Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 16, Problem 2P
(a)
Program Plan Intro
To design an
(b)
Program Plan Intro
Tasks are running in the preemptive fashion and cannot occur at the same time.Todesign algorithm to schedule tasks to minimizesthe average completion time and to show its complexity.
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[Job sequencing using deadlines]Let us suppose that there are n jobs (J1, J2, … Jn) each of which takes a unit oftime to be processed by a machine and there is just one single machine to processthe jobs. Let us suppose that (d1, d2, d3, …dn) are the deadlines in units of times to complete the jobs and (p1, p2, p3, …pn) are the profits earned if the jobs are processed within the deadline. The objective is obviously to select those jobs and complete them within their deadlines so that maximum profit is earned.Design a greedy method to obtain the optimal sequence of jobs that will earnmaximum profits. Demonstrate it on the case where there are four jobs, with n = 4,deadlines given by (d1 = 2, d2 = 1, d3 = 3, d4 = 1) and profits earned as (p1 = 100,p2 = 20, p3 = 50, p4 = 40).
Show three periodic tasks that do not satisfy the simple schedulable utilization (Schedulability Test 2) but can still be RM-scheduled.
(test 2 Utilization U = sum c_i / p_i Number of tasks n A task set is schedulable if U <= n(2^(1/n) – 1))
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Graph TheorySuppose that a random selection of students will be able to screen a new movie early. There arefour screening sessions. For scheduling purposes, each of the selected students will specify whichof the four screenings don’t conflict with their schedule—every student is available for at least twoout of the four screenings. However, each screening has only 20 available seats, not all of whichneed to be filled each time. The event organizers are faced with a difficult scheduling problem:how do they make sure each of the chosen students is able to find a seat at a screening? They’verecruited you to help solve this dilemma.
(a) Describe how to model this situation as a matching problem. Be sure to specify whatthe vertices/edges should be and briefly describe how a matching would determine seatassignments for each student in a screening for which they are available. (This is a modelingproblem; we aren’t looking for a description of an algorithm to solve the problem.)
(b) Suppose 41…
Chapter 16 Solutions
Introduction to Algorithms
Ch. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5E
Ch. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5P
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