### Abstract

We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex of P. Then, we must be able to route a data packet between any two vertices p and q of P, where each step must use only the label of the target node q and the routing table of the current node. For any fixed ε>0, we present a routing scheme that always achieves a routing path whose length exceeds the shortest path by a factor of at most 1+ε. The labels have O(logn) bits, and the routing tables are of size O((ε^{−1}+h)logn). The preprocessing time is O(n^{2}logn). It can be improved to O(n^{2}) for simple polygons.

Original language | English |
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Article number | 101593 |

Journal | Computational Geometry: Theory and Applications |

Volume | 87 |

DOIs | |

Publication status | Published - 2020 Apr |

### Keywords

- Polygonal domain
- Routing scheme

### ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

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## Cite this

*Computational Geometry: Theory and Applications*,

*87*, [101593]. https://doi.org/10.1016/j.comgeo.2019.101593