Paper
Optimal non-adaptive algorithm for edge estimation
Authors
Arijit Bishnu, Debarshi Chanda, Buddha Dev Das, Arijit Ghosh, Gopinath Mishra
Abstract
We present a simple nonadaptive randomized algorithm that estimates the number of edges in a simple, unweighted, undirected graph, possibly containing isolated vertices, using only degree and random edge queries. For an -vertex graph, our method requires only queries, achieving sublinear query complexity. The algorithm independently samples a set of vertices and queries their degrees, and also independently samples a set of edges, using the answers to these queries to estimate the total number of edges in the graph. We further prove a matching lower bound, establishing the optimality of our algorithm and resolving the non-adaptive query complexity of this problem with respect to degree and random-edge queries.