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Found 8 papers, 3 papers with code
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
1 x 1 Rush Hour with Fixed Blocks is PSPACE-complete
Consider $n^2-1$ unit-square blocks in an $n \times n$ square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable -- a variation of Rush Hour with only $1 \times 1$ cars and fixed blocks.
Computational Complexity Computational Geometry
Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible
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
Polyhedral Characterization of Reversible Hinged Dissections
We prove that two polygons $A$ and $B$ have a reversible hinged dissection (a chain hinged dissection that reverses inside and outside boundaries when folding between $A$ and $B$) if and only if $A$ and $B$ are two noncrossing nets of a common polyhedron.
Computational Geometry Metric Geometry
Solving the Rubik's Cube Optimally is NP-complete
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
Structural Sparsity of Complex Networks: Bounded Expansion in Random Models and Real-World Graphs
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis.
Social and Information Networks Discrete Mathematics Data Structures and Algorithms Physics and Society
The complexity of UNO
This paper investigates the popular card game UNO from the viewpoint of algorithmic combinatorial game theory.
Discrete Mathematics Computational Complexity G.2; F.1
Tetris is Hard, Even to Approximate
In the popular computer game of Tetris, the player is given a sequence of tetromino pieces and must pack them into a rectangular gameboard initially occupied by a given configuration of filled squares; any completely filled row of the gameboard is cleared and all pieces above it drop by one row.
Computational Complexity Computational Geometry Discrete Mathematics F.1.3; F.2.2; G.2.1; K.8.0
