LaserTank is NP-complete

We show that the classical game LaserTank is $\mathrm{NP}$-complete, even when the tank movement is restricted to a single column and the only blocks appearing on the board are mirrors and solid blocks. We show this by reducing $3$-SAT instances to LaserTank puzzles.Comment: 5 page

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

Parameterized Complexity of Graph Constraint Logic

Graph constraint logic is a framework introduced by Hearn and Demaine, which provides several problems that are often a convenient starting point for reductions. We study the parameterized complexity of Constraint Graph Satisfiability and both bounded and unbounded versions of Nondeterministic Constraint Logic (NCL) with respect to solution length, treewidth and maximum degree of the underlying constraint graph as parameters. As a main result we show that restricted NCL remains PSPACE-complete on graphs of bounded bandwidth, strengthening Hearn and Demaine's framework. This allows us to improve upon existing results obtained by reduction from NCL. We show that reconfiguration versions of several classical graph problems (including independent set, feedback vertex set and dominating set) are PSPACE-complete on planar graphs of bounded bandwidth and that Rush Hour, generalized to $k\times n$ boards, is PSPACE-complete even when $k$ is at most a constant

Push-Pull Block Puzzles are Hard

This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question by Zubaran and Ritt. Push-pull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a `robot' on a square grid with $1 \times 1$ obstacles. The obstacles cannot be traversed by the robot, but some can be pushed and pulled by the robot into adjacent squares. Thin walls prevent movement between two adjacent squares. This work follows in a long line of algorithms and complexity work on similar problems. The 2D push-pull block puzzle shows up in the video games Pukoban as well as The Legend of Zelda: A Link to the Past, giving another proof of hardness for the latter. This variant of block-pushing puzzles is of particular interest because of its connections to reversibility, since any action (e.g., push or pull) can be inverted by another valid action (e.g., pull or push).Comment: Full version of CIAC 2017 paper. 17 page

Route planning methods for a modular warehouse system

In this study, procedures are presented that can be used to determine the routes of the packages transported within a modular storage system. The problem is a variant of robot motion planning problem. The structures of the procedures are developed in three steps for the simultaneous movement of multiple unit-sized packages in a modular warehouse. The proposed heuristic methods consist of route planning, tagging, and main control components. In order to demonstrate the solution performance of the methods, various experiments were conducted with different data sets and the solution times and qualities of the proposed methods were compared with previous studies. It was found that the proposed methods provide better solutions when taking the number of steps and solution time into consideration

Multi-agent Path Planning in Known Dynamic Environments

We consider the problem of planning paths of multiple agents in a dynamic but predictable environment. Typical scenarios are evacuation, reconfiguration, and containment. We present a novel representation of abstract path-planning problems in which the stationary environment is explicitly coded as a graph (called the arena) while the dynamic environment is treated as just another agent. The complexity of planning using this representation is pspace-complete. The arena complexity (i.e., the complexity of the planning problem in which the graph is the only input, in particular, the number of agents is fixed) is np-hard. Thus, we provide structural restrictions that put the arena complexity of the planning problem into ptime(for any fixed number of agents). The importance of our work is that these structural conditions (and hence the complexity results) do not depend on graph-theoretic properties of the arena (such as clique- or tree-width), but rather on the abilities of the agents

High-density parking for autonomous vehicles.

In a common parking lot, much of the space is devoted to lanes. Lanes must not be blocked for one simple reason: a blocked car might need to leave before the car that blocks it. However, the advent of autonomous vehicles gives us an opportunity to overcome this constraint, and to achieve a higher storage capacity of cars. Taking advantage of self-parking and intelligent communication systems of autonomous vehicles, we propose puzzle-based parking, a high-density design for a parking lot. We introduce a novel method of vehicle parking, which leads to maximum parking density. We then propose a heuristic method to solve larger problems, and mathematically prove that the method produces near-optimal results. To improve layout designs reducing vehicular movements, we propose a use of a meta-heuristic algorithm integrated with a deep reinforcement learning method. Finally, to take advantage of these puzzle-based designs in large-scale, we propose a modular layout design. This design process consists of two steps: i) design of a high-density modular lot, which we call sub-lot, and ii) integration of these sub-lots into a large parking lot. We have conducted a set of experiments to determine which sub-lot size provide the best performance in terms of density and retrieval time