## Abstract

Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the number of edges. An algorithm for pointwise ε-approximate edge sampling with complexity O(n/√εm) has been given by Eden and Rosenbaum [SOSA 2018]. This has been later improved by Tětek and Thorup [STOC 2022] to O(nlog(ε^{−1})/√m). At the same time, Ω(n/√m) time is necessary. We close the problem, by giving an algorithm with complexity O(n/√m) for the task of sampling an edge exactly uniformly.

Original language | English |
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Title of host publication | Proceedings - 2023 SIAM Symposium on Simplicity in Algorithms, SOSA 2023 |

Editors | Telikepalli Kavitha, Kurt Mehlhorn |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 253-260 |

Number of pages | 8 |

ISBN (Electronic) | 9781611977585 |

State | Published - 2023 |

Event | 2023 SIAM Symposium on Simplicity in Algorithms, SOSA 2023 - Florence, Italy Duration: 23 Jan 2023 → 25 Jan 2023 |

### Publication series

Name | Proceedings - 2023 SIAM Symposium on Simplicity in Algorithms, SOSA 2023 |
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### Conference

Conference | 2023 SIAM Symposium on Simplicity in Algorithms, SOSA 2023 |
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Country/Territory | Italy |

City | Florence |

Period | 23/01/23 → 25/01/23 |

### Bibliographical note

Publisher Copyright:Copyright © 2023 by SIAM.