We show that, although an individual edge in a road network can have many crossings, real-world road networks have the property that the crossing graph of their edges is sparse. We prove that networks with this property are themselves sparse and have small separators, allowing many fast algorithms to be generalized from planar graphs to these networks.
Clustered planarity is the problem of simultaneously drawing a planar graph and a clustering of its vertices (as Jordan curves surrounding the cluster) with no unnecessary crossings between edges or cluster boundaries; it remains unknown whether it can be solved in polynomial time. We provide parameterized and subexponential exact algorithms for the case where the planar embedding is fixed and the clusters form a partition of the vertices.
Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine
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