## Abstract

Let S ⊆ R^{2} be a set of n sites in the plane, so that every site s ∈ S has an associated radius rs > 0. Let D(S) be the disk intersection graph defined by S, i.e., the graph with vertex set S and an edge between two distinct sites s, t ∈ S if and only if the disks with centers s, t and radii rs, rt intersect. Our goal is to design data structures that maintain the connectivity structure of D(S) as S changes dynamically over time. We consider the incremental case, where new sites can be inserted into S. While previous work focuses on data structures whose running time depends on the ratio between the smallest and the largest site in S, we present a data structure with O(α(n)) amortized query time and O(log^{6} n) expected amortized insertion time. We also show that the same approach can be used for arbitrary intersection graphs.

Original language | English |
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Title of host publication | 2024 Symposium on Simplicity in Algorithms, SOSA 2024 |

Editors | Merav Parter, Seth Pettie |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 299-305 |

Number of pages | 7 |

ISBN (Electronic) | 9781713887171 |

State | Published - 2024 |

Event | 7th SIAM Symposium on Simplicity in Algorithms, SOSA 2024 - Alexandria, United States Duration: 8 Jan 2024 → 10 Jan 2024 |

### Publication series

Name | 2024 Symposium on Simplicity in Algorithms, SOSA 2024 |
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### Conference

Conference | 7th SIAM Symposium on Simplicity in Algorithms, SOSA 2024 |
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Country/Territory | United States |

City | Alexandria |

Period | 8/01/24 → 10/01/24 |

### Bibliographical note

Publisher Copyright:Copyright © 2024 by SIAM.