Exploring and Triangulating a Region by a Swarm of Robots
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- Fekete S.P., Kamphans T., Kröller A., Mitchell J.S.B., Schmidt C. (2011) Exploring and Triangulating a Region by a Swarm of Robots. In: Goldberg L.A., Jansen K., Ravi R., Rolim J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Lecture Notes in Computer Science, vol 6845. Springer, Berlin, Heidelberg
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.
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