广度优先搜索与恒定深度重启随机游走的期望运行时间比较
Expected Runtime Comparisons Between Breadth-First Search and Constant-Depth Restarting Random Walks
AI总结：
本研究形式化分析广度优先搜索（BrFS）与恒定深度重启随机游走（RRW）的性能，推导BrFS期望运行时间，证明树上目标足够多时RRW更快，给出随分支因子等线性增长的交叉点界值并讨论其实际意义。
摘要：
当贪心搜索算法遇到局部极小值或平台期时，搜索通常会退化为广度优先搜索（BrFS），或是采用局部搜索技术试图找到出路。在本研究中，我们对BrFS和恒定深度重启随机游走（RRW）这两种常用于寻找平台期/局部极小值出口的方法的性能进行了形式化分析，以更好地理解各自的最佳适用场景。具体而言，我们形式化推导了在给定目标深度下目标集均匀分布时BrFS的期望运行时间。随后我们证明，当该目标深度下存在足够多的目标时，在树上RRW的速度将快于BrFS，我们将这一阈值称为交叉点。我们的界值表明，交叉点随树的分支因子、目标深度以及随机游走深度的误差线性增长，而树的规模随分支因子和目标深度呈指数增长。最后，我们讨论了该界值的实际意义与适用性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
