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.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
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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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