In this paper we consider a problem that occurs when
drawing public transportation networks. Given an
embedded graph G = (V;E) (e.g. the railroad network) and a set H of paths in G (e.g. the train lines),
we want to draw the paths along the edges of G such
that they cross each other as few times as possible.
For aesthetic reasons we insist that the relative order
of the paths that traverse a vertex does not change
within the area occupied by the vertex. We prove
that the problem, which is known to be NP-hard, can
be rewritten as an integer linear program that finds
the optimal solution for the problem.
In the case when the order of the endpoints of
the paths is fixed we prove that the problem can be
solved in polynomial time. This improves a recent
result by Bekos et al.
Cite as: Asquith, M., Gudmundsson, J. and Merrick, D. (2008). An ILP for the metro-line crossing problem. In Proc. Fourteenth Computing: The Australasian Theory Symposium (CATS 2008), Wollongong, NSW, Australia. CRPIT, 77. Harland, J. and Manyem, P., Eds. ACS. 49-56.
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