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You are tasked with shipping a number n of goods g¡ € {1,…, n} to a target location t;. In your very rural area, the roads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies you can use for the transport of any good g;. You have to order one truck for each good, and know the companies' routes Pi,1, Pi2 and P3 they would take to all specific locations, where each route consists of a sequence of road segments that it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transports to be obstructed, your aim is to pick the paths P;j for each good in such a way that max{EcEP 1|e e E} is as small as possible. (a) Formulate the problem as an ILP, and relax to an according LP. (b) Give a rounding algorithm to compute a feasible solution starting from the LP optimum that guarantees a 3- approximation to the optimal solution, and prove its approximation guarantee.

You are tasked with shipping a number n of goods g¡ € {1,…, n} to a target location t;. In your very rural area, the roads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies you can use for the transport of any good g;. You have to order one truck for each good, and know the companies' routes Pi,1, Pi2 and P3 they would take to all specific locations, where each route consists of a sequence of road segments that it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transports to be obstructed, your aim is to pick the paths P;j for each good in such a way that max{EcEP 1|e e E} is as small as possible. (a) Formulate the problem as an ILP, and relax to an according LP. (b) Give a rounding algorithm to compute a feasible solution starting from the LP optimum that guarantees a 3- approximation to the optimal solution, and prove its approximation guarantee.

Computer Networking: A Top-Down Approach (7th Edition)
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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You are tasked with shipping a number n of goods g; E {1, ... , n} to a target location t;. In your very rural area, the roads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies you can use for the transport of any good g;. You have to order one truck for each good, and know the companies' routes Pi,1, Pi2 and Pi3 they would take to all specific locations, where each route consists of a sequence of road segments that it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transports to be obstructed, your aim is to pick the paths Pij for each good in such a way that max{E.EP. 1|e e E} is as small as possible. (a) Formulate the problem as an ILP, and relax to an according LP. (b) Give a rounding algorithm to compute a feasible solution starting from the LP optimum that guarantees a 3- approximation to the optimal solution, and prove its approximation guarantee.
Transcribed Image Text:You are tasked with shipping a number n of goods g; E {1, ... , n} to a target location t;. In your very rural area, the roads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies you can use for the transport of any good g;. You have to order one truck for each good, and know the companies' routes Pi,1, Pi2 and Pi3 they would take to all specific locations, where each route consists of a sequence of road segments that it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transports to be obstructed, your aim is to pick the paths Pij for each good in such a way that max{E.EP. 1|e e E} is as small as possible. (a) Formulate the problem as an ILP, and relax to an according LP. (b) Give a rounding algorithm to compute a feasible solution starting from the LP optimum that guarantees a 3- approximation to the optimal solution, and prove its approximation guarantee.
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