Eager st-ordering

Abstract

Given a biconnected graph G = (V, E)with edge {s, t}Є E, an st-ordering is an ordering v1,…, vn of V such that s = v1, t = vn, and every other vertex has both a higher-numbered and a lower-numbered neighbor. Previous linear-time st-ordering algorithms are based on a preprocessing step in which depth-first search is used to compute lowpoints. The actual ordering is determined only in a second pass over the graph. We present a new, incremental algorithm that does not require lowpoint information and, throughout a single depth-first traversal, maintains an st-ordering of the biconnected component of {s, t} in the traversed subgraph. © Springer-Verlag Berlin Heidelberg 2002.