TY - GEN

T1 - Insertion-Only Dynamic Connectivity in General Disk Graphs

AU - Kaplan, Haim

AU - Klost, Katharina

AU - Knorr, Kristin

AU - Mulzer, Wolfgang

AU - Roditty, Liam

N1 - Publisher Copyright:
Copyright © 2024 by SIAM.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85191760834&partnerID=8YFLogxK

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AN - SCOPUS:85191760834

T3 - 2024 Symposium on Simplicity in Algorithms, SOSA 2024

SP - 299

EP - 305

BT - 2024 Symposium on Simplicity in Algorithms, SOSA 2024

A2 - Parter, Merav

A2 - Pettie, Seth

PB - Society for Industrial and Applied Mathematics (SIAM)

T2 - 7th SIAM Symposium on Simplicity in Algorithms, SOSA 2024

Y2 - 8 January 2024 through 10 January 2024

ER -