Exercise 2You are tasked with shipping a number n of goods g; € {1,..., n} to a target location t;. In your very rural area, theroads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies youcan use for the transport of any good g;. You have to order one truck for each good, and know the companies' routesPi,1, Pi,2 and Pi3 they would take to all specific locations, where each route consists of a sequence of road segmentsthat it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transportsto be obstructed, your aim is to pick the paths/companies for the goods in such a way that a single blocked road canintercept as few shipments as possible. I.e. choose a path Pj for every good g; such that maxee E {|{Pi,j|e € Pi,j}|}is as small as possible, where E is the set of all road segments.(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.

According to the question we have to (a) Formulate the problem as an ILP, and relax to an…

ou are tasked with shipping a number n of goods gi € {1,., n} to a target location t;. In your very rural area, bads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies an use for the transport of any good g;. You have to order one truck for each good, and know the companies' roi ,1, Pi,2 and P3 they would take to all specific locations, where each route consists of a sequence of road segme at it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transp be obstructed, your aim is to pick the paths/companies for the goods in such a way that a single blocked road tercept as few shipments as possible. I.e. choose a path Pij for every good g; such that maxeɛE {l{Pi.j|e E P;, as small as possible, where E is the set of all road segments. ) Formulate the problem as an ILP, and relax to an according LP. ) Give a rounding algorithm to compute a feasible solution starting from the LP optimum that guarantees oproximation to the optimal solution, and prove its approximation guarantee.

ou are tasked with shipping a number n of goods gi € {1,., n} to a target location t;. In your very rural area, bads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies an use for the transport of any good g;. You have to order one truck for each good, and know the companies' roi ,1, Pi,2 and P3 they would take to all specific locations, where each route consists of a sequence of road segme at it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transp be obstructed, your aim is to pick the paths/companies for the goods in such a way that a single blocked road tercept as few shipments as possible. I.e. choose a path Pij for every good g; such that maxeɛE {l{Pi.j|e E P;, as small as possible, where E is the set of all road segments. ) Formulate the problem as an ILP, and relax to an according LP. ) Give a rounding algorithm to compute a feasible solution starting from the LP optimum that guarantees oproximation to the optimal solution, and prove its approximation guarantee.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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