@inproceedings{f2dae45a14b14b99bc4bb8caabc16a4a,

title = "Mapping a polygon with holes using a compass",

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.",

author = "Yann Disser and Mat{\'u}s Mihal{\'a}k and Ghosh, {Subir Kumar} and Peter Widmayer",

year = "2012",

doi = "10.1007/978-3-642-36092-3_9",

language = "English",

series = "Lecture Notes in Computer Science",

publisher = "Springer Verlag",

pages = "78--89",

booktitle = "Proceedings of the 8th International Symposium on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities (Algosensors)",

address = "Germany",

}