Related papers: On Grid Graph Reachability and Puzzle Games
Machine playtesting tools and game moment search engines require exposure to the diversity of a game's state space if they are to report on or index the most interesting moments of possible play. Meanwhile, mobile app distribution services…
Living beings are able to solve a wide variety of problems that they encounter rarely or only once. Without the benefit of extensive and repeated experience with these problems, they can solve them in an ad-hoc manner. We call this capacity…
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of…
Games are often designed to shape player behavior in a desired way; however, it can be unclear how design decisions affect the space of behaviors in a game. Designers usually explore this space through human playtesting, which can be…
Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a…
The localization game is a variant of the game of Cops and Robber in which the robber is invisible and moves between adjacent vertices, but the cops can probe any $k$ vertices of the graph to obtain the distance between probed vertices and…
We consider monotonicity problems for graph searching games. Variants of these games - defined by the type of moves allowed for the players - have been found to be closely connected to graph decompositions and associated width measures such…
Multi-Agent Path Finding (MAPF) is a fundamental motion coordination problem arising in multi-agent systems with a wide range of applications. The problem's intractability has led to extensive research on improving the scalability of…
We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the…
The mathematical structure of the widely popular Sudoku puzzles is akin to typical hard constraint satisfaction problems that lie at the heart of many applications, including protein folding and the general problem of finding the ground…
Understanding player strategies is a key question when analyzing player behavior both for academic researchers and industry practitioners. For game designers and game user researchers, it is important to gauge the distance between intended…
To enable automated software testing, the ability to automatically navigate to a state of interest and to explore all, or at least sufficient number of, instances of such a state is fundamental. When testing a computer game the problem has…
Being able to reach any desired location in the environment can be a valuable asset for an agent. Learning a policy to navigate between all pairs of states individually is often not feasible. An all-goals updating algorithm uses each…
We analyze the computational complexity of motion planning through local "input/output" gadgets with separate entrances and exits, and a subset of allowed traversals from entrances to exits, each of which changes the state of the gadget and…
Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…
We introduce a new abstract graph game, Swap Planarity, where the goal is to reach a state without edge intersections and a move consists of swapping the locations of two vertices connected by an edge. We analyze this puzzle game using…
Recent superhuman results in games have largely been achieved in a variety of zero-sum settings, such as Go and Poker, in which agents need to compete against others. However, just like humans, real-world AI systems have to coordinate and…
We study a game of pursuit and evasion introduced by Seager in 2012, in which a cop searches the robber from outside the graph, using distance queries. A graph on which the cop wins is called locatable. In her original paper, Seager asked…
We study versions of cop and robber pursuit-evasion games on the visibility graphs of polygons, and inside polygons with straight and curved sides. Each player has full information about the other player's location, players take turns, and…
Value methods for solving stochastic games with partial observability model the uncertainty about states of the game as a probability distribution over possible states. The dimension of this belief space is the number of states. For many…