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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 30ES

Textbook Problem

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Computer Networks A small office wishes to network its six computers in one large loop (see Check Your Progress 6 on page 255). The lengths of cables in meters, required between machines are given in the table below. Use the edge-picking algorithm to find an efficient cable configuration in which to network the computers.

To determine

To find an efficient cable configuration in which to network the computers using the edge-picking algorithm.

**Given information:**

Given, a small office wishes to network its six computers in one large loop.

The lengths of cable, in meters, required between machines are given in the table below:

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**Calculation:**

Given, there are six computers.

Hence six vertices corresponding to the six computers are marked with respective names.

And then making the complete graph by marking every possible edge with every edge marked with the weight represented in the table between the locations.

The length of cable between Computer A and Computer B is 10. Hence the edge drawn between them has a weight of 10.

Similarly marking all the edges with respective weights, the graph is given as:

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Edge-picking algorithm:

A path in a Hamiltonian graph is said to be a Hamiltonian Circuit if it begins and ends at the same vertex and passes through each vertex of a graph exactly once.

The edge-picking algorithm states to mark the edge that has the smallest weight in the complete graph. Then, the edge with the next smallest weight is marked as long as it does not complete a circuit and does not add a third marked edge to a single vertex. This process continues till no longer an edge can be marked. Then the final edge completing the Hamiltonian circuit is marked...

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