### 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.

### License

BSD License

### History

June 29, 2021
  added theory Center_Selection by Ujkan Sulejmani
February 8, 2021
  added theory Approx_SC_Hoare (Set Cover) by Robin Eßmann

### Topics

- Computer science/Algorithms/Approximation

### Related publications

- Eßmann, R., Nipkow, T., Robillard, S., & Sulejmani, U. (2022). Verified Approximation Algorithms. Logical Methods in Computer Science, Volume 18, Issue 1. https://doi.org/10.46298/lmcs-18(1:36)2022

### Session Approximation_Algorithms

- Approx_VC_Hoare
- Approx_SC_Hoare
- Approx_MIS_Hoare
- Approx_LB_Hoare
- Approx_BP_Hoare
- Center_Selection

## Cite

×

Approximation_Algorithms-AFP

    @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   = {January},
      year    = {2020},
      note    = {\url{https://isa-afp.org/entries/Approximation_Algorithms.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
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- Apr 18, 2020 : Isabelle2020
- Jan 16, 2020 : Isabelle2019