An Expansion Tester for Bounded Degree Graphs

  • Satyen Kale
  • C. Seshadhri
Conference paper

DOI: 10.1007/978-3-540-70575-8_43

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)
Cite this paper as:
Kale S., Seshadhri C. (2008) An Expansion Tester for Bounded Degree Graphs. In: Aceto L., Damgård I., Goldberg L.A., Halldórsson M.M., Ingólfsdóttir A., Walukiewicz I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg

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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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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