Santa is worried about his employee relations, since christmas preparations have led to a lot of overtime. To make sure all the elves are happy, he wants to recruit some of them as complaint officers, with weekly meetings to report any complaints or worries to him. His worker elves W are pretty busy already, so Santa wants to task no more than k elves with this additional workload. Still, Santa wants to make sure that for as many elves e e W as possible, at least one of his friends (whose identities he knows) is a complaint officer. 1. Give an intuitive greedy algorithm that outputs k elves that will serve as compliant officers. 2. Prove that for large numbers of k the algorithm approximates a solution with ratio no more than (1 – 2).

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
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Santa is worried about his employee relations, since christmas preparations have led to a lot of overtime. To make
sure all the elves are happy, he wants to recruit some of them as complaint officers, with weekly meetings to report any
complaints or worries to him. His worker elves W are pretty busy already, so Santa wants to task no more than k
elves with this additional workload. Still, Santa wants to make sure that for as many elves e e W as possible, at least
one of his friends (whose identities he knows) is a complaint officer.
1. Give an intuitive greedy algorithm that outputs k elves that will serve as compliant officers.
2. Prove that for large numbers of k the algorithm approximates a solution with ratio no more than (1 - ).
Transcribed Image Text:Santa is worried about his employee relations, since christmas preparations have led to a lot of overtime. To make sure all the elves are happy, he wants to recruit some of them as complaint officers, with weekly meetings to report any complaints or worries to him. His worker elves W are pretty busy already, so Santa wants to task no more than k elves with this additional workload. Still, Santa wants to make sure that for as many elves e e W as possible, at least one of his friends (whose identities he knows) is a complaint officer. 1. Give an intuitive greedy algorithm that outputs k elves that will serve as compliant officers. 2. Prove that for large numbers of k the algorithm approximates a solution with ratio no more than (1 - ).
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