An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
Arc crossing minimization in hierarchical digraphs with tabu search
Computers and Operations Research
A new lower bound for the bipartite crossing number with applications
Theoretical Computer Science
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
On Bipartite Drawings and the Linear Arrangement Problem
SIAM Journal on Computing
An Alternative Method to Crossing Minimization on Hierarchical Graphs
SIAM Journal on Optimization
One Sided Crossing Minimization Is NP-Hard for Sparse Graphs
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Simple and Efficient Bilayer Cross Counting
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Heuristics, Experimental Subjects, and Treatment Evaluation in Bigraph Crossing Minimization
Journal of Experimental Algorithmics (JEA)
On the one-sided crossing minimization in a bipartite graph with large degrees
Theoretical Computer Science
High-contrast algorithm behavior: observation, hypothesis, and experimental design
Proceedings of the 2007 workshop on Experimental computer science
On the Parameterized Complexity of Layered Graph Drawing
Algorithmica - Parameterized and Exact Algorithms
A New Approach to Exact Crossing Minimization
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Crossing minimization in weighted bipartite graphs
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Experiments on exact crossing minimization using column generation
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
GD'05 Proceedings of the 13th international conference on Graph Drawing
A global k-level crossing reduction algorithm
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
A method for reducing the target fault list of crosstalk faults in synchronous sequential circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Extensive research over the last 20 or more years has been devoted to the problem of minimizing the total number of crossings in layered directed acyclic graphs (dags). Algorithms for this problem are used for graph drawing, to implement one of the stages in the multistage approach proposed by Sugiyama et al. [1981]. In some applications, such as minimizing the deleterious effects of crosstalk in VLSI circuits, it may be more appropriate to minimize the maximum number of crossings over all the edges. We refer to this as the bottleneck crossing problem. This article proposes a new heuristic, maximum crossings edge (MCE), designed specifically for the bottleneck problem. It is no surprise that MCE universally outperforms other heuristics with respect to bottleneck crossings. What is surprising, and the focus of this article, is that, in many settings, the MCE heuristic excels at minimizing the total number of crossings. Experiments on sparse graphs support the hypothesis that MCE gives better results (vis a vis barycenter) when the maximum degree of the dag is large. In contrast to barycenter, the number of crossings yielded by MCE is further reduced as runtime is increased. Even better results are obtained when the two heuristics are combined and/or barycenter is followed by the sifting heuristic reported in Matuszewski et al. [1999].