Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Convergence of Autonomous Mobile Robots with Inaccurate Sensors and Movements
SIAM Journal on Computing
Simple Robots with Minimal Sensing: From Local Visibility to Global Geometry
International Journal of Robotics Research
Simple Robots in Polygonal Environments: A Hierarchy
Algorithmic Aspects of Wireless Sensor Networks
Bitbots: simple robots solving complex tasks
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Mobile agent algorithms versus message passing algorithms
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Reconstructing visibility graphs with simple robots
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
A polygon is determined by its angles
Computational Geometry: Theory and Applications
Reconstructing a simple polygon from its angles
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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We study the sensor and movement capabilities that simple robots need in order to create a map of an unknown polygon of size n, and to meet. We consider robots that can move from vertex to vertex, can backtrack movements, and see distant vertices in counter-clockwise order but have no means of visibly identifying them. We show that such robots can always solve the weak rendezvous problem and reconstruct the visibility graph, given an upper bound on n. Our results are tight: The strong rendezvous problem, in which robots need to gather at a common location, cannot be solved in general, and without a bound on n, not even n can be determined. In terms of mobile agents exploring a graph, our result implies that they can reconstruct any graph that is the visibility graph of a simple polygon. This is in contrast to the known result that the reconstruction of arbitrary graphs is impossible in general, even if n is known.