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Consider the classroom CS 206. There are a variety of groups that want to use this room - CS club, CTF club, tutors, faculty, etc. Consider a set of of requests to use the room at a specific time, for a specific interval of whole hours. For example, 3/2/22 11pm-3pm, 3/2/22 9am-12pm, and so on. Some of these requests are split into multiple chunks, for example the faculty might want to use the room from 10am-11am and from 1pm-2pm, and this is considered a single request. We want to maximize the number of requests that we can fit in. Define the 206 request problem as this: determine if there exists a way to schedule room 206 that fits k or more requests, with no overlaps. Show that the independent set problem is polynomial-time reducible to the 206 request problem, and therefore the 206 room request problem is at least as hard as independent set, making it NP-complete. Please type your answer here.

Consider the classroom CS 206. There are a variety of groups that want to use this room - CS club, CTF club, tutors, faculty, etc. Consider a set of of requests to use the room at a specific time, for a specific interval of whole hours. For example, 3/2/22 11pm-3pm, 3/2/22 9am-12pm, and so on. Some of these requests are split into multiple chunks, for example the faculty might want to use the room from 10am-11am and from 1pm-2pm, and this is considered a single request. We want to maximize the number of requests that we can fit in. Define the 206 request problem as this: determine if there exists a way to schedule room 206 that fits k or more requests, with no overlaps. Show that the independent set problem is polynomial-time reducible to the 206 request problem, and therefore the 206 room request problem is at least as hard as independent set, making it NP-complete. Please type your answer here.

Principles Of Marketing
Principles Of Marketing
17th Edition
ISBN:9780134492513
Author:Kotler, Philip, Armstrong, Gary (gary M.)
Publisher:Kotler, Philip, Armstrong, Gary (gary M.)
Chapter1: Marketing: Creating Customer Value And Engagement
Section: Chapter Questions
Problem 1.1DQ
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Consider the classroom CS 206. There are a variety of groups that want to use this room - CS club, CTF club, tutors, faculty, etc. Consider a set of of requests to use the room at a specific time, for a specific interval of whole hours. For example, 3/2/22 11pm-3pm, 3/2/22 9am-12pm, and so on. Some of these requests are split into multiple chunks, for example the faculty might want to use the room from 10am-11am and from 1pm-2pm, and this is considered a single request. We want to maximize the number of requests that we can fit in. Define the 206 request problem as this: determine if there exists a way to schedule room 206 that fits k or more requests, with no overlaps. Show that the independent set problem is polynomial-time reducible to the 206 request problem, and therefore the 206 room request problem is at least as hard as independent set, making it NP-complete. Please type your answer here.
Transcribed Image Text:Consider the classroom CS 206. There are a variety of groups that want to use this room - CS club, CTF club, tutors, faculty, etc. Consider a set of of requests to use the room at a specific time, for a specific interval of whole hours. For example, 3/2/22 11pm-3pm, 3/2/22 9am-12pm, and so on. Some of these requests are split into multiple chunks, for example the faculty might want to use the room from 10am-11am and from 1pm-2pm, and this is considered a single request. We want to maximize the number of requests that we can fit in. Define the 206 request problem as this: determine if there exists a way to schedule room 206 that fits k or more requests, with no overlaps. Show that the independent set problem is polynomial-time reducible to the 206 request problem, and therefore the 206 room request problem is at least as hard as independent set, making it NP-complete. Please type your answer here.
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