A Topological Approach to Meta-heuristics: Analytical Results on the BFS vs. DFS Algorithm Selection Problem

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.