Question: Let G-(V E) be an (undirected) graph with costs ce>O on the edges e & E. Assume you are given a minimum-cost spanning tree T

Let G-(V E) be an (undirected) graph with costs ce>O on

Let G-(V E) be an (undirected) graph with costs ce>O on the edges e & E. Assume you are given a minimum-cost spanning tree T in G. Now assume that a new edge is added to G connecting two nodes v, w V with cost. (a) Give an efficient algorithm to test if T remains the minimum-cost spanning tree with the new edge added to G (but not to the tree T. Make your algorithm run in time O(EI). can you do it in O(IVI) time? Please note any assumptions you make about what data structure is used to represent the tree T and the graph G. (b) Suppose T is no longer the minimum-cost spanning tree. Give a linear-time algorithm (time O(EI)) to update the tree T to the new minimum-cost spanning tree

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