Consider the following different (and less efficient) algorithm for computing an MST of a given undirected and connected graph G = (V, E) with edge weight we on each e € E: 1. Sort the edges in decreasing (non-increasing) order of their weights. 2. Let H = G be a copy of the graph G. 3. For i = 1 to m (in the sorted ordering of edges): (a) If removing e; from H does not make H disconnected, remove e; from H. 4. Return H as a minimum spanning tree of G. Prove the correctness of this algorithm, i.e., that it outputs an MST of any given graph G (we ignore the runtime of this algorithm in this problem).
Consider the following different (and less efficient) algorithm for computing an MST of a given undirected and connected graph G = (V, E) with edge weight we on each e € E: 1. Sort the edges in decreasing (non-increasing) order of their weights. 2. Let H = G be a copy of the graph G. 3. For i = 1 to m (in the sorted ordering of edges): (a) If removing e; from H does not make H disconnected, remove e; from H. 4. Return H as a minimum spanning tree of G. Prove the correctness of this algorithm, i.e., that it outputs an MST of any given graph G (we ignore the runtime of this algorithm in this problem).
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
Chapter1: Introduction
Section: Chapter Questions
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Only the proof of correctness is needed for the
![Consider the following different (and less efficient) algorithm for computing
an MST of a given undirected and connected graph G = (V, E) with edge weight we on each e € E:
1. Sort the edges in decreasing (non-increasing) order of their weights.
2. Let H = G be a copy of the graph G.
3. For i = 1 to m (in the sorted ordering of edges):
(a) If removing e; from H does not make H disconnected, remove e; from H.
4. Return H as a minimum spanning tree of G.
Prove the correctness of this algorithm, i.e., that it outputs an MST of any given graph G (we ignore the
runtime of this algorithm in this problem).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98182d17-9434-4dd7-9261-6c7c628c58da%2F2e628ca2-4af8-42d2-a015-4d64df8870dd%2F0sio90x_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following different (and less efficient) algorithm for computing
an MST of a given undirected and connected graph G = (V, E) with edge weight we on each e € E:
1. Sort the edges in decreasing (non-increasing) order of their weights.
2. Let H = G be a copy of the graph G.
3. For i = 1 to m (in the sorted ordering of edges):
(a) If removing e; from H does not make H disconnected, remove e; from H.
4. Return H as a minimum spanning tree of G.
Prove the correctness of this algorithm, i.e., that it outputs an MST of any given graph G (we ignore the
runtime of this algorithm in this problem).
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