Exercise 12.9 Given a weighted (connected) undirected graph G = (V, E, w), with m =n+ 0(1) edges (ie., the number of edges is at most the number of vertices plus some constant), give an O(n)-time algorithm to compute the minimum spanning tree of G. Prove the correctness and the running time of your algorithm. (Hint: Think of how one can eliminate an edge from being in the MST.)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Exercise 12.9
Given a weighted (connected) undirected graph G = (V, E, w), with m =n+ 0(1) edges (i.e.,
the number of edges is at most the number of vertices plus some constant), give an O(n)-time
algorithm to compute the minimum spanning tree of G. Prove the correctness and the running
time of your algorithm. (Hint: Think of how one can eliminate an edge from being in the MST.)
Transcribed Image Text:Exercise 12.9 Given a weighted (connected) undirected graph G = (V, E, w), with m =n+ 0(1) edges (i.e., the number of edges is at most the number of vertices plus some constant), give an O(n)-time algorithm to compute the minimum spanning tree of G. Prove the correctness and the running time of your algorithm. (Hint: Think of how one can eliminate an edge from being in the MST.)
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