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.

翻译：当贪婪搜索算法遭遇局部极小值或平台区时，搜索通常会退化为广度优先搜索（BrFS），或者采用局部搜索技术尝试寻找出路。本研究对BrFS与恒定深度重启随机游走（RRW）——两种常用于寻找平台区/局部极小值出口的方法——进行形式化性能分析，以深入理解各自的最佳适用场景。具体而言，我们形式化推导了当目标均匀分布于给定目标深度时BrFS的期望运行时间。随后证明在树结构上，若该目标深度存在足够多的目标，RRW将比BrFS更快。我们将此临界阈值称为交叉点。理论界表明：交叉点随树的分支因子、目标深度及随机游走深度误差呈线性增长，而树的规模随分支因子和目标深度呈指数增长。最后，我们讨论了该理论界的实际意义与适用性。