On finding the rectangular duals of planar triangular graphs
SIAM Journal on Computing
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
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Regular Edge Labelings and Drawings of Planar Graphs
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Graph Theory With Applications
Graph Theory With Applications
Algorithms for computing a parameterized st-orientation
Theoretical Computer Science
Applications of parameterized st-orientations in graph drawing algorithms
GD'05 Proceedings of the 13th international conference on Graph Drawing
Compact visibility representation of 4-connected plane graphs
Theoretical Computer Science
| Hi-index | 5.24 |
An st-orientation or bipolar orientation of a 2-connected graph G is an orientation of its edges to generate a directed acyclic graph with a single source s and a single sink t. Given a plane graph G and two exterior vertices s and t, the problem of finding an optimum st-orientation, i.e., an st-orientation in which the length of a longest st-path is minimized, was first proposed indirectly by Rosenstiehl and Tarjan in and then later directly by He and Kao in . In this paper, we prove that, given a 2-connected plane graph G, two exterior vertices s, t, and a positive integer K, the decision problem of whether G has an st-orientation, where the maximum length of an st-path is @?K, is NP-Complete. This solves a long standing open problem on the complexity of optimum st-orientations for plane graphs. As a by-product, we prove that the NP-Completeness result holds for planar graphs as well.