Verified Approximation Algorithms

 

Title: Verified Approximation Algorithms
Authors: Robin Eßmann (robin /dot/ essmann /at/ tum /dot/ de), Tobias Nipkow, Simon Robillard and Ujkan Sulejmani
Submission date: 2020-01-16
Abstract: We present the first formal verification of approximation algorithms for NP-complete optimization problems: vertex cover, set cover, independent set, center selection, load balancing, and bin packing. The proofs correct incompletenesses in existing proofs and improve the approximation ratio in one case. A detailed description of our work (excluding center selection) has been published in the proceedings of IJCAR 2020.
Change history: [2021-02-08]: added theory Approx_SC_Hoare (Set Cover) by Robin Eßmann
[2021-06-29]: added theory Center_Selection by Ujkan Sulejmani
BibTeX:
@article{Approximation_Algorithms-AFP,
  author  = {Robin Eßmann and Tobias Nipkow and Simon Robillard and Ujkan Sulejmani},
  title   = {Verified Approximation Algorithms},
  journal = {Archive of Formal Proofs},
  month   = jan,
  year    = 2020,
  note    = {\url{https://isa-afp.org/entries/Approximation_Algorithms.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License