We consider the problem of sampling an edge almost uniformly from an unknown graph, G = (V, E). Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries. We describe an algorithm that returns a random edge e ∈ E usingÕ(n/ √ εm) queries in expectation, where n = |V | is the number of vertices, and m = |E| is the number of edges, such that each edge e is sampled with probability (1 ± ε)/m. We prove that our algorithm is optimal in the sense that any algorithm that samples an edge from an almost-uniform distribution must perform Ω(n/ √ m) queries.
The related problem of sampling edges from an almost-uniform distribution was recently studied by Eden and Rosenbaum in REF .
On Sampling Edges Almost Uniformly
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Computer Science Mathematics