Edge Estimation with Independent Set Oracles

We study the problem of estimating the number of edges in a graph with access to only an independent set oracle. Independent set queries draw motivation from group testing and have applications to the complexity of decision versus counting problems. We give two algorithms to estimate the number of edges in an $n$-vertex graph: one that uses only $\mathrm{polylog}(n)$ bipartite independent set queries, and another one that uses ${n}^{2/3}\cdot \mathrm{polylog}(n)$ independent set queries.