### Abstract

We consider a simple robot inside a polygon \mathcal{p}\mathcal{p} with holes. The robot can move between vertices of \mathcal{p}\mathcal{p} along lines of sight. When sitting at a vertex, the robot observes the vertices visible from its current location, and it can use a compass to measure the angle of the boundary of \mathcal{p}\mathcal{p} towards north. The robot initially only knows an upper bound \bar{n}\bar{n} on the total number of vertices of \mathcal{p}\mathcal{p}. We study the mapping problem in which the robot needs to infer the visibility graph g vis of \mathcal{p}\mathcal{p} and needs to localize itself within g vis. We show that the robot can always solve this mapping problem. To do this, we show that the minimum base graph of g vis is identical to g vis itself. This proves that the robot can solve the mapping problem, since knowing an upper bound on the number of vertices was previously shown to suffice for computing g vis.

Original language | English |
---|---|

Title of host publication | Proceedings of the 8th International Symposium on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities (Algosensors) |

Publisher | Springer Verlag |

Pages | 78-89 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2012 |

### Publication series

Series | Lecture Notes in Computer Science |
---|---|

Volume | 7718 |

## Cite this

Disser, Y., Mihalák, M., Ghosh, S. K., & Widmayer, P. (2012). Mapping a polygon with holes using a compass. In

*Proceedings of the 8th International Symposium on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities (Algosensors)*(pp. 78-89). Springer Verlag. Lecture Notes in Computer Science, Vol.. 7718 https://doi.org/10.1007/978-3-642-36092-3_9