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Revision #1 to TR07-076 | 29th November 2007 00:00

#### Testing Expansion in Bounded Degree Graphs

Revision #1
Authors: Satyen Kale, Satyen Kale, C. Seshadhri
Accepted on: 29th November 2007 00:00
Keywords:

Abstract:

We consider the problem of testing graph expansion (either vertex or edge) in the bounded degree model~\cite{GR}. We give a property tester that given a graph with degree bound $d$, an expansion bound $\alpha$, and a parameter $\epsilon > 0$, accepts the graph with high probability if its expansion is more than $\alpha$, and rejects it with high probability if it is $\epsilon$-far from a graph with expansion $\alpha'$ with degree bound $d$, where $\alpha' < \alpha$ is a function of $\alpha$. 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 $\mu > 0$.

### Paper:

TR07-076 | 25th July 2007 00:00

#### Testing Expansion in Bounded Degree Graphs

TR07-076
We consider the problem of testing graph expansion in the bounded degree model. We give a property tester that given a graph with degree bound $d$, an expansion bound $\alpha$, and a parameter $\epsilon > 0$, accepts the graph with high probability if its expansion is more than $\alpha$, and rejects it with high probability if it is $\epsilon$-far from any graph (with degree bound $2d$) with expansion $\Omega(\alpha^2)$. The algorithm runs in time $\tilde{O}(\frac{n^{0.5 + \mu}d^2}{\epsilon\alpha^2})$ for any given constant $\mu > 0$.