Spot-Checkers

Ergün, Funda; Kannan, Sampath; Kumar, Saravana; Rubinfeld, Ronitt; Viswanathan, Mahesh

doi:10.1006/jcss.1999.1692

Cited by 127 publications

(115 citation statements)

References 15 publications

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“…Recently, many researchers started studying a relaxation of the "exact decision task" and considered various forms of approximation algorithms for decision problems. In property testing (see, e.g., [1,11,13,17,16,18,19,26,29]), one considers the following class of problems:…”

Section: Introductionmentioning

confidence: 99%

Testing Hypergraph Coloring

Czumaj

Sohler

2001

Automata, Languages and Programming

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Abstract. In this paper we initiate the study of testing properties of hypergraphs. The goal of property testing is to distinguish between the case whether a given object has a certain property or is "far away" from the property. We prove that the fundamental problem of -colorability of k-uniform hypergraphs can be tested in time independent of the size of the hypergraph. We present a testing algorithm that examines only (k / ) O(k) entries of the adjacency matrix of the input hypergraph, where is a distance parameter independent of the size of the hypergraph. Notice that this algorithm tests only a constant number of entries in the adjacency matrix provided that , k, and are constant.

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Section: Introductionmentioning

confidence: 99%

Testing Hypergraph Coloring

Czumaj

Sohler

2001

Automata, Languages and Programming

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“…Ergün et al [7] designed two Hamming testers for sortedness that run in time O log n . Later, Bhattacharyya et al [3] and Chakrabarty and Seshadhri [5] gave different testers with the same complexity, with additional features that made them useful as subroutines in testing monotonicity of high-dimensional functions.…”

Section: Key Resultsmentioning

confidence: 99%

“…The Hamming testers for sortedness were first studied by Ergün et al [7]. The L 1 -testers (and, more generally, L p -testers, which use the L p distance for some p ≥ 1) were introduced by Berman, Raskhodnikova, and Yaroslavtsev [2].…”

Section: Bibliographical Notesmentioning

confidence: 99%

“…A Tester Based on Binary Search [7] We present and analyze the first tester for sortedness (Algorithm 1) with the assumption that all entries in the array a are distinct. This assumption can be removed by treating element a i as a i , i for all i ∈ [n].…”

Section: Hamming Testers For Sortednessmentioning

confidence: 99%

“…Testers for sortedness are used as subroutines in other property testers, e.g., for monotonicity of high-dimensional functions [6; 5; 2] and for the property that given points represent ordered vertices of a convex polygon [7]. They are also used to construct fast approximate probabilistically checkable proofs for different optimization problems [8].…”

Section: Applicationsmentioning

confidence: 99%

See 2 more Smart Citations

Testing if an Array Is Sorted

Raskhodnikova¹

2015

Encyclopedia of Algorithms

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Testing monotonicity over graph products

Halevy

Kushilevitz

2008

Random Struct Algorithms

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ABSTRACT:We consider the problem of monotonicity testing over graph products. Monotonicity testing is one of the central problems studied in the field of property testing. We present a testing approach that enables us to use known monotonicity testers for given graphs G 1 , G 2 , to test monotonicity over their product G 1 × G 2 . Such an approach of reducing monotonicity testing over a graph product to monotonicity testing over the original graphs, has been previously used in the special case of monotonicity testing over [n] d for a limited type of testers; in this article, we show that this approach can be applied to allow modular design of testers in many interesting cases: this approach works whenever the functions are boolean, and also in certain cases for functions with a general range. We demonstrate the usefulness of our results by showing how a careful use of this approach improves the query complexity of known testers. Specifically, based on our results, we provide a new analysis for the known tester for [n] d which significantly improves its query complexity analysis in the low-dimensional case. For example, when d = O(1), we reduce the best known query complexity from O(log 2 n/ ) to O(log n/ ).

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Spot-Checkers

Cited by 127 publications

References 15 publications

Testing Hypergraph Coloring

Testing Hypergraph Coloring

Testing if an Array Is Sorted

Testing monotonicity over graph products

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