Suppose you have gone to the grocery store and stocked up with a week of groceries. You would like to make it home in a reasonable amount of time without traveling too far so that your ice cream does not melt. The grocery store will be your starting location, referred to as s, and your house will be the final destination, referred to as t. The table below shows all connections in the transportation network you will use to travel home (if a connection is not in the table, that arc does not exist in the network). The table also gives the distance and time between any pair of nodes for which a connection exist. Connection Distance |(s,1) (5,2) (1,3) (1,4) (2,3) (2,4) (3,t) (4,t) Time 4 1 3 4 2 1 3 2 4 3 2 2 2 2 2 (a) Draw the network, labeling each node with the appropriate node number {s,t, 1,2,3,4} and labeling each arc with the cost (dg,ty) where dy is the distance of the connection and ty is the time of the connection (b) Use the multi-label algorithm to find the minimum cost paths from the grocery store s to your home t, where the two types of costs being considered are described below. Show your work in the form of a table as we did in class. i. Find the minimum distance path from s to t. ii. Find the path from s to t that minimizes the total time. (c) Are the two paths you found in part (b), (i) and (ii), the same? If not, which path do you think you should use?
Suppose you have gone to the grocery store and stocked up with a week of groceries. You would like to make it home in a reasonable amount of time without traveling too far so that your ice cream does not melt. The grocery store will be your starting location, referred to as s, and your house will be the final destination, referred to as t. The table below shows all connections in the transportation network you will use to travel home (if a connection is not in the table, that arc does not exist in the network). The table also gives the distance and time between any pair of nodes for which a connection exist. Connection Distance |(s,1) (5,2) (1,3) (1,4) (2,3) (2,4) (3,t) (4,t) Time 4 1 3 4 2 1 3 2 4 3 2 2 2 2 2 (a) Draw the network, labeling each node with the appropriate node number {s,t, 1,2,3,4} and labeling each arc with the cost (dg,ty) where dy is the distance of the connection and ty is the time of the connection (b) Use the multi-label algorithm to find the minimum cost paths from the grocery store s to your home t, where the two types of costs being considered are described below. Show your work in the form of a table as we did in class. i. Find the minimum distance path from s to t. ii. Find the path from s to t that minimizes the total time. (c) Are the two paths you found in part (b), (i) and (ii), the same? If not, which path do you think you should use?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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hello
can someone solve this homework?
its about Minimum Cost Paths
Transcribed Image Text:Suppose you have gone to the grocery store and stocked up with a week of groceries. You would like to
make it home in a reasonable amount of time without traveling too far so that your ice cream does not
melt. The grocery store will be your starting location, referred to as s, and your house will be the final
destination, referred to as t. The table below shows all connections in the transportation network you
will use to travel home (if a connection is not in the table, that arc does not exist in the network). The
table also gives the distance and time between any pair of nodes for which a connection exist.
Connection Distance
|(s,1)
(5,2)
(1,3)
(1,4)
(2,3)
(2,4)
(3,t)
(4,t)
Time
4
1
3
4
2
1
3
2
4
3
2
2
2
2
2
(a) Draw the network, labeling each node with the appropriate node number {s,t, 1,2,3,4} and labeling
each arc with the cost (dg,ty) where dy is the distance of the connection and ty is the time of the
connection
(b) Use the multi-label algorithm to find the minimum cost paths from the grocery store s to your
home t, where the two types of costs being considered are described below. Show your work in the
form of a table as we did in class.
i. Find the minimum distance path from s to t.
ii. Find the path from s to t that minimizes the total time.
(c) Are the two paths you found in part (b), (i) and (ii), the same? If not, which path do you think you
should use?
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