We present a sublinear time algorithm that allows one to sample multiple edges from a distribution that is pointwise \epsilon-close to the uniform distribution, in an amortized-efficient fashion. We consider the adjacency list query model, where access to a graph G is given via degree and neighbor queries. The problem of sampling a single edge in this model has been raised by Eden and Rosenbaum (SOSA 18). Let n and m denote the number of vertices and edges of G, respectively. Eden and Rosenbaum provided upper and lower bounds of \Theta^*(n/\sqrt m) for sampling a single edge in general graphs (where O^*(\cdot) suppresses poly \poly (1/\epsilon) and poly \poly (\log n) dependencies). We ask whether the query complexity lower bound for sampling a single edge can be circumvented when multiple samples are required. That is, can we get an improved amortized per-sample cost if we allow a preprocessing phase? We answer in the affirmative. We present an algorithm that, if one knows the number of required samples q in advance, has an overall cost that is sublinear in q, namely, O^*(\sqrt q \cdot(n/\sqrt m)), which is strictly preferable to O^*(q\cdot (n/\sqrt m)) cost resulting from q invocations of the algorithm by Eden and Rosenbaum  .
We present a sublinear time algorithm that allows one to sample multiple edges from a distribution that is pointwise \epsilon-close to the uniform distribution, in an amortized-efficient fashion. We consider the adjacency list query model, where access to a graph G is given via degree and neighbor queries. The problem of sampling a single edge in this model has been raised by Eden and Rosenbaum (SOSA 18). Let n and m denote the number of vertices and edges of G, respectively. Eden and Rosenbaum provided upper and lower bounds of \Theta^*(n/\sqrt m) for sampling a single edge in general graphs (where O^*(\cdot) suppresses \poly (1/\epsilon) and \poly (\log n) dependencies). We ask whether the query complexity lower bound for sampling a single edge can be circumvented when multiple samples are required. That is, can we get an improved amortized per-sample cost if we allow a preprocessing phase? We answer in the affirmative. We present an algorithm that, if one knows the number of required samples q in advance, has an overall cost that is sublinear in q, namely, O^*(\sqrt q \cdot(n/\sqrt m)), which is strictly preferable to O^*(q\cdot (n/\sqrt m)) cost resulting from q invocations of the algorithm by Eden and Rosenbaum . Subsequent to a preliminary version of this work, T\v{e .
D
poly
D
poly
A
. Subsequent to a preliminary version of this work, T\v{e