# 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 Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.