Testing if an Array Is Sorted

Raskhodnikova, Sofya

doi:10.1007/978-3-642-27848-8_700-1

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…A significant body of work has been dedicated to such properties, with the examples of monotonicity [12,2,9,13,7,24], the Lipschitz property [19,7], convexity [23], and k-monotonicity [5,17]. Very recently, Newman, Rabinovich, Rajendraprasad, and Sohler [22] initiated the study of a massively parameterized property, 1 order pattern freeness, which generalizes and subsumes some of the aforementioned properties as special cases.…”

Section: Background and Motivationmentioning

confidence: 99%

Improved Bounds for Testing Forbidden Order Patterns

Ben‐Eliezer

Canonne

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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Section: Background and Motivationmentioning

confidence: 99%

Improved Bounds for Testing Forbidden Order Patterns

Ben‐Eliezer

Canonne

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Monotonicity Perhaps the most thoroughly investigated property in the testing literature: see e.g. the entries related to monotonicity testing in the Encyclopedia of Algorithms [13,31] and the references within. An [n] d -array A over an ordered alphabet Σ is monotone (nondecreasing) if A(x) ≤ A(y) for any x = (x 1 , .…”

Section: Local Propertiesmentioning

confidence: 99%

Testing local properties of arrays

Ben-Eliezer

2018

Preprint

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We study testing of local properties in one-dimensional and multi-dimensional arrays. A property of d-dimensional arrays f :can be defined by a family of k × . . . × k forbidden consecutive patterns. This definition captures numerous interesting properties. For example, monotonicity, Lipschitz continuity and submodularity are 2-local; convexity is (usually) 3-local; and many typical problems in computational biology and computer vision involve o(n)-local properties.In this work, we present a generic approach to test all local properties of arrays over any finite (and not necessarily bounded size) alphabet. We show that any k-local property of d-dimensional arrays is testable by a simple canonical one-sided error non-adaptive ε-test, whose query complexity isThe queries made by the canonical test constitute sphere-like structures of varying sizes, and are completely independent of the property and the alphabet Σ. The query complexity is optimal for a wide range of parameters: For d = 1, this matches the query complexity of many previously investigated local properties, while for d > 1 we design and analyze new constructions of k-local properties whose one-sided non-adaptive query complexity matches our upper bounds. For some previously studied properties, our method provides the first known sublinear upper bound on the query complexity.

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“…Testing of various properties of functions, including monotonicity (see, e.g., [26,21,22,33,24,23,28,1,29,3,8,7,10,13,9,6,14,15,12,18,17,31,4,5,20,34] and recent surveys [35,11]), the Lipschitz property [30,13,9], bounded-derivative properties [12], and unateness [26,32], has been studied extensively over the past two decades. Even though unateness testing was initially discussed in the seminal paper by Goldreich et al [26] that gave first testers for properties of functions, relatively little is known about testing this property.…”

Section: Introductionmentioning

confidence: 99%

Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps

Baleshzar¹,

Chakrabarty²,

Pallavoor³

et al. 2017

Preprint

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We study the problem of testing unateness of functions f : {0, 1} d → R. We give a O( d ε •log d ε )query nonadaptive tester and a O( d ε )-query adaptive tester and show that both testers are optimal for a fixed distance parameter ε. Previously known unateness testers worked only for Boolean functions, and their query complexity had worse dependence on the dimension both for the adaptive and the nonadaptive case. Moreover, no lower bounds for testing unateness were known 1 . We also generalize our results to obtain optimal unateness testers for functionsOur results establish that adaptivity helps with testing unateness of real-valued functions on domains of the form {0, 1} d and, more generally, [n] d . This stands in contrast to the situation for monotonicity testing where there is no adaptivity gap for functions f : [n] d → R. * Preliminary (much weaker) versions of this paper were posted as [16] and [2].

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Testing if an Array Is Sorted

Cited by 3 publications

References 13 publications

Improved Bounds for Testing Forbidden Order Patterns

Improved Bounds for Testing Forbidden Order Patterns

Testing local properties of arrays

Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps

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