Edge Estimation with Independent Set Oracles

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

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

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Paul Beame, Sariel Har-Peled, Sivaramakrishnan Natarajan Ramamoorthy, Cyrus Rashtchian, and Makrand Sinha. Edge Estimation with Independent Set Oracles. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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 polylog(n) bipartite independent set queries, and another one that uses n^{2/3} polylog(n) independent set queries.
  • Approximate Counting
  • Independent Set Queries
  • Sparsification
  • Importance Sampling


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