The Vertex-Exchange Graph: A New Concept for Multi-level Crossing Minimisation

In this paper we consider the problems of testing a multi- level graph for planarity and laying out a multi-level graph.We introduce a new abstraction that we call a vertex-exchange graph. We demonstrate how this concept can be used to solve these problems by providing clear and simple algorithms for testing a multi-level graph for planarity and laying out a multi-level graph when planar.We also show how the concept can be used to solve other problems relating to multi-level graph layout.

[1]  Mitsuhiko Toda,et al.  Methods for Visual Understanding of Hierarchical System Structures , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  Xuemin Lin,et al.  How to draw a directed graph , 1989, [Proceedings] 1989 IEEE Workshop on Visual Languages.

[3]  Michael Jünger,et al.  Exact and Heuristic Algorithms for 2-Layer Straightline Crossing Minimization , 1995, GD.

[4]  Michael Jünger,et al.  A Polyhedral Approach to the Multi-Layer Crossing Minimization Problem , 1997, GD.