An Expansion Tester for Bounded Degree Graphs

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 εfar from any graph with expansion α with degree bound d, where α < α is a function of α. For edge expansion, we obtain α = Ω(α2 d ), and for vertex expansion, we obtain α = Ω(α2 d2 ). In either case, the algorithm runs in time ˜O(n(1+µ)/2 d2 εα2 ) for any given constant µ > 0.

• Type: Journal
• Year: 2011
• Where: SIAMCOMP
• Authors: Satyen Kale, C. Seshadhri
• Keywords: Degree Model, Formal Methods, Graph, SIAMCOMP 2011, Vertex