### Abstract

The flow complex is a data structure, similar to the Delaunay triangulation, to organize a set of (weighted) points in Rd. Its structure has been examined in detail in two and three dimensions but only little is known about its structure in general. Here we propose the first algorithm for computing the flow complex in any dimension which reflects its recursive structure. On the basis of the algorithm we give a generalized and simplified proof of the homotopy equivalence of alpha- and
flow-shapes.

Original language | English |
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Title of host publication | Proceedings 17th Canadian Conference on Computational Geometry (CCCG'05, Windsor, Ontario, Canada, August 10-12, 2005), Electronic proceedings |

Publisher | The CCCG Library |

Pages | 270-273 |

Publication status | Published - 2005 |

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## Cite this

Buchin, K., & Giesen, J. (2005). Flow complex: general structure and algorithm. In

*Proceedings 17th Canadian Conference on Computational Geometry (CCCG'05, Windsor, Ontario, Canada, August 10-12, 2005), Electronic proceedings*(pp. 270-273). The CCCG Library.