Testing Graph Properties in the General Graph Model

Teaching note: Although it is possible to study the current chapter without first studying the Chapter 9, we strongly recommend not doing so. Basic familiarity with the bounded-degree graph model seems necessary for a good perspective on the general graph model. In addition, familarity with some of the results and ideas of Chapter 9 will greatly facilitate the study of current chapter. Specifically, it will be most beneficial to be familiar with the connectivity tester and the bipartiteness tester.

[1]  Dana Ron,et al.  Property testing and its connection to learning and approximation , 1998, JACM.

[2]  Dana Ron,et al.  A Sublinear Bipartiteness Tester for Bounded Degree Graphs , 1998, STOC '98.

[3]  Dana Ron,et al.  Testing the diameter of graphs , 1999, RANDOM-APPROX.

[4]  N. Alon,et al.  Testing triangle-freeness in general graphs , 2006, SODA 2006.

[5]  Noga Alon.  Testing subgraphs in large graphs , 2002, Random Struct. Algorithms.

[6]  Dana Ron,et al.  Algorithmic Aspects of Property Testing in the Dense Graphs Model , 2009, APPROX-RANDOM.

[7]  Uriel Feige,et al.  On sums of independent random variables with unbounded variance, and estimating the average degree in a graph , 2004, STOC '04.

[8]  Bernard Chazelle,et al.  Approximating the Minimum Spanning Tree Weight in Sublinear Time , 2001, ICALP.

[9]  Dana Ron,et al.  A pr 2 01 6 Sublinear Time Estimation of Degree Distribution Moments : The Arboricity Connection ( Full Version ) Talya Eden , 2016 .

[10]  Dana Ron,et al.  Tight Bounds for Testing Bipartiteness in General Graphs , 2004, SIAM J. Comput..

[11]  Dana Ron,et al.  Approximating average parameters of graphs , 2008, Random Struct. Algorithms.

[12]  Dana Ron,et al.  Finding cycles and trees in sublinear time , 2010, Random Struct. Algorithms.

[13]  Dana Ron,et al.  Property Testing in Bounded Degree Graphs , 1997, STOC.

[14]  Dana Ron,et al.  Comparing the strength of query types in property testing: the case of testing k-colorability , 2008, SODA '08.

[15]  Uriel Feige,et al.  On Sums of Independent Random Variables with Unbounded Variance and Estimating the Average Degree in a Graph , 2006, SIAM J. Comput..