Parallel ear decomposition search (EDS) and st-numbering in graphs
Theoretical Computer Science
Bipolar orientations revisited
Discrete Applied Mathematics - Special issue: Fifth Franco-Japanese Days, Kyoto, October 1992
A linear-time algorithm for four-partitioning four-connected planar graphs
Information Processing Letters
Algorithms for area-efficient orthogonal drawings
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Directional Routing via Generalized st-Numberings
SIAM Journal on Discrete Mathematics
Algorithm 447: efficient algorithms for graph manipulation
Communications of the ACM
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Applications of parameterized st-orientations in graph drawing algorithms
GD'05 Proceedings of the 13th international conference on Graph Drawing
Algorithms for computing a parameterized st-orientation
Theoretical Computer Science
Compact visibility representation of 4-connected plane graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Compact visibility representation of 4-connected plane graphs
Theoretical Computer Science
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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(mlog n) 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.