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Mathematical Excursions (MindTap Course List)4th Edition
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Use the greedy algorithm and the weighted graph below to generate a Hamiltonian circuit starting from each vertex. Then compare the different circuits to find the one of smallest total weight.

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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.2, Problem 2EE
Textbook Problem
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Use the greedy algorithm and the weighted graph below to generate a Hamiltonian circuit starting from each vertex. Then compare the different circuits to find the one of smallest total weight.

Chapter 5.2, Problem 2EE, Use the greedy algorithm and the weighted graph below to generate a Hamiltonian circuit starting

To determine

The Hamiltonian circuits using greedy algorithm starting at each vertex. Then compare the various Hamiltonian circuits to identify the one with the smallest total weight.

Explanation of Solution

Given information:

The graph of Hamiltonian circuit is

Calculation:

  1. Using Greedy algorithm, the Hamiltonian circuit starting at vertices A is:

    2. The circuit starting at A: A − F − C − D − E − B − A.

    Total weight of this circuit is 8 + 7 + 8 + 3 + 15 + 24 = 65

  2. The Hamiltonian circuit starting at vertices B is:

    3. The circuit starting at B: B − D − E − F − C − A − B.

    Total weight of this circuit is 5 + 3 + 16 + 7 + 11 + 24 = 66

  3. The Hamiltonian circuit starting at vertices C is:

    4. The circuit starting at C: C − F − A − D − E − B − C.

    Total weight of this circuit is 7 + 8 + 20 + 3 + 15 + 17 = 70

  4. The Hamiltonian circuit starting at vertices D is:

    5. The circuit starting at D: D − E − B − C − F − A − D...

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Mathematical Excursions (MindTap Course List)
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Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - Explain why the following pen-tracing puzzle is...Ch. 5.1 - Transportation An X in the table below indicates a...Ch. 5.1 - Transportation The table below shows the nonstop...Ch. 5.1 - Social Network A group of friends is represented...Ch. 5.1 - Baseball The local Little League baseball teams...Ch. 5.1 - Determine (a) the number of edges in the graph,...
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