Summary of Expected Runtime Comparisons Between Breadth-first Search and Constant-depth Restarting Random Walks, by Daniel Platnick et al.

Expected Runtime Comparisons Between Breadth-First Search and Constant-Depth Restarting Random Walks

by Daniel Platnick, Richard Anthony Valenzano

First submitted to arxiv on: 24 Jun 2024

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Summary difficulty	Written by	Summary
High	Paper authors	High Difficulty Summary Read the original abstract here
Medium	GrooveSquid.com (original content)	Medium Difficulty Summary The paper formally analyzes two methods used to find exits from local minima or plateaus: breadth-first search (BrFS) and constant-depth restarting random walks (RRW). It derives the expected runtime for BrFS in uniformly distributed goal sets at a given depth, and proves RRW is faster on trees if there are enough goals. The crossover point, where RRW outperforms BrFS, grows linearly with tree size, branching factor, and goal depth. This bound has practical implications and applicability.
Low	GrooveSquid.com (original content)	Low Difficulty Summary This paper compares two ways to get out of a local minimum or plateau: trying all options (BrFS) or randomly trying different paths until you find the way out (RRW). It figures out when each method is best for finding exits in trees with lots of branches. The results show that if there are enough goals, the random walk approach is faster. The study also finds that the crossover point, where the two methods switch being the fastest, grows as the tree gets bigger and has more branches.