Related papers: Push-Pull Block Puzzles are Hard
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…
We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of…
In this work we face a challenging puzzle video game: A Good Snowman is Hard to Build. The objective of the game is to build snowmen by moving and stacking snowballs on a discrete grid. For the sake of player engagement with the game, it is…
We consider the following modification of annihilation game called node blocking. Given a directed graph, each vertex can be occupied by at most one token. There are two types of tokens, each player can move his type of tokens. The players…
We consider a set of challenging sequential manipulation puzzles, where an agent has to interact with multiple movable objects and navigate narrow passages. Such settings are notoriously difficult for Task-and-Motion Planners, as they…
We study the computational complexity of distance games, a class of combinatorial games played on graphs. A move consists of colouring an uncoloured vertex subject to it not being at certain distances determined by two sets, D and S. D is…
The author presents two tricks to accelerate depth-first search algorithms for a class of combinatorial puzzle problems, such as tiling a tray by a fixed set of polyominoes. The first trick is to implement each assumption of the search with…
Micro- and nanorobots are often controlled by global input signals, such as an electromagnetic or gravitational field. These fields move each robot maximally until it hits a stationary obstacle or another stationary robot. This paper…
We study the classic sliding cube model for programmable matter under parallel reconfiguration in three dimensions, providing novel algorithmic and surprising complexity results in addition to generalizing the best known bounds from two to…
We study a new reconfiguration problem inspired by classic mechanical puzzles: a colored token is placed on each vertex of a given graph; we are also given a set of distinguished cycles on the graph. We are tasked with rearranging the…
We study multiple elastic collisions of a block and a ball against a rigid wall in one dimension. The complete trajectory of the block is solved as an analytic function of time. Near the turning point of the block the force carried by the…
We consider the problem of determining the minimum number of moves needed to solve a certain one-dimensional peg puzzle. Let N be a positive integer. The puzzle apparatus consists of a block with a single row of 2N+1 equally spaced holes…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…
Cohn and Umans proposed a framework for developing fast matrix multiplication algorithms based on the embedding computation in certain groups algebras. In subsequent work with Kleinberg and Szegedy, they connected this to the search for…
Recent demonstrations indicate that silicon-spin QPUs will be able to shuttle physical qubits rapidly and with high fidelity - a desirable feature for maximising logical connectivity, supporting new codes, and routing around damage. However…
Physically disentangling entangled objects from each other is a problem encountered in waste segregation or in any task that requires disassembly of structures. Often there are no object models, and, especially with cluttered irregularly…
Based on a previous generalization by the author of Latin squares to Latin boards, this paper generalizes partial Latin squares and related objects like partial Latin squares, completable partial Latin squares and Latin square puzzles. The…
We study two well-known reconfiguration problems. Given a start and a target configuration of geometric objects in a polygon, we wonder whether we can move the objects from the start configuration to the target configuration while avoiding…
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…
Random motion in disordered media is sensitive to the presence of obstacles that prevent atoms, molecules, and other particles from moving freely in space. When obstacles are static, a sharp transition between confined motion and free…