Verified Approximation Algorithms

Robin Eßmann, Tobias Nipkow, Simon Robillard and Ujkan Sulejmani

16 January 2020

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.
BSD License

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

Topics

Theories

Cite

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@article{Approximation_Algorithms-AFP,
  author  = {Robin Eßmann, Tobias Nipkow, Simon Robillard and Ujkan Sulejmani},
  title   = {Verified Approximation Algorithms},
  journal = {Archive of Formal Proofs},
  month   = January,
  year    = 2020,
  note    = {\url{http://isa-afp.org/entries/Approximation_Algorithms.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
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