Insertion-Only Dynamic Connectivity in General Disk Graphs

Haim Kaplan, Katharina Klost, Kristin Knorr, Wolfgang Mulzer, Liam Roditty

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publication2024 Symposium on Simplicity in Algorithms, SOSA 2024
EditorsMerav Parter, Seth Pettie
PublisherSociety for Industrial and Applied Mathematics Publications
Pages299-305
Number of pages7
ISBN (Electronic)9781713887171
StatePublished - 2024
Event7th SIAM Symposium on Simplicity in Algorithms, SOSA 2024 - Alexandria, United States
Duration: 8 Jan 202410 Jan 2024

Publication series

Name2024 Symposium on Simplicity in Algorithms, SOSA 2024

Conference

Conference7th SIAM Symposium on Simplicity in Algorithms, SOSA 2024
Country/TerritoryUnited States
CityAlexandria
Period8/01/2410/01/24

Bibliographical note

Publisher Copyright:
Copyright © 2024 by SIAM.

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