## Abstract

We study the problem of estimating the number of edges of an unknown, undirected graph G = ([n], E) with access to an independent set oracle. When queried about a subset S ⊆ [n] of vertices, the independent set oracle answers whether S is an independent set in G or not. Our first main result is an algorithm that computes a (1 + ε)-approximation of the number of edges m of the graph using min(^{√}m, n/√m) · poly(log n, 1/ε) independent set queries. This improves the upper bound of min(^{√}m, n^{2}/m) · poly(log n, 1/ε) by Beame et al. [3]. Our second main result shows that min(^{√}m, n/√m)/polylog(n) independent set queries are necessary, thus establishing that our algorithm is optimal up to a factor of poly(log n, 1/∈).

Original language | English |
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Title of host publication | 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 |

Editors | Shuchi Chawla |

Publisher | Association for Computing Machinery |

Pages | 2916-2935 |

Number of pages | 20 |

ISBN (Electronic) | 9781611975994 |

State | Published - 2020 |

Externally published | Yes |

Event | 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 - Salt Lake City, United States Duration: 5 Jan 2020 → 8 Jan 2020 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 2020-January |

### Conference

Conference | 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 |
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Country/Territory | United States |

City | Salt Lake City |

Period | 5/01/20 → 8/01/20 |

### Bibliographical note

Publisher Copyright:Copyright © 2020 by SIAM

## ASJC Scopus subject areas

- Software
- General Mathematics