AMUSEMENT PARK PROJECT MODULE 1 GRAPH THEORY PART

PART I – EULER CIRCUITS DUE AT THE END OF CLASS ON THURSDAY, SEPTEMBER

GUIDELINES #1 Make a graph of all of the attractions and the paths between

GUIDELINES #2 Attraction (vertex) Splash Mountain Describe the valence of the graph. • for

GUIDELINES #3 Create an Euler Circuit of the rides/attractions. *Note that you may need

GUIDELINES #4 What effect will this have on a guest at the park? *Word

COVER PAGE REQUIREMENTS • Title of Project • Amusement Park Project Part I –

PART II – HAMILTONIAN CIRCUITS DUE AT THE BEGINNING OF CLASS ON FRIDAY, OCTOBER

GUIDELINES #1 • Make a graph of all of the attractions and the paths

GUIDELINES #2 • Use each of the algorithms discussed in the textbook to find

GUIDELINES #3 • Compare the results of the algorithms you applied; what circuit takes

GUIDELINES #4 • Estimate the minimum time you would need at the amusement park

EXTRA CREDIT • Minimum Cost Spanning Tree • • A reason for finding the

COVER PAGE REQUIRED • Title of Project • Amusement Park Project Part II –

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AMUSEMENT PARK PROJECT MODULE 1 GRAPH THEORY

PART I – EULER CIRCUITS DUE AT THE END OF CLASS ON THURSDAY, SEPTEMBER 27 ND

GUIDELINES #1 Make a graph of all of the attractions and the paths between them that are described in the given table. *extra credit offered for word processed document* • transfer each attraction to a vertex on a graph • label each attraction with letters • create a “key” naming each attraction • connect all of the vertices with edges according to the given table

GUIDELINES #1

GUIDELINES #2 Attraction (vertex) Splash Mountain Describe the valence of the graph. • for each vertex, describe the valence • if eulerization is needed, indicate change in valence Indiana Jones Adventure Tarzan’s Treehouse Valence (original) Valence (change)

GUIDELINES #3 Create an Euler Circuit of the rides/attractions. *Note that you may need to Eulerize the graph!* • describe the path that would be traveled by the guest • include order and direction (numbers & arrows) • if eulerization is needed, indicate edges added

GUIDELINES #4 What effect will this have on a guest at the park? *Word processed document* • Discuss the paths the guests will have to take as a result of creating an Euler circuit of the graph of the park. • Describe in a few sentences the objectives of creating an Euler circuit. • Describe the benefits and any drawbacks of traveling an Euler circuit at the park.

CHECK THE RUBRIC

COVER PAGE REQUIREMENTS • Title of Project • Amusement Park Project Part I – Euler Circuits • Class Title • Math Applications & Reasoning • Graphic • Period • Group Member Names • First and last • Capitalization!

PART II – HAMILTONIAN CIRCUITS DUE AT THE BEGINNING OF CLASS ON FRIDAY, OCTOBER 28 TH

GUIDELINES #1 • Make a graph of all of the attractions and the paths connecting them; include the walking times along the edges, from the information given in the tables • Computer Generated or done on Poster Board

GUIDELINES #2 • Use each of the algorithms discussed in the textbook to find an efficient (in terms of time) circuit of the rides. • Nearest-Neighbor • • Starting at Splash Mountain Sorted Edges

GUIDELINES #3 • Compare the results of the algorithms you applied; what circuit takes the least amount of time.

GUIDELINES #4 • Estimate the minimum time you would need at the amusement park to ride each attraction listed in these tables • Note you need to include the waiting/riding times in addition to the total walking time. • Must be word processed

EXTRA CREDIT • Minimum Cost Spanning Tree • • A reason for finding the MSP Use Kruskal’s Algorithm Weights will be cost of MSP (thousands of dollars) Include the spanning tree

CHECK THE RUBRIC

COVER PAGE REQUIRED • Title of Project • Amusement Park Project Part II – Hamiltonian Circuits • Class Title • Math Applications & Reasoning • Graphic • Period • Group Member Names • • First and last Capitalization!