Kruskal's Algorithm for Minimum Spanning Forest

 

Title: Kruskal's Algorithm for Minimum Spanning Forest
Authors: Maximilian P.L. Haslbeck, Peter Lammich and Julian Biendarra
Submission date: 2019-02-14
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.
BibTeX:
@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   = feb,
  year    = 2019,
  note    = {\url{https://isa-afp.org/entries/Kruskal.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Collections, Matroids, Refine_Imperative_HOL, Refine_Monadic