MAT 2051  Unit 7 Assignment 2 Graph Applications and the Traveling Salesperson

MAT 2051  Unit 7 Assignment 2 Graph Applications and the Traveling Salesperson

In the class discussions, we have talked about how the traveling salesperson (TSP) problem and how it can be modeled using graphs. We also looked at finding a minimum length in a graph as well as Hamiltonian cycles.

Graphs, graph algorithms and methods, and graph theory are integral to IT and computer science applications and coding. For this assignment, write a two- to three-page paper that responds to each of the following questions:

What is a Hamiltonian cycle?

What is a Euler cycle?

What is a minimum length Hamiltonian cycle?

Given a graph with n edges, what is the time complexity of finding a Euler path? Is this a polynomial time algorithm? Explain and show all work and the graph. Hint: Include the algorithm and pseudocode.

Given a graph with n edges, can one find a minimum Hamiltonian cycle (TSP) in polynomial time? Has anyone ever proved that a polynomial time algorithm does not exist for this problem? Explain your answers and show the graph. Hint: Consider NP complete problems.

Offer one example of an IT or computer application that can be modeled as the TSP problem. This must be at least one paragraph.

Your calculations and work must be shown. Include references to any resources you use to complete the assignment.

Review the Graph Applications and the Traveling Sales Person Scoring Guide to understand how the assignment will be graded.