## 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 May 24 - 11:55pm May 29.
• 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 May 29 will be given a zero. No exceptions!

## Homework Assignments (Sakai-> Assignments)

• Chapter 2
pages 62 - 71 Problems 4, 7, 12, 26, 34, 46a, 55, 74
Due by 11:59pm May 29.
• Use the Assignments tool to submit homework.
• Homework help.
• Problems 4 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.
• Problems 26 and 34. Carefully read Example 2 in Section 2.1 before responding to these exercises. These exercises involve applying the fundamental counting principle.
• Problem 46a. Carefully read Section 2.3 and the examples before responding to this exercise. You are using Graph (a) AND Graph (b) and you provide a nearest neighbor solution and a sorted edge solution. There should be FOUR answers. All solutions start and end at B.
• 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.

## 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)

• Due by 11:59 pm Tuesday May 27
• 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 Saturday May 24.
• You are required to participate in the discussion boards.
• Discussion topic will end at 11:55 pm Thursday May 29.
• See the syllabus on the grading rubric for discussions.

## James Baglama

Texting Number: (401) 268-7160
Email: jbaglama@math.uri.edu
Office hours: by appointment
Office: Lippitt Hall 202H
Office Phone: (401) 874-4412

## 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.