Related papers: ZHED is NP-complete
The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and…
We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…
A dyadic tile of order n is any rectangle obtained from the unit square by n successive bisections by horizontal or vertical cuts. Let each dyadic tile of order n be available with probability p, independently of the others. We prove that…
In [BNRR], it was shown that tiling of general regions with two rectangles is NP-complete, except for a few trivial special cases. In a different direction, R\'emila showed that for simply connected regions by two rectangles, the…
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…
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z}^d$ which tiles that lattice by translations, in fact tiles periodically. In this work we disprove this conjecture for sufficiently large $d$, which also…
In this article we study linear complementarity problem with hidden $Z$-matrix. We extend the results of Fiedler and Pt{\'a}k for the linear system in complementarity problem using game theoretic approach. We establish a result related to…
Holzer and Holzer (Discrete Applied Mathematics 144(3):345--358, 2004) proved that the Tantrix(TM) rotation puzzle problem is NP-complete. They also showed that for infinite rotation puzzles, this problem becomes undecidable. We study the…
We study the complexity of the popular one player combinatorial game known as Flood-It. In this game the player is given an n by n board of tiles where each tile is allocated one of c colours. The goal is to make the colours of all tiles…
Continuing results from JCDCGGG 2016 and 2017, we solve several new cases of the simple foldability problem -- deciding which crease patterns can be folded flat by a sequence of (some model of) simple folds. We give new efficient algorithms…
We investigate the complexity of a puzzle that turns out to be NL-complete.
Let $T$ be a tile in $\mathbb{Z}^n$, meaning a finite subset of $\mathbb{Z}^n$. It may or may not tile $\mathbb{Z}^n$, in the sense of $\mathbb{Z}^n$ having a partition into copies of $T$. However, we prove that $T$ does tile $\mathbb{Z}^d$…
To generalize complementarities for games, we introduce some conditions weaker than quasisupermodularity and the single crossing property. We prove that the Nash equilibria of a game satisfying these conditions form a nonempty complete…
We are going to show that some variants of a puzzle called Pull in which the boxes have handles (i.e. we can only pull the boxes in certain directions) are NP-hard
Concavity and its refinements underpin tractability in multiplayer games, where players independently choose actions to maximize their own payoffs which depend on other players' actions. In concave games, where players' strategy sets are…
We investigate the reconfiguration of $n$ blocks, or "tokens", in the square grid using "line pushes". A line push is performed from one of the four cardinal directions and pushes all tokens that are maximum in that direction to the…
We characterize the complexity of the PATS problem for patterns of fixed height and color count in variants of the model where seed glues are either chosen or fixed and identical (so-called non-uniform and uniform variants). We prove that…
Edge-matching problems, also called edge matching puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem…
We study the puzzle graphs of hexagonal sliding puzzles of various shapes and with various numbers of holes. The puzzle graph is a combinatorial model which captures the solvability and the complexity of sequential mechanical puzzles.…
Some classical graph problems such as finding minimal spanning tree, shortest path or maximal flow can be done efficiently. We describe slight variations of such problems which are shown to be NP-complete. Our proofs use straightforward…