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Introduction to Testing Graph Properties

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Property Testing

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6390))

Abstract

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.

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References

  1. Alon, N.: Testing subgraphs of large graphs. Random Structures and Algorithms 21, 359–370 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alon, N., Fischer, E., Krivelevich, M., Szegedy, M.: Efficient Testing of Large Graphs. Combinatorica 20, 451–476 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Alon, N., Fischer, E., Newman, I., Shapira, A.: A Combinatorial Characterization of the Testable Graph Properties: It’s All About Regularity. In: 38th STOC, pp. 251–260 (2006)

    Google Scholar 

  4. Alon, N., Krivelevich, M.: Testing k-Colorability. SIAM Journal on Disc. Math. 15(2), 211–227 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Alon, N., Kaufman, T., Krivelevich, M., Ron, D.: Testing triangle freeness in general graphs. In: 17th SODA, pp. 279–288 (2006)

    Google Scholar 

  6. Alon, N., Shapira, A.: Testing subgraphs in directed graphs. JCSS 69, 354–482 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Alon, N., Shapira, A.: Every Monotone Graph Property is Testable. In: 37th STOC, pp. 128–137 (2005)

    Google Scholar 

  8. Alon, N., Shapira, A.: A Characterization of the (natural) Graph Properties Testable with One-Sided. In: 46th FOCS, pp. 429–438 (2005)

    Google Scholar 

  9. Alon, N., Shapira, A.: A Characterization of Easily Testable Induced Subgraphs. Combinatorics Probability and Computing 15, 791–805 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Alon, N., Shapira, A.: A Separation Theorem in Property Testing. Combinatorica 28(3), 261–281 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Alon, N., Spencer, J.H.: The Probabilistic Method. John Wiley & Sons, Inc., Chichester (1992)

    MATH  Google Scholar 

  12. Arora, S., Karger, D., Karpinski, M.: Polynomial time approximation schemes for dense instances of NP-hard problems. JCSS 58(1), 193–210 (1999)

    MathSciNet  MATH  Google Scholar 

  13. Batu, T., Fortnow, L., Rubinfeld, R., Smith, W.D., White, P.: Testing that Distributions are Close. In: 41st FOCS, pp. 259–269 (2000)

    Google Scholar 

  14. Bellare, M., Coppersmith, D., Håstad, J., Kiwi, M., Sudan, M.: Linearity testing in characteristic two. In: The 36th FOCS, pp. 432–441 (1995)

    Google Scholar 

  15. Bellare, M., Goldreich, O., Sudan, M.: Free Bits, PCPs and Non-approximability – Towards Tight Results. SIAM Journal on Computing 27(3), 804–915 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bender, M., Ron, D.: Testing acyclicity of directed graphs in sublinear time. Random Structures and Algorithms, 184–205 (2002)

    Google Scholar 

  17. Ben-Eliezer, I., Kaufman, T., Krivelevich, M., Ron, D.: Comparing the strength of query types in property testing: the case of testing k-colorability. In: 19th SODA (2008)

    Google Scholar 

  18. Benjamini, I., Schramm, O., Shapira, A.: Every Minor-Closed Property of Sparse Graphs is Testable. In: 40th STOC, pp. 393–402 (2008)

    Google Scholar 

  19. Blum, M., Luby, M., Rubinfeld, R.: Self-Testing/Correcting with Applications to Numerical Problems. JCSS 47(3), 549–595 (1993)

    MathSciNet  MATH  Google Scholar 

  20. Bogdanov, A., Obata, K., Trevisan, L.: A lower bound for testing 3-colorability in bounded-degree graphs. In: 43rd FOCS, pp. 93–102 (2002)

    Google Scholar 

  21. Bogdanov, A., Trevisan, L.: Lower Bounds for Testing Bipartiteness in Dense Graphs. In: IEEE Conference on Computational Complexity, pp. 75–81 (2004)

    Google Scholar 

  22. Canetti, R., Even, G., Goldreich, O.: Lower Bounds for Sampling Algorithms for Estimating the Average. In: IPL, vol. 53, pp. 17–25 (1995)

    Google Scholar 

  23. Chazelle, B., Rubinfeld, R., Trevisan, L.: Approximating the minimum spanning tree weight in sublinear time. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 190–200. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  24. de la Vega, W.F.: MAX-CUT has a randomized approximation scheme in dense graphs. Random Structures and Algorithms 8(3), 187–198 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  25. Even, S.: Graph Algorithms. Computer Science Press, Rockville (1979)

    MATH  Google Scholar 

  26. Even, S., Selman, A.L., Yacobi, Y.: The Complexity of Promise Problems with Applications to Public-Key Cryptography. Inform. and Control 61, 159–173 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  27. Fischer, E., Matsliah, A.: Testing graph isomorphism. In: 17th SODA, pp. 299–308 (2006)

    Google Scholar 

  28. Fischer, E., Matsliah, A., Shapira, A.: Approximate hypergraph partitioning and applications. In: Proceedings of 48th FOCS, pp. 579–589 (2007)

    Google Scholar 

  29. Fischer, E., Newman, I.: Testing versus estimation of graph properties. In: 37th STOC, pp. 138–146 (2005)

    Google Scholar 

  30. Goldreich, O.: On Promise Problems. In: memory of Shimon Even (1935–2004). ECCC, TR05-018 (January 2005); See also in Theoretical Computer Science: Essays in Memory of Shimon Even, Springer, LNCS Festschrift, Vol. 3895 (March 2006)

    Google Scholar 

  31. Goldreich, O.: Computational Complexity: A Conceptual Perspective. Cambridge University Press, Cambridge (2008)

    Book  MATH  Google Scholar 

  32. Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. Journal of the ACM, 653–750 (July 1998); Extended abstract in 37th FOCS (1996)

    Google Scholar 

  33. Goldreich, O., Krivelevich, M., Newman, I., Rozenberg, E.: Hierarchy Theorems for Property Testing. In: Goldreich, O. (ed.) Property Testing. LNCS, vol. 6390, pp. 105–141. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  34. Goldreich, O., Ron, D.: Property testing in bounded degree graphs. Algorithmica, 302–343 (2002)

    Google Scholar 

  35. Goldreich, O., Ron, D.: A sublinear bipartite tester for bounded degree graphs. Combinatorica 19(3), 335–373 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  36. Goldreich, O., Ron, D.: On Testing Expansion in Bounded-Degree Graphs. ECCC, TR00-020 (March 2000)

    Google Scholar 

  37. Goldreich, O., Ron, D.: Approximating Average Parameters of Graphs. Random Structures and Algorithms 32(3), 473–493 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  38. Goldreich, O., Ron, D.: Algorithmic Aspects of Property Testing in the Dense Graphs Model. In: Goldreich, O. (ed.) Property Testing. LNCS, vol. 6390, pp. 105–141. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  39. Goldreich, O., Ron, D.: On Proximity Oblivious Testing. ECCC, TR08-041 (2008); Also in the proceedings of the 41st STOC (2009)

    Google Scholar 

  40. Goldreich, O., Trevisan, L.: Three theorems regarding testing graph properties. Random Structures and Algorithms 23(1), 23–57 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  41. Gonen, M., Ron, D.: On the Benefit of Adaptivity in Property Testing of Dense Graphs. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) RANDOM 2007 and APPROX 2007. LNCS, vol. 4627, pp. 525–539. Springer, Heidelberg (2007); To appear in Algorithmica (special issue of RANDOM and APPROX 2007)

    Chapter  Google Scholar 

  42. Håstad, J.: Clique is hard to approximate within n 1 − ε. Acta Mathematica 182, 105–142 (1999) (Preliminary Version in 28th STOC, 1996 and 37th FOCS, 1996)

    Article  MathSciNet  Google Scholar 

  43. Hassidim, A., Kelner, J., Nguyen, H., Onak, K.: Local Graph Partitions for Approximation and Testing. In: 50th FOCS, pp. 22–31 (2009)

    Google Scholar 

  44. Hochbaum, D. (ed.): Approximation Algorithms for NP-Hard Problems. PWS (1996)

    Google Scholar 

  45. Kale, S., Seshadhri, C.: Testing expansion in bounded degree graphs. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 527–538. Springer, Heidelberg (2008); Preliminary version appeared as TR07-076, ECCC (2007)

    Chapter  Google Scholar 

  46. Kaufman, T., Krivelevich, M., Ron, D.: Tight Bounds for Testing Bipartiteness in General Graphs. SIAM Journal on Computing 33(6), 1441–1483 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  47. Lovász, L., Young, N.: Lecture notes on evasiveness of graph properties. Technical Report TR–317–91, Princeton University, Computer Science Department (1991)

    Google Scholar 

  48. Marko, S., Ron, D.: Distance approximation in bounded-degree and general sparse graphs. Transactions on Algorithms 5(2), Article no. 22 (2009)

    Google Scholar 

  49. Mihail, M.: Conductance and convergence of Markov chains– A combinatorial treatment of expanders. In: 30th FOCS, pp. 526–531 (1989)

    Google Scholar 

  50. Nachmias, A., Shapira, A.: Testing the expansion of a graph. TR07-118, ECCC (2007)

    Google Scholar 

  51. Orenstein, Y.: Testing properties of directed graphs. Master’s thesis, School of Electrical Engineering (2010)

    Google Scholar 

  52. Parnas, M., Ron, D.: Testing the diameter of graphs. Random Structures and Algorithms 20(2), 165–183 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  53. Parnas, M., Ron, D., Rubinfeld, R.: Tolerant Property Testing and Distance Approximation. Journal of Computer and System Sciences 72(6), 1012–1042 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  54. Raskhodnikova, S., Smith, A.: A note on adaptivity in testing properties of bounded-degree graphs. ECCC, TR06-089 (2006)

    Google Scholar 

  55. Ron, D.: Algorithmic and Analysis Techniques in Property Testing. Foundations and Trends in TCS 5(2), 73–205 (2010)

    MathSciNet  MATH  Google Scholar 

  56. Rubinfeld, R., Sudan, M.: Robust characterization of polynomials with applications to program testing. SIAM Journal on Computing 25(2), 252–271 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  57. E. Szemeredi. Regular partitions of graphs. In: Proceedings, Collogue Inter. CNRS, pp. 399–401 (1978)

    Google Scholar 

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Goldreich, O. (2010). Introduction to Testing Graph Properties. In: Goldreich, O. (eds) Property Testing. Lecture Notes in Computer Science, vol 6390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16367-8_7

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  • DOI: https://doi.org/10.1007/978-3-642-16367-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16366-1

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