Closest Pair of Points Algorithms

Martin Rau 📧 and Tobias Nipkow 🌐

January 13, 2020

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

This entry provides two related verified divide-and-conquer algorithms solving the fundamental Closest Pair of Points problem in Computational Geometry. Functional correctness and the optimal running time of O(n log n) are proved. Executable code is generated which is empirically competitive with handwritten reference implementations.

License

BSD License

History

April 14, 2020
Incorporate Time_Monad of the AFP entry Root_Balanced_Tree.

Topics

Related publications

Session Closest_Pair_Points

Depends on

Used by

Cite

× 
@article{Closest_Pair_Points-AFP,
  author  = {Martin Rau and Tobias Nipkow},
  title   = {Closest Pair of Points Algorithms},
  journal = {Archive of Formal Proofs},
  month   = {January},
  year    = {2020},
  note    = {\url{https://isa-afp.org/entries/Closest_Pair_Points.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
Download

Download

× Download latest

Older releases: