Answered: Part (a) MST: An MST T with respect to…

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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Part (a) MST: An MST T with respect to the original weights is still a MST with the new weights (of course the weight of the tree changes but the tree itself is still a MST):

True or False?

If you said True then give a short explanation why, and if you said False then give a counterexample (you can upload a picture).

Note, you cannot assume the MST was constructed using a specific algorithm, but you can assume each edge satisfies the cut property for some cut.

Part (b) Shortest paths: The shortest paths with respect to the original weights are still shortest paths with the new weights (of course the weights of the path change but the paths themselves are still shortest paths):

True or False?

If you said True then give a short explanation why, and if you said False then give a counterexample

Consider an undirected graph G = (V, E) with nonnegative edge weights we ≥ 0. Suppose that
you have computed a minimum spanning tree of G, and that you have also computed shortest
paths to all nodes from a particular node s € V.
Now suppose each edge weight is increased by 1: the new weights are w
=
We + 1.
(a) Does the minimum spanning tree change? Give an example where it changes or prove it
cannot change.
(b) Do the shortest paths change? Give an example where they change or prove they cannot
change.

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