Algorithm for Constructing Related Spanning Directed Forests of Minimum Weight

TL;DR

This paper introduces an algorithm for constructing minimum weight directed spanning forests that maintains maximum affinity between forests as the number of trees varies, with proven correctness and polynomial complexity.

Contribution

It presents a novel algorithm for related spanning minimal forests of varying tree counts, ensuring maximum affinity and efficiency.

Findings

Algorithm correctly constructs minimum weight forests.

Complexity does not exceed O(N^3) for dense graphs.

Produces related forests for all admissible numbers of trees.

Abstract

An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the algorithm is checked and its complexity is determined, which does not exceed $ O (N ^ 3) $ for dense graphs. The result of the algorithm is a set of related spanning minimal forests consisting of $ k $ trees for all admissible $ k $.