Chapter

Automata, Languages and Programming

Volume 5125 of the series Lecture Notes in Computer Science pp 527-538

An Expansion Tester for Bounded Degree Graphs

  • Satyen KaleAffiliated withMicrosoft Research
  • , C. SeshadhriAffiliated withDept. of Computer Science, Princeton University

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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.