Deterministic Distributed DFS via Cycle Separators in Planar Graphs

One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through separator sets. Given a graph G = (V, E), a subset of nodes S ⊆ V is called a separator set of G if the size of each connected component of G - S is at most 2/3 · |V|. The most useful separator sets are those that satisfy certain restrictions of cardinality or structure.