Exercises
You live in Chicago, and you need to visit New York, Los Angeles, Miami, and Seattle.
a. How many different circuits does your graph have?
b. Approximate the cheapest route, using the nearest neighbor algorithm. Draw this route's graph.
c. Approximate the cheapest route, using the repetitive nearest neighbor algorithm. Draw this route's graph.
d. Approximate the cheapest route, using the cheapest edge algorithm. Draw this route's graph.
e. Why would it not be appropriate to find the cheapest route, using the brute force method?
From: | |||||||
CHI | NYC | LAX | MIA | SEA | HOU | ||
CHI |
|
|
|
|
|
||
To: | NYC |
|
|
|
|
|
|
LAX |
|
|
|
|
|
||
MIA |
|
|
|
|
|
||
SEA |
|
|
|
|
|
||
HOU |
|
|
|
|
$294 |
Figure 9.119 Flight costs between Chicago, New York, Los Angeles, Miami, Seattle, and Houston. Source: www.travelocity.com.
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Mathematics: A Practical Odyssey
- Suppose you wish to install a drip sprinkler system and need to run a drip water line to five areas, as shown in the given graph. TI numbers show the distances in feet. What is the smallest number of feet of drip hose necessary to install? 43 70 72 40 46arrow_forwardA delivery person must visit each street once before returning home (node E). What ordering of the streets minimize the total distance the delivery person must travel before returning home. (The numbers next to arc indicates the distance in meters for travelling). Based on the network below;arrow_forward17. Determine how many components the graph has, and explain why does it have that number. Marrow_forward
- How many edges will you have in a complete graph made of 40 vertices? Show all steps of your calculation.arrow_forwardGiven the figure below. Redraw again the figure to determine the shortest path using The Edge – Picking Algorithm/Cheapest Link Methodarrow_forwardA floor plan of a museum is shown. Draw a graph that represents the floor plan, where each vertex represents a room and an edge connects two vertices if there is a doorway between the two rooms. Is it possible to walk through the museum and pass through each doorway without going through any doorway twice? Does it depend on whether you return to the room you started at? Justify your conclusion.arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education