@inproceedings{320154e0314c469fa16bd3ef71098691,

title = "Insertion-Only Dynamic Connectivity in General Disk Graphs",

abstract = "Let S ⊆ R2 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(log6 n) expected amortized insertion time. We also show that the same approach can be used for arbitrary intersection graphs.",

author = "Haim Kaplan and Katharina Klost and Kristin Knorr and Wolfgang Mulzer and Liam Roditty",

note = "Publisher Copyright: Copyright {\textcopyright} 2024 by SIAM.; 7th SIAM Symposium on Simplicity in Algorithms, SOSA 2024 ; Conference date: 08-01-2024 Through 10-01-2024",

year = "2024",

language = "الإنجليزيّة",

series = "2024 Symposium on Simplicity in Algorithms, SOSA 2024",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

pages = "299--305",

editor = "Merav Parter and Seth Pettie",

booktitle = "2024 Symposium on Simplicity in Algorithms, SOSA 2024",

address = "الولايات المتّحدة",

}