Related papers: Trainyard is NP-Hard
Tetravex is a widely played one person computer game in which you are given $n^2$ unit tiles, each edge of which is labelled with a number. The objective is to place each tile within a $n$ by $n$ square such that all neighbouring edges are…
We prove the computational intractability of rotating and placing $n$ square tiles into a $1 \times n$ array such that adjacent tiles are compatible--either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as…
We present a new game, Dots & Polygons, played on a planar point set. Players take turns connecting two points, and when a player closes a (simple) polygon, the player scores its area. We show that deciding whether the game can be won from…
This work shows new results on the complexity of games Jelly-No and Hanano with various constraints on the size of the board and number of colours. Hanano and Jelly-No are one-player, 2D side-view puzzle games with a dynamic board…
Minesweeper is an interesting single player game based on logic, memory and guessing. Solving Minesweeper has been shown to be an NP-hard task. Deterministic solvers are the best known approach for solving Minesweeper. This project proposes…
Motivated by understanding non-strict and strict pure strategy equilibria in network anti-coordination games, we define notions of stable and, respectively, strictly stable colorings in graphs. We characterize the cases when such colorings…
LR(1) parsing was a focus of extensive research in the past 50 years. Though most fundamental mysteries have been resolved, a few remain hidden in the dark corners. The one we bumped into is the minimization of the LR(1) state machines,…
We analyze the computational complexity of solving the three "temporal rift" puzzles in the recent popular video game Final Fantasy XIII-2. We show that the Tile Trial puzzle is NP-hard and we provide an efficient algorithm for solving the…
We present a new problem called the incomplete Traveling Tournament problem, which introduces the well known Traveling Tournament Problem into the realm of incomplete round-robin tournaments. We focus on the case where teams can face each…
Ridge Rider (RR) is an algorithm for finding diverse solutions to optimization problems by following eigenvectors of the Hessian ("ridges"). RR is designed for conservative gradient systems (i.e., settings involving a single loss function),…
We classify the computational complexity of the popular video games Portal and Portal 2. We isolate individual mechanics of the game and prove NP-hardness, PSPACE-completeness, or (pseudo)polynomiality depending on the specific game…
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…
Creating robots that can perform general-purpose service tasks in a human-populated environment has been a longstanding grand challenge for AI and Robotics research. One particularly valuable skill that is relevant to a wide variety of…
We prove that a particular pushing-blocks puzzle is intractable in 2D, improving an earlier result that established intractability in 3D [OS99]. The puzzle, inspired by the game *PushPush*, consists of unit square blocks on an integer…
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…
This paper introduces the Packing While Traveling problem as a new non-linear knapsack problem. Given are a set of cities that have a set of items of distinct profits and weights and a vehicle that may collect the items when visiting all…
We study three problems related to the computational complexity of the popular game Minesweeper. The first is consistency: given a set of clues, is there any arrangement of mines that satisfies it? This problem has been known to be…
Building on the results published in arxiv:2004.12849 we present a general framework for demonstrating the NP-hardness of satisfying many genres of loop and path puzzles using a 'T-metacell' gadget. We then use this to prove the…
Designing Public Transport (PT) networks able to satisfy mobility needs of people is essential to reduce the number of individual vehicles on the road, and thus pollution and congestion. Urban sustainability is thus tightly coupled to an…
Recently, Dohrau et al. studied a zero-player game on switch graphs and proved that deciding the termination of the game is in NP $\cap$ coNP. In this short paper, we show that the search version of this game on switch graphs, i.e., the…