### Abstract

This Isabelle/HOL formalization defines a greedy algorithm for finding a minimum weight basis on a weighted matroid and proves its correctness. This algorithm is an abstract version of Kruskal's algorithm. We interpret the abstract algorithm for the cycle matroid (i.e. forests in a graph) and refine it to imperative executable code using an efficient union-find data structure. Our formalization can be instantiated for different graph representations. We provide instantiations for undirected graphs and symmetric directed graphs.

### License

BSD License

### Topics

- Computer science/Algorithms/Graph

### Session Kruskal

- Kruskal_Misc
- SeprefUF
- MinWeightBasis
- Kruskal
- Kruskal_Refine
- Kruskal_Impl
- UGraph
- UGraph_Impl
- Graph_Definition
- Graph_Definition_Aux
- Graph_Definition_Impl

### Depends on

- Collections Framework
- Matroids
- The Imperative Refinement Framework
- Refinement for Monadic Programs

### Auto-related entries

- Menger’s Theorem

## Cite

×

Kruskal-AFP

    @article{Kruskal-AFP,
      author  = {Maximilian P. L. Haslbeck and Peter Lammich and Julian Biendarra},
      title   = {Kruskal's Algorithm for Minimum Spanning Forest},
      journal = {Archive of Formal Proofs},
      month   = {February},
      year    = {2019},
      note    = {\url{https://isa-afp.org/entries/Kruskal.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
- Feb 23, 2021 : Isabelle2021
- Apr 18, 2020 : Isabelle2020
- Jun 11, 2019 : Isabelle2019
- Feb 19, 2019 : Isabelle2018