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Suppose that you are given a set T of projects where each project t T is associ- ated with • a positive integer e, denoting the amount of effort (e.g., the amount of time or energy) required to complete the project t, and • a positive integer p, denoting the profit gained by completing the project t. Given a positive integer c denoting the maximum amount of effort that you can spend on these projects, the goal is to find the largest amount of profit that you can make by completing a subset of these projects such that the total amount of effort spent to complete the projects is at most c. State the decision version of this optimization problem: Input? Output? Prove that the decision version is in NP.

Suppose that you are given a set T of projects where each project t T is associ- ated with • a positive integer e, denoting the amount of effort (e.g., the amount of time or energy) required to complete the project t, and • a positive integer p, denoting the profit gained by completing the project t. Given a positive integer c denoting the maximum amount of effort that you can spend on these projects, the goal is to find the largest amount of profit that you can make by completing a subset of these projects such that the total amount of effort spent to complete the projects is at most c. State the decision version of this optimization problem: Input? Output? Prove that the decision version is in NP.

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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Suppose that you are given a set T of projects where each project t € T' is associ- ated with • a positive integer e, denoting the amount of effort (e.g., the amount of time or energy) required to complete the project t, and • a positive integer pi denoting the profit gained by completing the project t. Given a positive integer c denoting the maximum amount of effort that you can spend on these projects, the goal is to find the largest amount of profit that you can make by completing a subset of these projects such that the total amount of effort spent to complete the projects is at most c. State the decision version of this optimization problem: Input? Output? Prove that the decision version is in NP.
Transcribed Image Text:Suppose that you are given a set T of projects where each project t € T' is associ- ated with • a positive integer e, denoting the amount of effort (e.g., the amount of time or energy) required to complete the project t, and • a positive integer pi denoting the profit gained by completing the project t. Given a positive integer c denoting the maximum amount of effort that you can spend on these projects, the goal is to find the largest amount of profit that you can make by completing a subset of these projects such that the total amount of effort spent to complete the projects is at most c. State the decision version of this optimization problem: Input? Output? Prove that the decision version is in NP.
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