Let SβR2 be a set of n \emph{sites} in the plane, so
that every site sβS has an \emph{associated radius} rsβ>0. Let D(S)
be the \emph{disk intersection graph} defined by S, i.e., the graph with
vertex set S and an edge between two distinct sites s,tβS if and only
if the disks with centers s, t and radii rsβ, rtβ 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(Ξ±(n)) amortized
query time and O(log6n) expected amortized insertion time.Comment: 7 pages, 6 figures. Presented at EuroCG 2023. This version corrects a
missing log-factor in the insertion tim