Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Theoretical Computer Science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Computing crossing numbers in quadratic time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Proceedings of the 7th International Symposium on Graph Drawing
GD '99 Proceedings of the 7th International Symposium on Graph Drawing
Embeddings of k-Connected Graphs of Pathwidth k
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Two-Layer Planarization in Graph Drawing
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
An Alternative Method to Crossing Minimization on Hierarchical Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
A Polyhedral Approach to the Multi-Layer Crossing Minimization Problem
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Level Planarity Testing in Linear Time
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
A Fast Layout Algorithm for k-Level Graphs
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Parameterized Complexity
An Efficient Fixed Parameter Tractable Algorithm for 1-Sided Crossing Minimization
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Path-Width and Three-Dimensional Straight-Line Grid Drawings of Graphs
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Theoretical Computer Science
Minimum-layer drawings of trees
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Proper and planar drawings of graphs on three layers
GD'05 Proceedings of the 13th international conference on Graph Drawing
Two-Layer planarization: improving on parameterized algorithmics
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Fixed-Parameter tractable algorithms for testing upward planarity
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
| Hi-index | 0.00 |
We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight line-segments between vertices on adjacent layers. We prove that graphs admitting crossing-free h-layer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for a linear-time algorithm to decide if a graph has a crossing-free h-layer drawing (for fixed h). This algorithm is extended to solve a large number of related problems, including allowing at most k crossings, or removing at most r edges to leave a crossing-free drawing (for fixed k or r). If the number of crossings or deleted edges is a non-fixed parameter then these problems are NP-complete. For each setting, we can also permit downward drawings of directed graphs and drawings in which edges may span multiple layers, in which case the total span or the maximum span of edges can be minimized. In contrast to the so-called Sugiyama method for layered graph drawing, our algorithms do not assume a preassignment of the vertices to layers.