Advertisement
Published in:
2011 | OriginalPaper | Chapter
Exploring and Triangulating a Region by a Swarm of Robots
Authors : Sándor P. Fekete, Tom Kamphans, Alexander Kröller, Joseph S. B. Mitchell, Christiane Schmidt
Published in: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
We consider online and offline problems related to exploring and surveying a region by a swarm of robots with limited communication range. The minimum relay triangulation problem (MRTP) asks for placing a minimum number of robots, such that their communication graph is a triangulated cover of the region. The maximum area triangulation problem (MATP) aims at finding a placement of
n
robots such that their communication graph contains a root and forms a triangulated cover of a maximum possible amount of area. Both problems are geometric versions of natural graph optimization problems.
The offline version of both problems share a decision problem, which we prove to be NP-hard. For the online version of the MRTP, we give a lower bound of 6/5 for the competitive ratio, and a strategy that achieves a ratio of 3; for different offline versions, we describe polynomial-time approximation schemes. For the MATP we show that no competitive ratio exists for the online problem, and give polynomial-time approximation schemes for offline versions.