Brandes U. (2002) Eager st-Ordering. In: Möhring R., Raman R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg
Given a biconnected graph G = (V,E) with edge s, t ∈ 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.