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Journals and Conferences
We prove that it is NP-hard to dissect one simple orthogonal polygon into another using a given number of pieces, as is approximating the fewest pieces to within a factor of 1 + 1/1080 − ε.
Clickomania is a classic computer puzzle game (also known as SameGame, Chain-Shot!, and Swell-Foop, among other names). Originally developed by Kuniaki “Morisuke” Moribe under the name Chain-Shot! for the Fujitsu FM-8, and announced in the November 1985 issue of ASCII Monthly magazine, it has since been made available for a variety of digital platforms… (More)
In this paper, we introduce a new problem called Tree-Residue Vertex-Breaking (TRVB): given a multigraph G some of whose vertices are marked “breakable,” is it possible to convert G into a tree via a sequence of “vertex-breaking” operations (disconnecting the edges at a degree-k breakable vertex by replacing that vertex with k degree-1 vertices)? We… (More)
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 with missing stickers is NP-complete. We prove this result first for the simpler case of the Rubik’s Square—an n× n× 1… (More)
The 15 puzzle is a classic reconfiguration puzzle with fifteen uniquely labeled unit squares within a 4× 4 board in which the goal is to slide the squares (without ever overlapping) into a target configuration. By generalizing the puzzle to an n× n board with n − 1 squares, we can study the computational complexity of problems related to the puzzle; in… (More)
Shakashaka, like Sudoku, is a pencil-and-paper puzzle. In this paper we show that Shakashaka is NP-complete in the case of numberless black squares.
In 2007, Arkin et al.  initiated a systematic study of the complexity of the Hamiltonian cycle problem on square, triangular, or hexagonal grid graphs, restricted to polygonal, thin, superthin, degree-bounded, or solid grid graphs. They solved many combinations of these problems, proving them either polynomially solvable or NP-complete, but left three… (More)