Edge Estimation with Independent Set Oracles

Paul Beame; Sariel Har-Peled; Sivaramakrishnan Natarajan Ramamoorthy; Cyrus Rashtchian; Makrand Sinha

Edge Estimation with Independent Set Oracles

Data Structures and Algorithms 2020-03-13 v4

Authors: Paul Beame , Sariel Har-Peled , Sivaramakrishnan Natarajan Ramamoorthy , Cyrus Rashtchian , Makrand Sinha

Abstract

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) $\mathrm{polylog}(n)$ bipartite independent set queries, or (ii) ${n}^{2/3} \cdot\mathrm{polylog}(n)$ independent set queries.

Keywords

graph theory graph algorithms planar graph drawing

Cite

@article{arxiv.1711.07567,
  title  = {Edge Estimation with Independent Set Oracles},
  author = {Paul Beame and Sariel Har-Peled and Sivaramakrishnan Natarajan Ramamoorthy and Cyrus Rashtchian and Makrand Sinha},
  journal= {arXiv preprint arXiv:1711.07567},
  year   = {2020}
}

Comments

A preliminary version appeared in the proceedings of ITCS 2018

Edge Estimation with Independent Set Oracles

Abstract

Keywords

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