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
no code implementations • 7 Mar 2016 • Jean-Francois Baffier, Man-Kwun Chiu, Yago Diez, Matias Korman, Valia Mitsou, André van Renssen, Marcel Roeloffzen, Yushi Uno
On the positive side, we show that the decision version of the problem---to decide whether or not numbers from $1$ through $n$ can be played for every color---can be solved in (almost) linear time for some restricted cases.
Discrete Mathematics Computational Complexity