If there is a graph G with V vertices and E edges and I already know its minimum spanning tree T of G, and then if some of the edges from E are taken and their weights are increased by say 50, these edges may or may not be in the minimum spanning tree. Keeping the above scenario in mind is there a way to regenerate a new minimum spanning tree in linear time ? note: the number of edges whose weights have been modified are only 5.
regenerating Minimum Spanning Tree in linear time?
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You may want to take a look at the SO question here . I believe this is directly addressed in this paper by Szpira & Pan and can be done in O(n) time .