An Expansion Tester for Bounded Degree Graphs

  • Satyen Kale
  • C. Seshadhri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)

Abstract

We consider the problem of testing graph expansion (either vertex or edge) in the bounded degree model [10]. We give a property tester that given a graph with degree bound d, an expansion bound α, and a parameter ε> 0, accepts the graph with high probability if its expansion is more than α, and rejects it with high probability if it is ε-far from any graph with expansion α′ with degree bound d, where α′ < α is a function of α. For edge expansion, we obtain \(\alpha' = \Omega(\frac{\alpha^2}{d})\), and for vertex expansion, we obtain \(\alpha' = \Omega(\frac{\alpha^2}{d^2})\). In either case, the algorithm runs in time \(\tilde{O}(\frac{n^{(1+\mu)/2}d^2}{\epsilon\alpha^2})\) for any given constant μ> 0.

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References

  1. 1.
    Alon, N., Fischer, E., Newman, I., Shapira, A.: A Combinatorial Characterization of the Testable Graph Properties: it’s all about Regularity. In: Proc. 38th STOC, pp. 251–260 (2006)Google Scholar
  2. 2.
    Alon, N., Shapira, A.: A Charaterization of the (Natural) Graph Properties Testable with One-sided Error. In: Proc. 46th FOCS, pp. 429–438 (2005)Google Scholar
  3. 3.
    Czumaj, A., Sohler, C.: On Testable Properties in Bounded Degree Graphs. In: Proc. 18th SODA, pp. 494–501 (2007)Google Scholar
  4. 4.
    Czumaj, A., Sohler, C.: Testing Expansion in Bounded Degree Graphs. In: Proc. 48th FOCS, pp. 570–578 (2007)Google Scholar
  5. 5.
    Fischer, E.: The Art of Uninformed Decisions: A Primer to Property Testing. Bulletin of EATCS 75, 97–126 (2001)MATHGoogle Scholar
  6. 6.
    Goldreich, O.: Combinatorial property testing - A survey. In: Randomization Methods in Algorithm Design, pp. 45–60 (1998)Google Scholar
  7. 7.
    Goldreich, O., Goldwasser, S., Ron, D.: Property Testing and its Connection to Learning and Approximation. J. ACM 45, 653–750 (1998)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Goldreich, O., Ron, D.: Property Testing in Bounded Degree Graphs. Algorithmica 32(2), 302–343 (2002)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Goldreich, O., Ron, D.: A Sublinear Bipartiteness Property Tester for Bounded Degree Graphs. Combinatorica 19(3), 335–373 (1999)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Goldreich, O., Ron, D.: On Testing Expansion in Bounded-Degree Graphs. ECCC, TR00-020 (2000)Google Scholar
  11. 11.
    Kale, S., Seshadhri, C.: Testing Expansion in Bounded Degree Graphs. ECCC, TR07-076 (2007)Google Scholar
  12. 12.
    Nachmias, A., Shapira, A.: Testing the Expansion of a Graph ECCC, TR07-118 (2007)Google Scholar
  13. 13.
    Ron, D.: Property testing. In: Handbook on Randomization, vol. II, pp. 597–649 (2001)Google Scholar
  14. 14.
    Rubinfeld, R., Sudan, M.: Robust characterization of polynomials with applications to program testing. SIAM J. Comput. 25, 647–668 (1996)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Sinclair, A.: Algorithms for Random Generation and Counting: a Markov Chain Approach. Birkhaüser Progress In Theoretical Computer Science Series (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Satyen Kale
    • 1
  • C. Seshadhri
    • 2
  1. 1.Microsoft ResearchRedmond 
  2. 2.Dept. of Computer SciencePrinceton UniversityPrinceton

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