# Edge Estimation with Independent Set Oracles

arXiv: https://arxiv.org/abs/1711.07567 · HTML: https://mlsanity.com/paper/1711.07567/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2017.

## Built on by (most cited first, 3 of 3)

- [Sampling a Near Neighbor in High Dimensions -- Who is the Fairest of Them All?](https://mlsanity.com/paper/2101.10905/) (2021)
- [Clustering with Non-adaptive Subset Queries](https://mlsanity.com/paper/2409.10908/) (2024)
- [Prior Knowledge Makes It Possible: From Sublinear Graph Algorithms to LLM Test-Time Methods](https://mlsanity.com/paper/2510.16609/) (2025)

## Abstract (arXiv)

We study the task 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, using (i) polylog(n) bipartite independent set queries, or (ii) n2/3 ·polylog(n) independent set queries.