Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6650))

  • 1397 Accesses

Abstract

This article documents two programmatic comments regarding testing graph properties, which I made during the Dagstuhl workshop on Sublinear-Time Algorithms (July 2005). The first comment advocates paying more attention to the dependence of the tester’s complexity on the proximity parameter. The second comment advocates paying more attention to the question of testing general graphs (rather than dense or bounded-degree ones). In addition, this article includes a suggestion to view and discuss property testing within the framework of promise problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  6. Alon, N., Shapira, A.: A Characterization of the (natural) Graph Properties Testable with One-Sided. In: 46th FOCS (2005) (to appear)

    Google Scholar 

  7. Alon, N., Shapira, A.: A Separation Theorem in Property Testing (2004) (unpublished manuscript)

    Google Scholar 

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

    Google Scholar 

  9. 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 

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

    Google Scholar 

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

    Chapter  Google Scholar 

  12. 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 

  13. Fischer, E.: The art of uninformed decisions: A primer to property testing. Bulletin of the European Association for Theoretical Computer Science 75, 97–126 (2001)

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  15. Goldreich, O.: Introduction to Testing Graph Properties. In: Goldreich, O., et al.: Studies in Complexity and Cryptography. LNCS, vol. 6650, pp. 549–556. Springer, Heidelberg (2011)

    Google Scholar 

  16. Goldreich, O.: On Promise Problems. In: memory of Shimon Even (1935–2004). ECCC, TR05-018 (January 2005)

    Google Scholar 

  17. Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. Journal of the ACM, 653–750 (July 1998)

    Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  21. Goldreich, O., Ron, D.: Approximating Average Parameters of Graphs. In: ECCC, TR05-073 (July 2005)

    Google Scholar 

  22. Goldreich, O., Ron, D.: Algorithmic Aspects of Property Testing in the Dense Graphs Model. In: ECCC, TR08-039 (2008)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  24. Gonen, M., Ron, D.: On the Benefits 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)

    Chapter  Google Scholar 

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

    Google Scholar 

  26. 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 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  29. 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 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Goldreich, O. (2011). Contemplations on Testing Graph Properties. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22670-0_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22669-4

  • Online ISBN: 978-3-642-22670-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics