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.
In REF , the authors proved matching upper and lower bounds of Θ * ( √ m d) for the problem of sampling an edge from an almost uniform distribution in an arbitrary graph using degree, neighbor, and pair queries.
On Sampling Edges Almost Uniformly
ArXiv
ArXiv
Computer Science Mathematics