### Abstract

We introduce a new variant of the geometric Steiner arborescence problem, motivated by the layout of flow maps. Flow maps show the movement of objects between places. They reduce visual clutter by bundling lines smoothly and avoiding self-intersections. To capture these properties, our angle-restricted Steiner arborescences, or flux trees, connect several targets to a source with a tree of minimal length whose arcs obey a certain restriction on the angle they form with the source.
We study the properties of optimal flux trees and show that they are planar and consist of logarithmic spirals and straight lines. Flux trees have the shallow-light property. Computing optimal flux trees is NP-hard. Hence we consider a variant of flux trees which uses only logarithmic spirals. Spiral trees approximate flux trees within a factor depending on the angle restriction. Computing optimal spiral trees remains NP-hard, but we present an efficient 2-approximation, which can be extended to avoid "positive monotone" obstacles.

Original language | English |
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Title of host publication | Algorithms and Computation (22nd International Symposium, ISAAC 2011, Yokohama, Japan, December 5-8, 2011. Proceedings) |

Editors | T. Asano, S. Nakano, Y. Okamoto, O. Watanabe |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 250-259 |

ISBN (Print) | 978-3-642-25590-8 |

DOIs | |

Publication status | Published - 2011 |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 7074 |

ISSN (Print) | 0302-9743 |

## Cite this

Buchin, K., Speckmann, B., & Verbeek, K. A. B. (2011). Angle-restricted Steiner arborescences for flow map layout. In T. Asano, S. Nakano, Y. Okamoto, & O. Watanabe (Eds.),

*Algorithms and Computation (22nd International Symposium, ISAAC 2011, Yokohama, Japan, December 5-8, 2011. Proceedings)*(pp. 250-259). (Lecture Notes in Computer Science; Vol. 7074). Springer. https://doi.org/10.1007/978-3-642-25591-5_27