LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
New bounds on the Barycenter heuristic for bipartite graph drawing
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
One Sided Crossing Minimization Is NP-Hard for Sparse Graphs
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Applying Crossing Reduction Strategies to Layered Compound Graphs
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Breaking cycles for minimizing crossings
Journal of Experimental Algorithmics (JEA)
Heuristics, Experimental Subjects, and Treatment Evaluation in Bigraph Crossing Minimization
Journal of Experimental Algorithmics (JEA)
QCA channel routing with wire crossing minimization
GLSVLSI '05 Proceedings of the 15th ACM Great Lakes symposium on VLSI
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
GD'05 Proceedings of the 13th international conference on Graph Drawing
Ranking and drawing in subexponential time
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
A rearrangement of adjacency matrix based approach for solving the crossing minimization problem
Journal of Combinatorial Optimization
Journal of Experimental Algorithmics (JEA)
Hi-index | 0.00 |
Given a bipartite graph G = (L0, L1, E) and a fixed ordering of the nodes in L0, the problem of finding an ordering of the nodes in L1 that minimizes the number of crossings has received much attention in literature. The problem is NP-complete in general and several practically efficient heuristics and polynomial-time algorithms with a constant approximation ratio have been suggested. We generalize the problem and consider the version where the edges have nonnegative weights. Although this problem is more general and finds specific applications in automatic graph layout problems similar to those of the unweighted case, it has not received as much attention. We provide a new technique that efficiently approximates a solution to this more general problem within a constant approximation ratio of 3. In addition we provide appropriate generalizations of some common heuristics usually employed for the unweighted case and compare their performances.