Related papers: On Grid Graph Reachability and Puzzle Games
Many popular puzzle and matching games have been analyzed through the lens of computational complexity. Prominent examples include Sudoku, Candy Crush, and Flood-It. A common theme among these widely played games is that their generalized…
Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
The Keke AI Competition introduces an artificial agent competition for the game Baba is You - a Sokoban-like puzzle game where players can create rules that influence the mechanics of the game. Altering a rule can cause temporary or…
Modern AAA video games feature huge game levels and maps which are increasingly hard for level testers to cover exhaustively. As a result, games often ship with catastrophic bugs such as the player falling through the floor or being stuck…
Humans excel in solving complex reasoning tasks through a mental process of moving from one idea to a related one. Inspired by this, we propose Subgoal Search (kSubS) method. Its key component is a learned subgoal generator that produces a…
In recent years, we have witnessed tremendous progress in deep reinforcement learning (RL) for tasks such as Go, Chess, video games, and robot control. Nevertheless, other combinatorial domains, such as AI planning, still pose considerable…
We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph that defines which vertex sets are…
Sudoku is a widely popular $\mathcal{NP}$-Complete combinatorial puzzle whose prospects for studying human computation have recently received attention, but the algorithmic hardness of Sudoku solving is yet largely unexplored. In this…
This study focuses on reachability problems in differential games. An improved level set method for computing reachable tubes is proposed in this paper. The reachable tube is described as a sublevel set of a value function, which is the…
Semi-supervised learning is a popular class of techniques to learn from labeled and unlabeled data. The paper proposes an application of a recently proposed approach of graph transduction that exploits game theoretic notions to the problem…
We study a new modification of the Arrival problem, which allows for nodes that exhibit random as well as controlled behaviour, in addition to switching nodes. We study the computational complexity of these extensions, building on existing…
The problem of graph Reachability is to decide whether there is a path from one vertex to another in a given graph. In this paper, we study the Reachability problem on three distinct graph families - intersection graphs of Jordan regions,…
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…
Graph reachability is the task of understanding whether two distinct points in a graph are interconnected by arcs to which in general a semantic is attached. Reachability has plenty of applications, ranging from motion planning to routing.…
The cops-and-robber (CR) game has been used in mobile robotics as a discretized model (played on a graph G) of pursuit/evasion problems. The "classic" CR version is a perfect information game: the cops' (pursuer's) location is always known…
We define reachability games based on Dynamic Epistemic Logic (DEL), where the players' actions are finely described as DEL action models. We first consider the setting where an external controller with perfect information interacts with an…
Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations…
Despite seminal advances in reinforcement learning in recent years, many domains where the rewards are sparse, e.g. given only at task completion, remain quite challenging. In such cases, it can be beneficial to tackle the task both from…
Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…