Search Results for author: Oswin Aichholzer

Found 2 papers, 0 papers with code

Hardness of Token Swapping on Trees

no code implementations11 Mar 2021 Oswin Aichholzer, Erik D. Demaine, Matias Korman, Jayson Lynch, Anna Lubiw, Zuzana Mas, Mikhail Rudoy, Virginia Vassilevska Williams, Nicole Wein

We also show limitations on approximation of sequential token swapping on trees: we identify a broad class of algorithms that encompass all three known polynomial-time algorithms that achieve the best known approximation factor (which is $2$) and show that no such algorithm can achieve an approximation factor less than $2$.

Motion Planning Data Structures and Algorithms Computational Complexity

On Compatible Matchings

no code implementations11 Jan 2021 Oswin Aichholzer, Alan Arroyo, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, Birgit Vogtenhuber

We show that for any two labeled convex sets of $n$ points there exists a compatible matching with $\lfloor \sqrt {2n}\rfloor$ edges.

Computational Geometry

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