Parameterized st-Orientations of Graphs: Algorithms and Experiments

st-orientations (st-numberings) or bipolar orientations of undirected graphs are central to many graph algorithms and applications. Several algorithms have been proposed in the past to compute an st-orientation of a biconnected graph. However, as indicated in [1], the computation of more than one st-orientation is very important for many applications in multiple research areas, such as this of Graph Drawing. In this paper we show how to compute such orientations with certain (parameterized) characteristics in the final st-oriented graph, such as the length of the longest path. Apart from Graph Drawing, this work applies in other areas such as Network Routing and in tackling difficult problems such as Graph Coloring and Longest Path. We present primary approaches to the problem of computing longest path parameterized st-orientations of graphs, an analytical presentation (together with proof of correctness) of a new O(mlog5 n) (O(mlogn) for planar graphs) time algorithm that computes such orientations (and which was used in [1]) and extensive computational results that reveal the robustness of the algorithm.