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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.

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.

**Given information:**

The graph of Hamiltonian circuit is

**Calculation:**

- Using Greedy algorithm, the Hamiltonian circuit starting at vertices A is:
- The Hamiltonian circuit starting at vertices B is:
- The Hamiltonian circuit starting at vertices C is:
- The Hamiltonian circuit starting at vertices D is:

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

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

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

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

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