Exploring and triangulating a region by a swarm of robots

Authors:
Sándor P. Fekete;Tom Kamphans;Alexander Kröller;Joseph S. B. Mitchell;Christiane Schmidt
Affiliations:
Braunschweig Institute of Technology, Germany;Braunschweig Institute of Technology, Germany;Braunschweig Institute of Technology, Germany;Department of Applied Mathematics and Statistics, Stony Brook University;Braunschweig Institute of Technology, Germany
Venue:
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Year:
2011

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Abstract

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.