23 research outputs found
Trainyard is NP-Hard
Recently, due to the widespread diffusion of smart-phones, mobile puzzle
games have experienced a huge increase in their popularity. A successful puzzle
has to be both captivating and challenging, and it has been suggested that this
features are somehow related to their computational complexity \cite{Eppstein}.
Indeed, many puzzle games --such as Mah-Jongg, Sokoban, Candy Crush, and 2048,
to name a few-- are known to be NP-hard \cite{CondonFLS97,
culberson1999sokoban, GualaLN14, Mehta14a}. In this paper we consider
Trainyard: a popular mobile puzzle game whose goal is to get colored trains
from their initial stations to suitable destination stations. We prove that the
problem of determining whether there exists a solution to a given Trainyard
level is NP-hard. We also \href{http://trainyard.isnphard.com}{provide} an
implementation of our hardness reduction
Large Peg-Army Maneuvers
Despite its long history, the classical game of peg solitaire continues to
attract the attention of the scientific community. In this paper, we consider
two problems with an algorithmic flavour which are related with this game,
namely Solitaire-Reachability and Solitaire-Army. In the first one, we show
that deciding whether there is a sequence of jumps which allows a given initial
configuration of pegs to reach a target position is NP-complete. Regarding
Solitaire-Army, the aim is to successfully deploy an army of pegs in a given
region of the board in order to reach a target position. By solving an
auxiliary problem with relaxed constraints, we are able to answer some open
questions raised by Cs\'ak\'any and Juh\'asz (Mathematics Magazine, 2000). To
appreciate the combinatorial beauty of our solutions, we recommend to visit the
gallery of animations provided at http://solitairearmy.isnphard.com.Comment: Conference versio
A quantum procedure for map generation
Quantum computation is an emerging technology that promises a wide range of
possible use cases. This promise is primarily based on algorithms that are
unlikely to be viable over the coming decade. For near-term applications,
quantum software needs to be carefully tailored to the hardware available. In
this paper, we begin to explore whether near-term quantum computers could
provide tools that are useful in the creation and implementation of computer
games. The procedural generation of geopolitical maps and their associated
history is considered as a motivating example. This is performed by encoding a
rudimentary decision making process for the nations within a quantum procedure
that is well-suited to near-term devices. Given the novelty of quantum
computing within the field of procedural generation, we also provide an
introduction to the basic concepts involved.Comment: To be published in the proceedings of the IEEE Conference on Game
Lemmings is PSPACE-complete
Lemmings is a computer puzzle game developed by DMA Design and published by
Psygnosis in 1991, in which the player has to guide a tribe of lemming
creatures to safety through a hazardous landscape, by assigning them specific
skills that modify their behavior in different ways. In this paper we study the
optimization problem of saving the highest number of lemmings in a given
landscape with a given number of available skills.
We prove that the game is PSPACE-complete, even if there is only one lemming
to save, and only Builder and Basher skills are available. We thereby settle an
open problem posed by Cormode in 2004, and again by Forisek in 2010. However we
also prove that, if we restrict the game to levels in which the available
Builder skills are only polynomially many (and there is any number of other
skills), then the game is solvable in NP. Similarly, if the available Basher,
Miner, and Digger skills are polynomially many, the game is solvable in NP.
Furthermore, we show that saving the maximum number of lemmings is APX-hard,
even when only one type of skill is available, whatever this skill is. This
contrasts with the membership in P of the decision problem restricted to levels
with no "deadly areas" (such as water or traps) and only Climber and Floater
skills, as previously established by Cormode.Comment: 26 pages, 11 figure
NP-completeness of the game Kingdomino
Kingdomino is a board game designed by Bruno Cathala and edited by Blue
Orange since 2016. The goal is to place dominoes on a grid layout,
and get a better score than other players. Each domino cell has a
color that must match at least one adjacent cell, and an integer number of
crowns (possibly none) used to compute the score. We prove that even with full
knowledge of the future of the game, in order to maximize their score at
Kingdomino, players are faced with an NP-complete optimization problem
Triangle Packing on Tripartite Graphs Is Hard
The problem of finding a maximum matching on a bipartite graph is well-understood and can be solved using the augmenting path algorithm. However, the similar problem of finding a large set of vertex-disjoint triangles on tripartite graphs has not received much attention. In this paper, we define a set of vertex-disjoint triangles as a “tratching.” The problem of finding a tratching that covers all vertices of a tripartite graph can be shown to be NP-complete using a reduction from the three-dimensional matching problem. In this paper, however, we introduce a new construction that allows us to emulate Boolean circuits using tripartite graphs in order to prove that covering a given vertex subset of a tripartite graph with a tratching is NP-hard, thereby attacking the tratching problem from a new angle
Video Games as Time Machines: Video Game Nostalgia and the Success of Retro Gaming
This article conceptually integrates research on the experience of nostalgia—defined as a predominantly positive, social, and past-oriented emotion—into the fold of video game research. We emphasize the role of nostalgia as an explanation for contemporary retro gaming trends, and suggest that nostalgia towards gaming events is a necessary area of research. To those ends, we broadly review existing literature on nostalgia before specifically focusing on media-induced nostalgia, and demonstrate how theoretical and empirical observations from this work can be applied to understand video game nostalgia. In particular, we argue that engaging in older gaming experiences indirectly (via memories) and even directly (via replaying or recreating experiences) elicits nostalgia, which in turn contributes to players’ self-optimization and enhanced well-being. Moreover, as gamers and the medium mature together, nostalgic experiences with the medium are likely to become increasingly prevalent. The broad aim of this article is to offer future directions for research on video game nostalgia and provide a research agenda for research in this area
PSPACE-completeness of Pulling Blocks to Reach a Goal
We prove PSPACE-completeness of all but one problem in a large space of
pulling-block problems where the goal is for the agent to reach a target
destination. The problems are parameterized by whether pulling is optional, the
number of blocks which can be pulled simultaneously, whether there are fixed
blocks or thin walls, and whether there is gravity. We show NP-hardness for the
remaining problem, Pull?-1FG (optional pulling, strength 1, fixed blocks, with
gravity).Comment: Full version of JCDCGGG2019 paper, 22 pages, 25 figure