13 papers
A Strongly-Subquadratic -Approximation for the Fréchet Distance for Paths in Metric Spaces
Thijs van der Horst, Tim Ophelders
The Fréchet distance is a well-studied distance measure for paths in a metric space. It is mostly studied for paths in -dimensional Euclidean space. Here, computing the Fréche…
Which Vertical Graphs are Non VPHT Reconstructible?
Jette Gutzeit, Kalani Kistler, Tim Ophelders +1
The verbose persistent homology transform (VPHT) is a topological summary of shapes in Euclidean space. Assuming general position, the VPHT is injective, meaning shapes can be reco…
Reconfiguration of Squares Using a Constant Number of Moves Each
Thijs van der Horst, Maarten Löffler, Tim Ophelders +1
Multi-robot motion planning is a hard problem. We investigate restricted variants of the problem where square robots are allowed to slide over an arbitrary curve to a new position…
Computing the Fréchet Distance When Just One Curve is -Packed: A Simple Almost-Tight Algorithm
Jacobus Conradi, Ivor van der Hoog, Thijs van der Horst +1
We study approximating the continuous Fréchet distance of two curves with complexity and , under the assumption that only one of the two curves is -packed. Driemel, Har{…
Locally Correct Interleavings between Merge Trees
Thijs Beurskens, Tim Ophelders, Bettina Speckmann +1
Temporal sequences of terrains arise in various application areas. To analyze them efficiently, one generally needs a suitable abstraction of the data as well as a method to compar…
Counting Triangulations of Fixed Cardinal Degrees
Erin Chambers, Tim Ophelders, Anna Schenfisch +1
A fixed set of vertices in the plane may have multiple planar straight-line triangulations in which the degree of each vertex is the same. As such, the degree information does not…