When greedy search algorithms encounter a local minima or plateau, the search typically devolves into a breadth-first search (BrFS), or a local search technique is used in an attempt to find a way out. In this work, we formally analyze the performance of BrFS and constant-depth restarting random walks (RRW) -- two methods often used for finding exits to a plateau/local minima -- to better understand when each is best suited. In particular, we formally derive the expected runtime for BrFS in the case of a uniformly distributed set of goals at a given goal depth. We then prove RRW will be faster than BrFS on trees if there are enough goals at that goal depth. We refer to this threshold as the crossover point. Our bound shows that the crossover point grows linearly with the branching factor of the tree, the goal depth, and the error in the random walk depth, while the size of the tree grows exponentially in branching factor and goal depth. Finally, we discuss the practical implications and applicability of this bound.

We propose a new procedural content generation method which learns iterative level generators from a dataset of existing levels. The Path of Destruction method, as we call it, views level generation as repair; levels are created by iteratively repairing from a random starting level. The first step is to generate an artificial dataset from the original set of levels by introducing many different sequences of mutations to existing levels. In the generated dataset, features are observations of destroyed levels and targets are the specific actions that repair the mutated tile in the middle of the observations. Using this dataset, a convolutional network is trained to map from observations to their respective appropriate repair actions. The trained network is then used to iteratively produce levels from random starting maps. We demonstrate this method by applying it to generate unique and playable tile-based levels for several 2D games (Zelda, Danger Dave, and Sokoban) and vary key hyperparameters.

Search is a central problem in artificial intelligence, and breadth-first search (BFS) and depth-first search (DFS) are the two most fundamental ways to search. In this paper we derive estimates for average BFS and DFS runtime. The average runtime estimates can be used to allocate resources or judge the hardness of a problem. They can also be used for selecting the best graph representation, and for selecting the faster algorithm out of BFS and DFS. They may also form the basis for an analysis of more advanced search methods. The paper treats both tree search and graph search. For tree search, we employ a probabilistic model of goal distribution; for graph search, the analysis depends on an additional statistic of path redundancy and average branching factor. As an application, we use the results to predict BFS and DFS runtime on two concrete grammar problems and on the N-puzzle. Experimental verification shows that our analytical approximations come close to empirical reality.