Spherical coverage verification

Marko D. Petkovic; Dragoljub Pokrajac; Longin Jan Latecki

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arXiv · 1109.2361

Spherical coverage verification

Marko D. Petkovic·Dragoljub Pokrajac·Longin Jan Latecki

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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.

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BibTeX RIS

Marko D. Petkovic, Dragoljub Pokrajac, Longin Jan Latecki. 2011-09-11. Spherical coverage verification. https://arxiv.org/abs/1109.2361

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