New bounds on the Barycenter heuristic for bipartite graph drawing
Information Processing Letters
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
One Sided Crossing Minimization Is NP-Hard for Sparse Graphs
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
An Efficient Fixed Parameter Tractable Algorithm for 1-Sided Crossing Minimization
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
An Improved Bound on the One-Sided Minimum Crossing Number in Two-Layered Drawings
Discrete & Computational Geometry
An approximation algorithm for the two-layered graph drawing problem
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Journal of Experimental Algorithmics (JEA)
A fast and simple subexponential fixed parameter algorithm for one-sided crossing minimization
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
| Hi-index | 5.23 |
Given a bipartite graph G = (V, W, E), a 2-layered drawing consists of placing nodes in the first node set V on a straight line L1 and placing nodes in the second node set W on a parallel line L2. For a given ordering of nodes in W on L2, the one-sided crossing minimization problem asks to find an ordering of nodes in V on L1 so that the number of arc crossings is minimized. A well-known lower bound LB on the minimum number of crossings is obtained by summing up min{cuv, cvu} over all node pairs u, v ∈ V, where cuv denotes the number of crossings generated by arcs incident to u and v when u precedes v in an ordering. In this paper, we prove that there always exists a solution whose crossing number is at most (1.2964 + 12/(δ - 4))LB if the minimum degree δ of a node in V is at least 5.