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\title{Kruskal's Algorithm for Minimum Spanning Forest}
\author{Maximilian P.L. Haslbeck, Peter Lammich, Julian Biendarra}
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\begin{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.
\end{abstract}

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