Spherical coverage verification
Abstract
We consider the problem of covering hypersphere by a set of spherical hypercaps. This sort of problem has numerous practical applications such as error correcting codes and reverse k-nearest neighbor problem. Using the reduction of non degenerated concave quadratic programming (QP) problem, we demonstrate that spherical coverage verification is NP hard. We propose a recursive algorithm based on reducing the problem to several lower dimension subproblems. We test the performance of the proposed algorithm on a number of generated constellations. We demonstrate that the proposed algorithm, in spite of its exponential worst-case complexity, is applicable in practice. In contrast, our results indicate that spherical coverage verification using QP solvers that utilize heuristics, due to numerical instability, may produce false positives.
Cite
@article{arxiv.1109.2361,
title = {Spherical coverage verification},
author = {Marko D. Petkovic and Dragoljub Pokrajac and Longin Jan Latecki},
journal= {arXiv preprint arXiv:1109.2361},
year = {2015}
}