The art gallery problem is ∃ ℝ-complete

@article{Abrahamsen2018TheAG,
  title={The art gallery problem is ∃ ℝ-complete},
  author={Mikkel Abrahamsen and Anna Adamaszek and Tillmann Miltzow},
  journal={Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing},
  year={2018}
}
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whether a system of polynomial equations over the real numbers has a solution. The art gallery problem is a classic problem in computational geometry, introduced in 1973 by Victor Klee. Given a simple polygon P and an integer k, the goal is to decide if there exists a set G of k guards within P such that every point p ∈ P is seen by at least one guard g∈ G. Each guard corresponds to a point in the… 

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