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
1 code implementation • 26 Apr 2018 • Zachary Abel, Jeffrey Bosboom, Michael Coulombe, Erik D. Demaine, Linus Hamilton, Adam Hesterberg, Justin Kopinsky, Jayson Lynch, Mikhail Rudoy, Clemens Thielen
We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness.
Computational Complexity
no code implementations • 21 Jun 2017 • Erik D. Demaine, Sarah Eisenstat, Mikhail Rudoy
In this paper, we prove that optimally solving an $n \times n \times n$ Rubik's Cube is NP-complete by reducing from the Hamiltonian Cycle problem in square grid graphs.
Computational Complexity Computational Geometry Combinatorics F.1.3