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Link to original content: https://doi.org/10.1007/978-3-642-16367-8_9
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Sublinear Graph Approximation Algorithms

  • Chapter
Property Testing

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

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Abstract

We survey the recent research on algorithms that approximate the optimal solution size for problems such as vertex cover, maximum matching, and dominating set. Techniques developed for these problems have found applications in property testing in the bounded-degree graph model.

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References

  1. Chazelle, B., Rubinfeld, R., Trevisan, L.: Approximating the minimum spanning tree weight in sublinear time. SIAM J. Comput. 34(6), 1370–1379 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Parnas, M., Ron, D.: Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms. Theor. Comput. Sci. 381(1-3), 183–196 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kuhn, F., Moscibroda, T., Wattenhofer, R.: The price of being near-sighted. In: SODA, pp. 980–989 (2006)

    Google Scholar 

  4. Marko, S., Ron, D.: Approximating the distance to properties in bounded-degree and general sparse graphs. ACM Transactions on Algorithms 5(2) (2009)

    Google Scholar 

  5. Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput. 15(4), 1036–1053 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  6. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)

    MATH  Google Scholar 

  7. Nguyen, H.N., Onak, K.: Constant-time approximation algorithms via local improvements. In: FOCS, pp. 327–336 (2008)

    Google Scholar 

  8. Yoshida, Y., Yamamoto, M., Ito, H.: An improved constant-time approximation algorithm for maximum matchings. In: STOC, pp. 225–234 (2009)

    Google Scholar 

  9. Hopcroft, J.E., Karp, R.M.: An n 5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2(4), 225–231 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  10. Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9(3), 256–278 (1974)

    Article  MATH  Google Scholar 

  11. Lovász, L.: On the ratio of optimal integral and fractional covers. Discrete Mathematics 13, 383–390 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  12. Alon, N.: On constant time approximation of parameters of bounded degree graphs

    Google Scholar 

  13. Elek, G.: L 2-spectral invariants and convergent sequences of finite graphs. Journal of Functional Analysis 254(10), 2667–2689 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lipton, R.J., Tarjan, R.E.: A separator theorem for planar graphs. SIAM Journal on Applied Mathematics 36, 177–189 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  15. Alon, N., Seymour, P.D., Thomas, R.: A separator theorem for graphs with an excluded minor and its applications. In: STOC, pp. 293–299 (1990)

    Google Scholar 

  16. Czumaj, A., Shapira, A., Sohler, C.: Testing hereditary properties of nonexpanding bounded-degree graphs. SIAM J. Comput. 38(6), 2499–2510 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hassidim, A., Kelner, J.A., Nguyen, H.N., Onak, K.: Local graph partitions for approximation and testing. In: FOCS (2009)

    Google Scholar 

  18. Elek, G.: Parameter testing with bounded degree graphs of subexponential growth. arXiv:0711.2800v3 (2009)

    Google Scholar 

  19. Goldreich, O., Ron, D.: Property testing in bounded degree graphs. Algorithmica 32(2), 302–343 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  20. Benjamini, I., Schramm, O., Shapira, A.: Every minor-closed property of sparse graphs is testable. In: STOC, pp. 393–402 (2008)

    Google Scholar 

  21. Robertson, N., Seymour, P.D.: Graph minors. XX. Wagner’s conjecture. Journal of Combinatorial Theory, Series B 92(2), 325–357 (2004); Special Issue Dedicated to Professor W.T. Tutte

    Article  MathSciNet  MATH  Google Scholar 

  22. Alon, N., Shapira, A.: A characterization of the (natural) graph properties testable with one-sided error. SIAM J. Comput. 37(6), 1703–1727 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    Krzysztof Onak

Authors
  1. Krzysztof Onak
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Editors and Affiliations

  1. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, 76100, Rehovot, Israel

    Oded Goldreich

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Onak, K. (2010). Sublinear Graph Approximation Algorithms. 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_9

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  • DOI: https://doi.org/10.1007/978-3-642-16367-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16366-1

  • Online ISBN: 978-3-642-16367-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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