Edmonds' algorithm (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Edmonds' algorithm" in English language version.

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springer.com

The algorithm is applicable to finding a minimum spanning forest with given roots. However, when searching for the minimum spanning forest among all $k$ -component spanning forests, a multiplier arises in the complexity of the algorithm $C_{V}^{k}$ , corresponding to the choice of a subset of vertices designated as roots. This makes it unsuitable for such a task. Even when constructing a minimum spanning tree, regardless of the root, the algorithm must be used $V$ times, sequentially assigning each vertex as the root. An efficient algorithm for finding minimum spanning forests that solves the root assignment problem is presented in (https://link.springer.com/article/10.1007/s10958-023-06666-w). It builds a sequence of minimal $k$ -component spanning forests for all $k$ up to the minimum spanning tree. The Chu-Liu/Edmonds algorithm is a component of it.