Introduction to Testing Graph Properties

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 mentioned merely as illustrations of general themes.

[1]  E. Szemerédi Regular Partitions of Graphs , 1975 .

[2]  Yacov Yacobi,et al.  The Complexity of Promise Problems with Applications to Public-Key Cryptography , 1984, Inf. Control..

[3]  Milena Mihail,et al.  Conductance and convergence of Markov chains-a combinatorial treatment of expanders , 1989, 30th Annual Symposium on Foundations of Computer Science.

[4]  Manuel Blum,et al.  Self-testing/correcting with applications to numerical problems , 1990, STOC '90.

[5]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[6]  Marek Karpinski,et al.  Polynomial time approximation schemes for dense instances of NP-hard problems , 1995, STOC '95.

[7]  Ran Canetti,et al.  Lower Bounds for Sampling Algorithms for Estimating the Average , 1995, Inf. Process. Lett..

[8]  Mihir Bellare,et al.  Free bits, PCPs and non-approximability-towards tight results , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[9]  Mihir Bellare,et al.  Linearity testing in characteristic two , 1996, IEEE Trans. Inf. Theory.

[10]  J. Håstad Clique is hard to approximate within n 1-C , 1996 .

[11]  Ronitt Rubinfeld,et al.  Robust Characterizations of Polynomials with Applications to Program Testing , 1996, SIAM J. Comput..

[12]  Wenceslas Fernandez de la Vega,et al.  MAX-CUT has a randomized approximation scheme in dense graphs , 1996, Random Struct. Algorithms.

[13]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[14]  W. Vega,et al.  MAX-CUT has a randomized approximation scheme in dense graphs , 1996, Random Struct. Algorithms.

[15]  Dana Ron,et al.  Property Testing in Bounded Degree Graphs , 2002, STOC '97.

[16]  Dorit S. Hochba,et al.  Approximation Algorithms for NP-Hard Problems , 1997, SIGA.

[17]  Mihir Bellare,et al.  Free Bits, PCPs, and Nonapproximability-Towards Tight Results , 1998, SIAM J. Comput..

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

[19]  Noga Alon,et al.  Efficient Testing of Large Graphs , 2000, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[20]  J. Håstad Clique is hard to approximate withinn1−ε , 1999 .

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

[22]  Dana Ron,et al.  A Sublinear Bipartiteness Tester for Bounded Degree Graphs , 1999, Comb..

[23]  Ronitt Rubinfeld,et al.  Testing that distributions are close , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[24]  Michael A. Bender,et al.  Testing Acyclicity of Directed Graphs in Sublinear Time , 2000, ICALP.

[25]  Noga Alon,et al.  Testing subgraphs in large graphs , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[26]  Luca Trevisan,et al.  Three Theorems regarding Testing Graph Properties , 2001, Electron. Colloquium Comput. Complex..

[27]  Kenji Obata,et al.  A lower bound for testing 3-colorability in bounded-degree graphs , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[28]  Noga Alon,et al.  Testing k-colorability , 2002, SIAM J. Discret. Math..

[29]  D. Ron,et al.  Testing properties of directed graphs: acyclicity and connectivity , 2002 .

[30]  László Lovász,et al.  Lecture Notes on Evasiveness of Graph Properties , 2002, ArXiv.

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

[32]  Noga Alon,et al.  Testing subgraphs in directed graphs , 2003, STOC '03.

[33]  Dana Ron,et al.  Tight Bounds for Testing Bipartiteness in General Graphs , 2004, RANDOM-APPROX.

[34]  Noga Alon,et al.  A characterization of easily testable induced subgraphs , 2004, SODA '04.

[35]  Ronitt Rubinfeld,et al.  Tolerant property testing and distance approximation , 2006, J. Comput. Syst. Sci..

[36]  Luca Trevisan,et al.  Lower bounds for testing bipartiteness in dense graphs , 2004, Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004..

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

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

[39]  Eldar Fischer,et al.  Testing versus estimation of graph properties , 2005, STOC '05.

[40]  Noga Alon,et al.  A characterization of the (natural) graph properties testable with one-sided error , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[41]  Noga Alon,et al.  Testing triangle-freeness in general graphs , 2006, SODA '06.

[42]  Sofya Raskhodnikova,et al.  A Note on Adaptivity in Testing Properties of Bounded Degree Graphs , 2006, Electron. Colloquium Comput. Complex..

[43]  Oded Goldreich,et al.  On Promise Problems: A Survey , 2006, Essays in Memory of Shimon Even.

[44]  Noga Alon,et al.  A combinatorial characterization of the testable graph properties: it's all about regularity , 2006, STOC '06.

[45]  Dana Ron,et al.  Distance Approximation in Bounded-Degree and General Sparse Graphs , 2006, APPROX-RANDOM.

[46]  Eldar Fischer,et al.  Testing graph isomorphism , 2006, SODA '06.

[47]  Arnold L. Rosenberg,et al.  Theoretical Computer Science, Essays in Memory of Shimon Even , 2006, Essays in Memory of Shimon Even.

[48]  Dana Ron,et al.  On the Benefits of Adaptivity in Property Testing of Dense Graphs , 2007, APPROX-RANDOM.

[49]  Sudipto Guha,et al.  Approximation Algorithms for Partial-Information Based Stochastic Control with Markovian Rewards , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[50]  M. Weidner,et al.  Gauging hidden symmetries in two dimensions , 2007, 0705.2606.

[51]  Asaf Shapira,et al.  Approximate Hypergraph Partitioning and Applications , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[52]  Asaf Shapira,et al.  Testing the expansion of a graph , 2010, Inf. Comput..

[53]  Seshadhri Comandur,et al.  Testing Expansion in Bounded Degree Graphs , 2007, Electron. Colloquium Comput. Complex..

[54]  Oded Goldreich,et al.  Computational complexity: a conceptual perspective , 2008, SIGA.

[55]  Noga Alon,et al.  Every monotone graph property is testable , 2005, STOC '05.

[56]  Noga Alon,et al.  A separation theorem in property testing , 2008, Comb..

[57]  Dana Ron,et al.  Algorithmic Aspects of Property Testing in the Dense Graphs Model , 2009, Electron. Colloquium Comput. Complex..

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

[59]  Seshadhri Comandur,et al.  An Expansion Tester for Bounded Degree Graphs , 2008, SIAM J. Comput..

[60]  Dana Ron,et al.  On the Benefits of Adaptivity in Property Testing of Dense Graphs , 2010, Algorithmica.

[61]  Oded Schramm,et al.  Every minor-closed property of sparse graphs is testable , 2008, Electron. Colloquium Comput. Complex..

[62]  Krzysztof Onak,et al.  Local Graph Partitions for Approximation and Testing , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[63]  Dana Ron,et al.  On proximity oblivious testing , 2009, STOC '09.

[64]  Dana Ron,et al.  Approximating the distance to properties in bounded-degree and general sparse graphs , 2009, TALG.

[65]  Dana Ron,et al.  Algorithmic and Analysis Techniques in Property Testing , 2010, Found. Trends Theor. Comput. Sci..

[66]  Oded Goldreich A Brief Introduction to Property Testing , 2010, Property Testing.

[67]  David A. Bader,et al.  Graph Algorithms , 2011, Encyclopedia of Parallel Computing.

[68]  Oded Goldreich,et al.  Hierarchy Theorems for Property Testing , 2011, computational complexity.