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This withdrawn study on the computational complexity of drone coverage reveals that efficiently mapping planar regions with limited images is theoretically intractable to approximate well, a finding with implications for sensor placement and agricultural automation. The research highlights fundamental limits in optimization problems involving squares and circles, suggesting that practical solutions must rely on heuristics rather than exact algorithms. Despite the paper's retraction due to communication issues, the theoretical bounds established offer a baseline for evaluating future coverage strategies in robotics and environmental monitoring.
On The Computational Complexity of Minimum Aerial Photographs for Planar Region Coverage
arXiv:2512.18268v3 Announce Type: replace Abstract: With the popularity of drone technologies, aerial photography has become prevalent in many daily scenarios such as environment monitoring, structure inspection, law enforcement etc. A central challenge in this domain is the efficient coverage of a target area with photographs that can entirely capture the region, while respecting constraints such as the image resolution, and limited number of pictures that can be taken. This work investigates the computational complexity of covering a simple planar polygon using squares and circles. Specifically, it shows inapproximability gaps of $1.165$ (for squares) and $1.25$ (for restricted square centers) and develops a $2.828$-optimal approximation algorithm, demonstrating that these problems are computationally intractable to approximate. The intuitions of this work can extend beyond aerial photography to broader applications such as pesticide spraying and strategic sensor placement.
Abstract:With the popularity of drone technologies, aerial photography has become prevalent in many daily scenarios such as environment monitoring, structure inspection, law enforcement etc. A central challenge in this domain is the efficient coverage of a target area with photographs that can entirely capture the region, while respecting constraints such as the image resolution, and limited number of pictures that can be taken. This work investigates the computational complexity of covering a simple planar polygon using squares and circles. Specifically, it shows inapproximability gaps of $1.165$ (for squares) and $1.25$ (for restricted square centers) and develops a $2.828$-optimal approximation algorithm, demonstrating that these problems are computationally intractable to approximate. The intuitions of this work can extend beyond aerial photography to broader applications such as pesticide spraying and strategic sensor placement.
Robotics (cs.RO); Computational Geometry (cs.CG)
arXiv:2512.18268 [cs.RO]
(or arXiv:2512.18268v3 [cs.RO] for this version)
Text integral sub licența deschisă a publicației · 143 cuvinte
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