Reporting and counting segment intersections
Journal of Computer and System Sciences
Introduction to algorithms
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
The Stanford GraphBase: a platform for combinatorial computing
The Stanford GraphBase: a platform for combinatorial computing
Graph Drawing Algorithm Engineering with AGD
Revised Lectures on Software Visualization, International Seminar
Graph Layout through the VCG Tool
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
A data structure for orthogonal range queries
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Counting edge crossings in a 2-layered drawing
Information Processing Letters
Optimal leaf ordering for two and a half dimensional phylogenetic tree visualisation
APVis '04 Proceedings of the 2004 Australasian symposium on Information Visualisation - Volume 35
GD'07 Proceedings of the 15th international conference on Graph drawing
User-oriented graph visualization taxonomy: a data-oriented examination of visual features
HCD'11 Proceedings of the 2nd international conference on Human centered design
An efficient implementation of sugiyama's algorithm for layered graph drawing
GD'04 Proceedings of the 12th international conference on Graph Drawing
GD'04 Proceedings of the 12th international conference on Graph Drawing
Journal of Experimental Algorithmics (JEA)
Improved layout for data flow diagrams with port constraints
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
Drawing layered graphs with port constraints
Journal of Visual Languages and Computing
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We consider the problem of counting the interior edge crossings when a bipartite graph G = (V, E) with node set V and edge set E is drawn such that the nodes of the two shores of the bipartition are drawn as distinct points on two parallel lines and the edges as straight line segments. The efficient solution of this problem is important in layered graph drawing. Our main observation is that it can be reduced to counting the inversions of a certain sequence. This leads to an O(|E|+|C|) algorithm, where C denotes the set of pairwise interior edge crossings, as well as to a simple O(|E| log |Vsmall|) algorithm, where Vsmall is the smaller cardinality node set in the bipartition of the node set V of the graph. We present the algorithms and the results of computational experiments with these and other algorithms on a large collection of instances.