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On Compatible Matchings
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
Hardness of Token Swapping on Trees
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
