Given the outstanding performance of last month it is not surprising (though disappointing) that this month performance has not matched up to last months performance. We have only three paper on property testing this month. Please do let us know if we have missed anything. Hopefully next month will be more exciting.

A simpler sublinear algorithm for approximating the triangle count by C. Seshadhri (arXiv). Approximating number of triangles in a graph is a very important problem that also has applications in real life. Using a model (that is possibly more relevant for real life application), in which the queries are more powerful than those allowed in sparse graph and dense graph model, Eden, Levi and Ron gave a sublinear algorithm for approximating the number of triangles in an undirected graph. Seshadri has given an alternate algorithm with similar complexity but much simpler analysis.

Using higher-order Fourier analysis over general fields by Arnab Bhattacharyya and Abhishek Bhowmick (arXiv). The holy grail of property testing is to characterize properties that are testable. Many classes of properties have been proved to the testable. For most of results in this direction the main tool has been Fourier analysis. But classical Fourier analysis has its limitations. Recently higher-oder Fourier analysis has been used as a tool in many fields of theory. In this paper also higher-order Fourier analysis has been used to prove that a large class of property is testable.

Streaming Property Testing of Visibly Pushdown Languages by Nathanaël François, Frédéric Magniez, Michel de Rougemont, Olivier Serre (arXiv).  The subject of streaming property testing deals with the problem of distinguishing if a stream of data satisfies a property or is “far” from satisfying the property. The goal is to minimize the amount of memory space used (number of queries made is not relevant in this model. In this paper they give a streaming property tester for  Visibly Pushdown Languages using poly logarithmic space.