Consider the following task of building a zoo for Drexel! You've gathered m donors to fund the creation vour new park, and you've picked the location, so now you just need to choose the inhabitants. Ideally yo get every animal imaginable, except you just don't have space. As it is, you have room to comfortably s animals. Since you'd like to ensure that your funding doesn't dry up, you figure your donors should o make requests about which animals will be kept. After sending out a few emails, you collect from e lonor i a list of animals A; which donor i would like to have at the zoo. As you suspected, the total num of different animals appearing on the m lists exceeds k, so you won't be able to satisfy all of their reque You decide the fairest thing to do is to ensure that at least 1 animal from each A; is chosen. Given all these lists, we want to know whether we can select a set H of at most k animals to put in coo such that each donor i will be able to see at least one of the animals from her list A; (that is, Hn A

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...
Question
Problem 3
Consider the following task of building a zoo for Drexel! You've gathered m donors to fund the creation of
your new park, and you've picked the location, so now you just need to choose the inhabitants. Ideally you'd
get every animal imaginable, except you just don't have space. As it is, you have room to comfortably fit
k animals. Since you'd like to ensure that your funding doesn't dry up, you figure your donors should get
to make requests about which animals will be kept. After sending out a few emails, you collect from each
donor i a list of animals A; which donor i would like to have at the zoo. As you suspected, the total number
of different animals appearing on the m lists exceeds k, so you won't be able to satisfy all of their requests.
You decide the fairest thing to do is to ensure that at least 1 animal from each A; is chosen.
Given all these lists, we want to know whether we can select a set H of at mostk animals to put in the
zoo such that each donor i will be able to see at least one of the animals from her list A; (that is, HNA; is
non-empty for each i).
Prove that this problem is NP-complete.
Transcribed Image Text:Problem 3 Consider the following task of building a zoo for Drexel! You've gathered m donors to fund the creation of your new park, and you've picked the location, so now you just need to choose the inhabitants. Ideally you'd get every animal imaginable, except you just don't have space. As it is, you have room to comfortably fit k animals. Since you'd like to ensure that your funding doesn't dry up, you figure your donors should get to make requests about which animals will be kept. After sending out a few emails, you collect from each donor i a list of animals A; which donor i would like to have at the zoo. As you suspected, the total number of different animals appearing on the m lists exceeds k, so you won't be able to satisfy all of their requests. You decide the fairest thing to do is to ensure that at least 1 animal from each A; is chosen. Given all these lists, we want to know whether we can select a set H of at mostk animals to put in the zoo such that each donor i will be able to see at least one of the animals from her list A; (that is, HNA; is non-empty for each i). Prove that this problem is NP-complete.
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