## Chapter 2 Videos Business Efficiency and Lecture Notes

 Reading Assignment Video Lecture Notes 2.1 Hamiltonian Circuits pages 36 - 42 Section 2.1 Video Section 2.1 Lecture notes 2.2 Traveling Salesman Problem pages 42 - 43 Section 2.2 and Section 2.3 Video Section 2.2 and Section 2.3 Lecture notes 2.3 Helping Traveling Salesman pages 43 - 47 2.4 Minimum-Cost Spanning Trees pages 47 - 52 Section 2.4 Video Section 2.4 Lecture notes 2.5 Critical Path Analysis pages 53 - 57 Section 2.5 Video Section 2.5 Lecture notes

## Chapter 2 Objectives (Skills)

• Write in your own words the definition of a Hamiltonian circuit.
• Explain the difference between an Euler circuit and a Hamiltonian circuit.
• Identify a given application as being an Euler circuit problem or a Hamiltonian circuit problem.
• Calculate n! for a given value of n.
• Apply the formula (n −1)/2! to calculate the number of distinct Hamiltonian circuits in a complete graph with a given number of vertices.
• Define the term algorithm.
• Explain the term heuristic algorithm and list both an advantage and a disadvantage of using this algorithm.
• Discuss the difficulties inherent in the application of the brute force method for finding the shortest-route Hamiltonian circuit.
• Describe the steps in the nearest-neighbor algorithm.
• Find an approximate solution to the traveling salesman problem by applying the nearest-neighbor algorithm.
• Describe the steps in the sorted-edges algorithm.
• Find an approximate solution to the traveling salesman problem by applying the sorted-edges algorithm.
• Explain the difference between a graph and a tree.
• Determine from a weighted-edges graph a minimum-cost spanning tree.
• Identify the critical path on an order-requirement digraph.
• Find the earliest possible completion time for a collection of tasks by analyzing its critical path.
• Explain the difference between a graph and a directed graph.

## Quiz 2 Chapter 2 (Sakai-> Tests & Quizzes)

• The quiz for Chapter 2 will be available from 12:00am Feb. 13 - 11:55pm Feb. 26.
• The quiz will consist of 10 multiple choice questions.
• You will have a maximum of two hours to complete the quiz.
• You will be allow two tries. The computer will accept the best score.
• Failure to take the quiz by 11:55pm Feb. 26 will be given a zero. No exceptions!

## Homework Assignments (Sakai-> Assignments)

• Chapter 2
pages 62 - 71 Problems 2, 7, 12, 26, 48, 56, 74
Due by 11:55pm Feb. 26
• Use the Assignments tool to submit homework.
• Homework help.
• Problems 2 and 7. Carefully read Section 2.1 before responding to these exercises. Remember that a Hamiltonian circuit visits each vertex once returning where it started.
• Problem 12. Carefully read Section 2.1 and Example B (page 22 in this guide) before answering this exercise.
• Problem 26. Carefully read Example 2 in Section 2.1 before responding to this exercise. This exercise involves the fundamental counting principle.
• Problem 48. Carefully read Section 2.3 and the examples before responding to this exercise. There are 3 graphs and two methods, the nearest neighbor and a sorted edge. There should be 6 answers. All solutions start and end at vertex A.
• Problem 56. There are no costs on the edges, hence no minimum cost spanning trees. Read section 2.4 and refer to Figure 2.14.
• Problem 74. Carefully read Section 2.5 and the examples before responding to this exercise. Read the definition of critical path very carefully.
• I will NOT accept homework with answers only. Show all work.

## Companion Website

• Go to the companion website and navigate to applets for chapter 2.
• Click on the Kruskal's Algorithm applet
• Click on Traveling Salesman Problem - Nearest Neighbor Algorithm applet
• Click on Traveling Salesman Problem - Sorted Edges Algorithm applet
• In the companion website navigate to Video Clips for chapter 2 and click on Strategies for Solving the TSP and Minimum-Cost Spanning Trees

## Chapter worksheets (Sakai -> Assignments)

Each worksheet will have 10 questions (each worth 1 point). The worksheets are designed to help you understand material. The worksheets are downloadable from the Assignment tool within Sakai as a Microsoft Word (or OpenOffice) and also as a pdf file. You can write on the worksheets and upload your answers or (similar to homework submissions) take a digital picture of your handwritten assignment with a camera or smart phone. I will not accept worksheets without worked out problems. Worksheets with answers only will be given a zero. You must show the work for credit. All worksheet answers must be submitted within Sakai. The due dates for the worksheets are one week before the due date for homework assignments, so that you can get feedback on problems before submitting your homework and doing your quizzes. DO NOT SUBMIT ASSIGNMENTS VIA EMAILS OR FAXES! I will not accept them! Do not ask to submit late worksheets.

• Due by 11:55 pm Feb. 19
• Use the Assignments tool to submit worksheet.

## Discussion Topic (Sakai-> Forums)

• Select a topic to respond.
• Topic 1: The Traveling Salesman Problem is one of the most intensively studied problems in mathematics. Why? What is the history behind the problem? What are the applications? How would improve the movie Strategies for Solving the TSP on the companion website, i.e. what would you do differently?
• Topic 2: Discuss how the nearest neighbor method differs from the sorted edges method. How are they similar? How are they different? Why might one be preferred over the other?
• Topic 3: What is Kruskal's algorithm? Give an application not yet mentioned in the Forum nor in the text and explain why Kruskal's algorithm is a good way to find the needed solution for your application.
• Topic 4: What is critical path analysis? Give an example of its use not yet mentioned in this forum nor in the text and explain why critical path analysis is a good choice for your application.
• Discussion for Chapter 2 will open at 12:00 am Feb. 13
• You are required to participate in the discussion boards.
• Discussion topic will end at 11:55 pm Feb. 26
• See the syllabus on the grading rubric for discussions.

## James Baglama

Email: jbaglama@uri.edu
Office hours: By appointment
Office: Lippitt Hall 200
Office Phone: (401) 874-2709

## For All Practical Purposes

The required textbook, "For All Practical Purposes", 9th edition by COMAP, Publisher W.H. Freeman. Do NOT use an older edition. All students must have either a phyiscal copy of the textbook or an ebook.Click on the textbook above to go to the ebook.

## For All Practical Purposes Campanion Site

The required textbook, The textbook "For All Practical Purposes", 9th edition by COMAP,Publisher W.H. Freeman has a campanion website. The campanion website contains a lot helpful material,e.g. Java Applets, falshcards, practice quizzes. The site can be accessed via the link Campanion or click on the picture above to go to the campanion website.