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In the maximum coverage problem, we have a set of n elements E, a set of m sets (which are subsets of E), S1, S2, .., Sm. We are also given an integer m ≥ k ≥ 1. Our goal is to pick k sets that cover the maximum number of elements. We say an element is covered if we pick at least one set from S1, S2, .., Sm in our solution that contains that element. Devise a greedy algorithm that is a (1 −1/e) approximation. That is if there is an optimum solution that can cover OPT number of elements, the greedy algorithm is guaranteed to cover at least  (1 −1/e) *OPT elements. Here e is the base of natural logarithm. Use the following relation (1-1/k)k ~1/e.

In the maximum coverage problem, we have a set of n elements E, a set of m sets (which are subsets of E), S1, S2, .., Sm. We are also given an integer m ≥ k ≥ 1. Our goal is to pick k sets that cover the maximum number of elements. We say an element is covered if we pick at least one set from S1, S2, .., Sm in our solution that contains that element. Devise a greedy algorithm that is a (1 −1/e) approximation. That is if there is an optimum solution that can cover OPT number of elements, the greedy algorithm is guaranteed to cover at least  (1 −1/e) *OPT elements. Here e is the base of natural logarithm. Use the following relation (1-1/k)k ~1/e.

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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In the maximum coverage problem, we have a set of n elements E, a set of m sets (which
are subsets of E), S1, S2, .., Sm. We are also given an integer m ≥ k ≥ 1. Our goal is to pick k sets that
cover the maximum number of elements. We say an element is covered if we pick at least one set from
S1, S2, .., Sm in our solution that contains that element.

Devise a greedy algorithm that is a (1 −1/e) approximation. That is if there is an optimum solution that
can cover OPT number of elements, the greedy algorithm is guaranteed to cover at least  (1 −1/e) *OPT elements. Here e is the base of natural logarithm. Use the following relation (1-1/k)k ~1/e.

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