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

Problem 1PE

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