Property Testing

Property Testing is the study of super-fast (randomized) algorithms for approximate decision making. These algorithms are given direct access to items of a huge data set, and determine, whether this data set has some predetermined (global) property or is far from having this property. Remarkably, this approximate decision is made by accessing a small portion of the data set. This state-of-the-art survey presents a collection of extended abstracts and surveys of leading researchers in property testing and related areas; it reflects the program of a mini-workshop on property testing that took place in January 2010 at the Institute for Computer Science (ITCS), Tsinghua University, Beijing, China. The volume contains two editor's introductions, 10 survey papers and 18 extended abstracts.

Inhalt

Editor's Introduction.- A Brief Introduction to Property Testing.- The Program of the Mini-Workshop.- Surveys.- Limitation on the Rate of Families of Locally Testable Codes.- Testing Juntas.- Sublinear-time Algorithms.- Short Locally Testable Codes and Proofs: A Survey in Two Parts.- Introduction to Testing Graph Properties.- Property Testing of Massively Parameterized Problems.- Sublinear Graph Approximation Algorithms.- Transitive-Closure Spanners.- Testing by Implicit Learning.- Invariance in Property Testing.- Extended Abstracts.- Testing Monotone Continuous Distributions on High-Dimensional Real Cubes.- On Constant Time Approximation of Parameters of Bounded Degree Graphs.- Sublinear Algorithms in the External Memory Model.- Polylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity.- Comparing the Strength of Query Types in Property Testing: The Case of Testing k-Colorability.- Testing Linear-Invariant Non-linear Properties: A Short Report.- Optimal Testing of Reed-Muller Codes.- Query-Efficient Dictatorship Testing with Perfect Completeness.- Composition of Low-Error 2-Query PCPs Using Decodable PCPs.- Hierarchy Theorems for Property Testing.- Algorithmic Aspects of Property Testing in the Dense Graphs Model.- Testing Euclidean Spanners.- Symmetric LDPCCodes and Local Testing.- Some Recent Results on Local Testing of Sparse Linear Codes.- Testing (Subclasses of) Halfspaces.- Dynamic Approximate Vertex Cover and Maximum Matching.- Local Property Reconstruction and Monotonicity.- Green's Conjecture and Testing Linear Invariant Properties.