DFSbased

DFSbased is a term used to describe algorithms and approaches that rely on depth-first search (DFS) as the core traversal mechanism for exploring graphs or tree-like structures. In a DFSbased traversal, the algorithm follows a branch as far as possible before backtracking, typically implemented via recursion or an explicit stack. When an edge or node is visited, it is marked to prevent revisiting. The DFSbased approach is foundational in graph theory and underpins many algorithmic techniques.

Characteristics of DFSbased methods include order of exploration dependent on adjacency representation, ability to identify reachability, and suitability for problems that require exhaustive search of paths. Time complexity is O(V+E) for a graph with V vertices and E edges, and memory usage is O(V) in the worst case due to the stack or recursion depth.

Common applications include traversal of graphs, cycle detection, topological sorting, finding connected components and articulation points, generation of spanning trees (including depth-first spanning trees), backtracking in constraint satisfaction problems, and as a subroutine in more complex algorithms such as Tarjan's strongly connected components or Kosaraju's algorithm.

Variants and considerations: iterative DFS vs recursive DFS; iterative deepening DFS combines DFS with increasing depth limits; DFS does not guarantee the shortest path, and in large graphs can suffer from deep recursion or stack overflow in environments with limited call stacks; graph representation and ordering of neighbors can affect practical performance; however, DFSbased methods are simple and memory-efficient relative to some alternatives.

See also DFS and depth-first search and graph traversal.