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.
APA Writing Checklist
Use this document as a checklist for each paper you will write throughout your GCU graduate program. Follow specific instructions indicated in the assignment and use this checklist to help ensure correct grammar and APA formatting. Refer to the APA resources available in the GCU Library and Student Success Center.
☐ APA paper template (located in the Student Success Center/Writing Center) is utilized for the correct format of the paper. APA style is applied, and format is correct throughout.
☐ The title page is present. APA format is applied correctly. There are no errors.
☐ The introduction is present. APA format is applied correctly. There are no errors.
☐ Topic is well defined.
☐ Strong thesis statement is included in the introduction of the paper.
☐ The thesis statement is consistently threaded throughout the paper and included in the conclusion.
☐ Paragraph development: Each paragraph has an introductory statement, two or three sentences as the body of the paragraph, and a transition sentence to facilitate the flow of information. The sections of the main body are organized to reflect the main points of the author. APA format is applied correctly. There are no errors.
☐ All sources are cited. APA style and format are correctly applied and are free from error.
☐ Sources are completely and correctly documented on a References page, as appropriate to assignment and APA style, and format is free of error.
Scholarly Resources: Scholarly resources are written with a focus on a specific subject discipline and usually written by an expert in the same subject field. Scholarly resources are written for an academic audience.
Examples of Scholarly Resources include: Academic journals, books written by experts in a field, and formally published encyclopedias and dictionaries.
Peer-Reviewed Journals: Peer-reviewed journals are evaluated prior to publication by experts in the journal’s subject discipline. This process ensures that the articles published within the journal are academically rigorous and meet the required expectations of an article in that subject discipline.
Empirical Journal Article: This type of scholarly resource is a subset of scholarly articles that reports the original finding of an observational or experimental research study. Common aspects found within an empirical article include: literature review, methodology, results, and discussion.
Adapted from “Evaluating Resources: Defining Scholarly Resources,” located in Research Guides in the GCU Library.
☐ The writer is clearly in command of standard, written, academic English. Utilize writing resources such as Grammarly, LopesWrite report, and ThinkingStorm to check your writing.
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