Radial Level Planarity Testing and Embedding in Linear Time

Radial Level Planarity Testing and Embedding in Linear Time (2005)

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by Christian Bachmaier , Franz J. Brandenburg , Michael Forster

Venue:	Journal of Graph Algorithms and Applications
Citations:	17 - 9 self

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@ARTICLE{Bachmaier05radiallevel,
    author = {Christian Bachmaier and Franz J. Brandenburg and Michael Forster},
    title = {Radial Level Planarity Testing and Embedding in Linear Time},
    journal = {Journal of Graph Algorithms and Applications},
    year = {2005},
    volume = {9},
    pages = {2005}
}

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Abstract

A graph with a given partition of the vertices on k concentric circles is radial level planar if there is a vertex permutation such that the edges can be routed strictly outwards without crossings. Radial level planarity extends level planarity, where the vertices are placed on k horizontal lines and the edges are routed strictly downwards without crossings. The extension is characterised by rings, which are level non-planar biconnected components. Our main results are linear time algorithms for radial level planarity testing and for computing an embedding. We introduce PQR-trees as a new data structure where R-nodes and associated templates for their manipulation are introduced to deal with rings. Our algorithms extend level planarity testing and embedding algorithms which use PQ-trees.

Citations

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