monotone patterns monotone decomposition adaptivity We investigate adaptive sublinear algorithms for finding monotone patterns in sequential data. Given fixed 2 ≤ k ∈ m N and ε > 0, consider the problem of finding a length-k increasing subsequence in a sequence f : [n] → ℝ, provided that f is ε-far from free of such subsequences. It was shown by Ben-Eliezer et al. [FOCS 2019] that the non-adaptive query complexity of the above task is Θ((log n)^⌊log₂ k⌋). In this work, we break the non-adaptive lower bound, presenting an adaptive algorithm for this problem which makes O(log n) queries. This is optimal, matching the classical Ω(log n) adaptive lower bound by Fischer [Inf. Comp. 2004] for monotonicity testing (which corresponds to the case k = 2). Equivalently, our result implies that testing whether a sequence decomposes into k monotone subsequences can be done with O(log n) queries. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Omri Ben-Eliezer and Shoham Letzter and Erik Waingarten 2022 Is Part Of LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2022.17 urn:nbn:de:0030-drops-163586 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.17 eng https://creativecommons.org/licenses/by/4.0/legalcode