BFSDFS

BFSDFS is a hybrid graph traversal concept that combines elements of breadth-first search (BFS) and depth-first search (DFS). It is not a single canonical algorithm, but rather a family of strategies described in some literature and practice to balance memory usage, exploration order, and search completeness.

The core idea is to leverage BFS to establish a level-based structure or frontier and then apply DFS within those levels or subgraphs to explore branches more selectively. Alternatively, implementations may switch between BFS and DFS dynamically based criteria such as frontier size, search depth, or available memory. This flexibility aims to retain the completeness benefits of BFS while using DFS’s lower memory footprint or locality advantages in certain parts of the search.

Key characteristics include completeness and optimality depending on the switching policy and duplicate handling. If each node is visited without repetition, the approach can be complete for finite graphs. In unweighted graphs, BFS guarantees shortest paths, while DFS-based components do not inherently provide optimality guarantees for path lengths. Therefore, the overall guarantees of BFSDFS depend on how the hybridization is enforced.

Typical complexities are implementation-dependent. Time complexity remains tied to the total number of nodes and edges explored, often O(N+E) in practice, but the constants and branching behavior vary with the switching rule. Memory usage is generally aimed to be lower than pure BFS, potentially approaching DFS-like memory of O(d) in favorable cases, where d is the depth of the explored region.

Common variants include layered DFS within BFS layers, adaptive switching based on frontier metrics, and hybrid data structures that combine queue and stack behavior. BFSDFS finds use in large or memory-constrained graphs, path finding, and AI search problems where conventional BFS or DFS alone is impractical.