4. This problem is about how we deal with intractable problems. The Traveling Salesperson Problem (TSP)* is a well-known problem that resembles many practical problems in vehicle routing, network design, computer chip layout, and even DNA sequencing. TSP is NP-HARD, meaning that if we can solve TSP in polynomial time, then we can solve any NP problem in polynomial time by converting it into a TSP problem. This quote from Wikipedia sums it up: The most direct solution would be to try all permutations (ordered combinations) and see which one is cheapest (using brute-force search). The running time for this approach lies within a polynomial factor of 0(n!), the factorial of the number of cities, so this solution becomes impractical even for only 20 cities. Select the most accurate statement about TSP: O A greedy algorithm can be used to solve TSP (produce an exact solution) in polynomial time. O A greedy algorithm can be used to approximate a solution to TSP in polynomial time, where the answer is within 25% of the exact solution. O An approximation algorithm exists for TSP but it requires exponential time and is thus also intractable. O A polynomial time approximation algorithm exists for TSP, which gives an answer guaranteed to be within a factor of 1.5 of the exact solution.
4. This problem is about how we deal with intractable problems. The Traveling Salesperson Problem (TSP)* is a well-known problem that resembles many practical problems in vehicle routing, network design, computer chip layout, and even DNA sequencing. TSP is NP-HARD, meaning that if we can solve TSP in polynomial time, then we can solve any NP problem in polynomial time by converting it into a TSP problem. This quote from Wikipedia sums it up: The most direct solution would be to try all permutations (ordered combinations) and see which one is cheapest (using brute-force search). The running time for this approach lies within a polynomial factor of 0(n!), the factorial of the number of cities, so this solution becomes impractical even for only 20 cities. Select the most accurate statement about TSP: O A greedy algorithm can be used to solve TSP (produce an exact solution) in polynomial time. O A greedy algorithm can be used to approximate a solution to TSP in polynomial time, where the answer is within 25% of the exact solution. O An approximation algorithm exists for TSP but it requires exponential time and is thus also intractable. O A polynomial time approximation algorithm exists for TSP, which gives an answer guaranteed to be within a factor of 1.5 of the exact solution.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Transcribed Image Text:4. This problem is about how we deal with intractable problems. The Traveling
Salesperson Problem (TSP)* is a well-known problem that resembles many practical
problems in vehicle routing, network design, computer chip layout, and even DNA
sequencing.
TSP is NP-HARD, meaning that if we can solve TSP in polynomial time, then we can solve
any NP problem in polynomial time by converting it into a TSP problem. This quote
from Wikipedia sums it up:
The most direct solution would be to try all permutations (ordered combinations)
and see which one is cheapest (using brute-force search). The running time for
this approach lies within a polynomial factor of 0(n!), the factorial of the number
of cities, so this solution becomes impractical even for only 20 cities.
Select the most accurate statement about TSP:
O A greedy algorithm can be used to solve TSP (produce an exact solution)
in polynomial time.
O A greedy algorithm can be used to approximate a solution to TSP in
polynomial time, where the answer is within 25% of the exact solution.
O An approximation algorithm exists for TSP but it requires exponential
time and is thus also intractable.
O A polynomial time approximation algorithm exists for TSP, which gives an
answer guaranteed to be within a factor of 1.5 of the exact solution.
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