Answered: When Bobby’s friends visit her on the…

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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Question

When Bobby’s friends visit her on the farm, she likes to show them around. The
farm consists of n fields numbered 1, 2, . . . , n, the first of which contains her house and the n-th of which
contains the big barn. A total of m directed paths connect the fields. The i-th path is from field ui to field
vi, and has a nonzero length wi.
1

Suppose there are k friends coming today. To show off the farm in the best way, Bobby designs a tour
for each friend that starts at her house, potentially travels through some fields, and ends at the barn.
Bobby wants the total length of the k tours to be as short as possible, where the length of a tour is the
total length of paths in the tour. However, she doesn’t want any two friends to share any path. That is,
for any two friends, their tours should not have any common paths (but they can travel through the same
fields). Write an LP that can calculate the shortest total length of k tours that satisfies Bobby. You can
assume that at least one feasible solution exists. (If you use min-cost flow as an intermediate step, you will
still need to provide an LP formulation in the end. Please avoid using shorthand notations such as out-in
notation.)

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