Related papers: ZHED is NP-complete
Seidel's switching is a graph operation which makes a given vertex adjacent to precisely those vertices to which it was non-adjacent before, while keeping the rest of the graph unchanged. Two graphs are called switching-equivalent if one…
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we formalize the pile shuffle and investigate its capabilities as a sorting device. Our study is novel in that we consider pile shuffle in three…
We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding…
Jigsaw puzzles are typically labeled with their finished area and number of pieces. With this information, is it possible to estimate the area required to lay each piece flat before assembly? We derive a simple formula based on…
A formula is presented for designing zero-determinant(ZD) strategies of general finite games, which have $n$ players and players can have different numbers of strategies. To this end, using semi-tensor product (STP) of matrices, the profile…
We show that the problem of covering a set of points in the plane with a minimum number of guillotine cuts is NP-complete. To that end, first we present a new NP-completeness proof for the problem of covering points with disjoint line…
In this document, we collected the most important complexity results of tilings. We also propose a definition of a so-called deterministic set of tile types, in order to capture deterministic classes without the notion of games. We also…
We prove NP-hardness and #P-hardness of Tetris clearing (clearing an initial board using a given sequence of pieces) with the Super Rotation System (SRS), even when the pieces are limited to any two of the seven Tetris piece types. This…
Our earlier article proved that if $n > 1$ translates of sublattices of $Z^d$ tile $Z^d$, and all the sublattices are Cartesian products of arithmetic progressions, then two of the tiles must be translates of each other. We re-prove this…
We analyze the puzzle video game This Game Is Not Going To Load Itself, where the player routes data packets of three different colors from given sources to given sinks of the correct color. Given the sources, sinks, and some previously…
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…
We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…
This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
We show that packing axis-aligned unit squares into a simple polygon $P$ is NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with half-integer coordinates. It has been known since the early 80s that packing unit…
We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given $n$ square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of…
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual…
A formal n-square is the set of positions in an square matrix of size n. A shuffle of a formal n-square consists of independent rotations of each row and of each column. A key result turns out to be valid at least for n <= 34 and n = 37:…
We prove that the quiver problem is NP complete.
A perfect matching cut is a perfect matching that is also a cutset, or equivalently a perfect matching containing an even number of edges on every cycle. The corresponding algorithmic problem, Perfect Matching Cut, is known to be…