Finding monotone patterns in sublinear time

Omri Ben-Eliezer; Clement Canonne; Shoham Letzter; Erik Waingarten

doi:10.1109/FOCS.2019.000-1

Finding monotone patterns in sublinear time

Omri Ben-Eliezer, Clement Canonne, Shoham Letzter, Erik Waingarten

COMPUTER SCIENCE

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We study the problem of finding monotone subsequences in an array from the viewpoint of sublinear algorithms. For fixed k N and ϵ > 0, we show that the non-Adaptive query complexity of finding a length-k monotone subsequence of f : [n] → R, assuming that f is ϵ-far from free of such subsequences, is Θ((log n) âŠlog-2kâ ). Prior to our work, the best algorithm for this problem, due to Newman, Rabinovich, Rajendraprasad, and Sohler (2017), made (log n)O(k2) non-Adaptive queries; and the only lower bound known, of Ω(log n) queries for the case k = 2, followed from that on testing monotonicity due to Ergün, Kannan, Kumar, Rubinfeld, and Viswanathan (2000) and Fischer (2004).

Original language	English
Title of host publication	Proceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019
Publisher	IEEE Computer Society
Pages	1469-1494
Number of pages	26
ISBN (Electronic)	9781728149523
DOIs	https://doi.org/10.1109/FOCS.2019.000-1
State	Published - Nov 2019
Event	60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019 - Baltimore, United States Duration: 9 Nov 2019 → 12 Nov 2019

Publication series

Name	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume	2019-November
ISSN (Print)	0272-5428

Conference

Conference	60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019
Country/Territory	United States
City	Baltimore
Period	9/11/19 → 12/11/19

Keywords

Algorithms
Forbidden patterns
Lower bounds
Monotone patterns
One sided tester
Property testing
Sublinear algorithms

Access to Document

10.1109/FOCS.2019.000-1

Cite this

Ben-Eliezer, O., Canonne, C., Letzter, S., & Waingarten, E. (2019). Finding monotone patterns in sublinear time. In Proceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019 (pp. 1469-1494). Article 8948694 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2019-November). IEEE Computer Society. https://doi.org/10.1109/FOCS.2019.000-1

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title = "Finding monotone patterns in sublinear time",

abstract = "We study the problem of finding monotone subsequences in an array from the viewpoint of sublinear algorithms. For fixed k N and ϵ > 0, we show that the non-Adaptive query complexity of finding a length-k monotone subsequence of f : [n] → R, assuming that f is ϵ-far from free of such subsequences, is Θ((log n) {\^a}{\v S}log-2k{\^a} ). Prior to our work, the best algorithm for this problem, due to Newman, Rabinovich, Rajendraprasad, and Sohler (2017), made (log n)O(k2) non-Adaptive queries; and the only lower bound known, of Ω(log n) queries for the case k = 2, followed from that on testing monotonicity due to Erg{\"u}n, Kannan, Kumar, Rubinfeld, and Viswanathan (2000) and Fischer (2004).",

keywords = "Algorithms, Forbidden patterns, Lower bounds, Monotone patterns, One sided tester, Property testing, Sublinear algorithms",

author = "Omri Ben-Eliezer and Clement Canonne and Shoham Letzter and Erik Waingarten",

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Ben-Eliezer, O, Canonne, C, Letzter, S & Waingarten, E 2019, Finding monotone patterns in sublinear time. in Proceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019., 8948694, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, vol. 2019-November, IEEE Computer Society, pp. 1469-1494, 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019, Baltimore, United States, 9/11/19. https://doi.org/10.1109/FOCS.2019.000-1

Finding monotone patterns in sublinear time. / Ben-Eliezer, Omri; Canonne, Clement; Letzter, Shoham et al.
Proceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019. IEEE Computer Society, 2019. p. 1469-1494 8948694 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2019-November).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We study the problem of finding monotone subsequences in an array from the viewpoint of sublinear algorithms. For fixed k N and ϵ > 0, we show that the non-Adaptive query complexity of finding a length-k monotone subsequence of f : [n] → R, assuming that f is ϵ-far from free of such subsequences, is Θ((log n) âŠlog-2kâ ). Prior to our work, the best algorithm for this problem, due to Newman, Rabinovich, Rajendraprasad, and Sohler (2017), made (log n)O(k2) non-Adaptive queries; and the only lower bound known, of Ω(log n) queries for the case k = 2, followed from that on testing monotonicity due to Ergün, Kannan, Kumar, Rubinfeld, and Viswanathan (2000) and Fischer (2004).

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Finding monotone patterns in sublinear time

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