no code implementations • 11 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
no code implementations • 11 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