Sarah Eisenstat
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Who needs crossings?: Noncrossing linkages are universal, and deciding (global) rigidity is hard Open
We exactly settle the complexity of graph realization, graph rigidity, and graph global rigidity as applied to three types of graphs: "globally noncrossing" graphs, which avoid crossings in all of their configurations; matchstick graphs, w…
Solving the Rubik's Cube Optimally is NP-complete Open
In this paper, we prove that optimally solving an n × n × n Rubik’s Cube is NP-complete by reducing from the Hamiltonian Cycle problem in square grid graphs. This improves the previous result that optimally solving an n×n×n Rubik’s Cube wi…
Solving the Rubik's Cube Optimally is NP-complete Open
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. This improves the previous result that optimally solving an $n \times…
View article: Total Tetris: Tetris with Monominoes, Dominoes, Trominoes, Pentominoes,...
Total Tetris: Tetris with Monominoes, Dominoes, Trominoes, Pentominoes,... Open
We consider variations on the classic video game Tetris where pieces are k-ominoes instead of the usual tetrominoes (k=4), as popularized by the video games ntris and Pentris. We prove that it is NP-complete to survive or clear a given ini…
Who Needs Crossings? Hardness of Plane Graph Rigidity Open
We exactly settle the complexity of graph realization, graph rigidity, and graph global rigidity as applied to three types of graphs: "globally noncrossing" graphs, which avoid crossings in all of their configurations; matchstick graphs, w…
Programming Biomolecules That Fold Greedily During Transcription Open
We introduce and study the computational power of Oritatami, a theoretical model to explore greedy molecular folding, by which a molecule begins to fold before awaiting the end of its production. This model is inspired by a recent experime…