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cs.DS2023
Dynamically Maintaining the Persistent Homology of Time Series
Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, Monika Henzinger +1
We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion…
math.CO2023
Maximum Betti numbers of Čech complexes
Herbert Edelsbrunner, János Pach
The Upper Bound Theorem for convex polytopes implies that the -th Betti number of the Čech complex of any set of points in and any radius satisfies $β_{p} = O(…
math.CO2023
Order-2 Delaunay Triangulations Optimize Angles
Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian
The local angle property of the (order-) Delaunay triangulations of a generic set in asserts that the sum of two angles opposite a common edge is less than . T…