Algorithms for updating minimal spanning trees (original) (raw)

This paper presents efficient algorithms for updating minimal spanning trees (MSTs) in undirected graphs in response to vertex and edge modifications. The proposed algorithms have a time complexity of O(n) for the insertion of a new vertex and O(n^2) for consistently labeling vertices to allow for fast deletion, as well as updating the MST when edges are inserted or deleted. Notably, these algorithms simplify existing methods while achieving similar performance, thereby enhancing the computational efficiency of MST updates.