Telling convex from reflex allows to map a polygon

Jérémie Chalopin, Shantanu Das, Yann Disser, Matúš Mihalák, Peter Widmayer

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

We consider the exploration of a simple polygon P by a robot that moves from vertex to vertex along edges of the visibility graph of P. The visibility graph has a vertex for every vertex of P and an edge between two vertices if they see each other, i.e.~if the line segment connecting them lies inside $P$ entirely. While located at a vertex, the robot is capable of ordering the vertices it sees in counter-clockwise order as they appear on the boundary, and for every two such vertices, it can distinguish whether the angle between them is convex ( pi). Other than that, distant vertices are indistinguishable to the robot. We assume that an upper bound on the number of vertices is known and show that the robot is always capable of reconstructing the visibility graph of P. We also show that multiple identical, indistinguishable and deterministic such robots can always position themselves such that they mutually see each other, i.e. such that they form a clique in the visibility graph.
Original languageEnglish
Title of host publicationProceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS)
Pages153-164
Number of pages12
DOIs
Publication statusPublished - 2011
Externally publishedYes

Keywords

  • polygon mapping
  • map construction
  • autonomous agent
  • simple robot
  • visibility graph reconstruction

Cite this

Chalopin, J., Das, S., Disser, Y., Mihalák, M., & Widmayer, P. (2011). Telling convex from reflex allows to map a polygon. In Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS) (pp. 153-164) https://doi.org/10.4230/LIPIcs.STACS.2011.153