Edge Estimation with Independent Set Oracles

We study the task of estimating the number of edges in a graph, where the access to the graph is provided via 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, using (i) polylog(n) bipartite independent set queries or (ii) n2/3 polylog(n) independent set queries.

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