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This short article provides a brief description of the main issues that underly the study of property testing. It is meant to serve as a general introduction to a collection of surveys and extended abstracts that cover various specific subareas and ...

This article provides an annotated version of the program of the mini-workshop on propoerty testing that took place in January 2010 in the Institute for Computer Science (ITCS) at Tsinghua University (Beijing). The mini-workshop brought together a ...

This paper describes recent results which revolve around the question of the rate attainable by families of error correcting codes that are locally testable. Emphasis is placed on motivating the problem of proving upper bounds on the rate of these codes ...

A function on n variables is called a k-junta if it depends on at most k of its variables. In this survey, we review three recent algorithms for testing k-juntas with few queries.

In this paperwe survey recent advances in the area of sublineartime algorithms.

We survey known results regarding locally testable codes and locally testable proofs (known as PCPs), with emphasis on the length of these constructs. Local testability refers to approximately testing large objects based on a very small number of probes,...

The aim of this article is to introduce the reader to the study of testing graph properties, while focusing on the main models and issues involved. No attempt is made to provide a comprehensive survey of this study, and specific results are often ...

We survey property testing results for the so called 'massively parametrized' model (or problems). The massively-parametrized framework studies problems such as: Given a graph G = (V,E), consider the property BI(G) containing all subgraphs of G that are ...

We survey the recent research on algorithms that approximate the optimal solution size for problems such as vertex cover, maximum matching, and dominating set. Techniques developed for these problems have found applications in property testing in the ...

We survey results on transitive-closure spanners and their applications. Given a directed graph G = (V, E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V, E_H) that has (1) the same transitive-closure ...

We give a high-level survey of the "testing by implicit learning" paradigm, and explain some of the property testing results for various Boolean function classes that have been obtained using this approach.

Property testing considers the task of testing rapidly (in particular, with very few samples into the data), if some massive data satisfies some given property, or is far from satisfying the property. For "global properties", i.e., properties that ...

We study the task of testing properties of probability distributions and our focus is on understanding the role of continuous distributions in this setting. We consider a scenario in which we have access to independent samples of an unknown distribution ...

How well can the maximum size of an independent set, or the minimum size of a dominating set of a graph in which all degrees are at most d be approximated by a randomized constant time algorithm ? Motivated by results and questions of Nguyen and Onak, ...

We initiate the study of sublinear-time algorithms in the external memory model. In this model, the data is stored in blocks of a certain size B, and the algorithm is charged a unit cost for each block access. This model is well-studied, since it ...

We present a near-linear time algorithm that approximates the edit distance between two strings within a polylogarithmic factor. More precisely, for strings of length n and every fixed ε > 0, it can compute a (log n)^O(1/ε) -approximation in n^1+ε time.

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We study the power of four query models in the context of property testing in general graphs (i.e., with arbitrary edge densities), where our main case study is the problem of testing k-colorability. Two query types, which have been studied extensively ...

The rich collection of successes in property testing raises a natural question: Why are so many different properties turning out to be locally testable? Are there some broad "features" of properties that make them testable? Kaufman and Sudan (STOC 2008) ...

We consider the problem of testing if a given function f : Fⁿ₂ → F₂ is close to any degree d polynomial in n variables, also known as the problem of testing Reed-Muller codes. We are interested in determining the query-complexity of distinguishing with ...

The problem of dictatorship testing is often used a starting in constructing a PCP system. Samorodnitsky and Trevisan in STOC 2006 designed a dictatorship test that makes q queries and has soundness approximately O(qċ^2-q). However, their test has ...

The main result of this paper is a generic composition theorem for low error two-query probabilistically checkable proofs (PCPs). Prior to this work, composition of PCPs was well-understood only in the constant error regime. Existing composition methods ...

Referring to the query complexity of property testing, we prove the existence of a rich hierarchy of corresponding complexity classes. That is, for any relevant function q, we prove the existence of properties that have testing complexity Θ(_q). Such ...

In this paper we consider two basic questions regarding the query complexity of testing graph properties in the adjacency matrix model. The first question refers to the relation between adaptive and non-adaptive testers, whereas the second question ...

In this paper we develop a property testing algorithm for the problem of testing whether a directed geometric graph is a (1 + δ)- spanner.

Coding theoretic and complexity theoretic considerations naturally lead to the question of generating symmetric, sparse, redundant linear systems. This paper provides new way of constructions with better parameters and new lower bounds.

Low Density ...

We study the local testability of linear codes. Our approach is based on a reformulation of this question in the language of tolerant linearity testing under a non-uniform distribution. We then study the question of linearity testing under non-uniform ...

We address the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x) = sgn(wċx-θ). We consider halfspaces over the continuous domain Rⁿ (endowed with the standard multivariate Gaussian distribution) as ...

We consider the problem of maintaining a large matching or a small vertex cover in a dynamically changing graph. Each update to the graph is either an edge deletion or an edge insertion. We give the first randomized data structure that simultaneously ...

We propose a general model of local property reconstruction. Suppose we have a function f on domain Γ, which is supposed to have a particular property P, but may not have the property. We would like a procedure that produces a function g that has ...

A system of l linear equations in p unknowns M x = b is said to have the removal property if every set S ⊆ {1, . . . , n} which contains o(n^p-l) solutions of M x = b can be turned into a set S′ containing no solution of M x = b, by the removal of o(n) ...