C&O 454 Scheduling Spring 2012
Assignment 4
Due: Thu, June 28, in class before lecture
Bonus problem: Due by Tue, July 3
Write your name and ID# clearly, and underline your last name.
Unless otherwise stated, all algorithms should be accompanied
with a pr

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C&O 454 Scheduling Spring 2012
Assignment 2
Due: Thur, May 31, in class before lecture
Bonus problem: Due by Tue, Jun 5
Write your name and ID# clearly, and underline your last name.
Unless otherwise stated, all algorithms should be accompanied
with a pro

C&O 454 Scheduling Spring 2012
Assignment 5
Due: Thu, July 12, in class before lecture
I will hold ofce hours on Wed, July 11 from 3-5pm.
Write your name and ID# clearly, and underline your last name.
Unless otherwise stated, all algorithms should be acco

C&O 454 Scheduling Spring 2013
Assignment 6
Due: Tue, July 30. The location for submitting the assignment will be announced shortly. Note the change.
Write your name and ID# clearly, and underline your last name.
Unless otherwise stated, all algorithms sh

CO 454 - Homework assignment 5
Spring 15
Page 1
CO 454 - Spring 15
Homework assignment #5: (Due on Friday, July 10th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: Textbook, your CO454 c

C&O 454 Scheduling Spring 2016
Assignment 1
Due: Wed, May 25 in class before lecture
Write your name and ID# clearly, and underline your last name. Acknowledge all collaborators.
Unless otherwise stated, all algorithms should be accompanied with a proof o

C&O 454 Scheduling Spring 2016
Assignment 3
Solutions
Problem 1: NP-hard problems
(10 marks)
(a) Recall that in the K NAPSACK problem, we are given a set J of n items, and a knapsack of capacity B. Each
item j has a profit pj and a weight wj . The goal is

C&O 454 Scheduling Spring 2016
Assignment 2
Solutions
Problem 1: Minimizing total (weighted) completion time with release dates
P
(a) Consider the following instance of 1|rj | j Cj .
Jobs
rj
pj
1
0
8
2
2
4
3
3
1
4
5
1
(15 marks)
5
6
5
P
Run the 2-approxim

Chapter 5
Shop scheduling
In the next three lectures, we will look at shop scheduling problems. We will be interested in
minimizing the makespan. To recall, in a shop scheduling problem, we have n jobs, but each job
has m operations corresponding to the m

CO 454 - Homework assignment 2
Spring 15
Page 1
CO 454 - Spring 15
Homework assignment #2: (Due on Friday, May 29th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: Textbook, your CO454 co

CO 454 - Homework assignment 1
Spring 15
Page 1
CO 454 - Spring 15
Homework assignment #1: (Due on Monday, May 18th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: Textbook, your CO454 co

Chapter 1
Introduction
1.1
Examples of Scheduling Problems
Example 1: Your team needs to nish a project as soon as possible. Several tasks must be
completed in order to nish this project. Assume there are m people in your team and n tasks
to be completed.

Chapter 2
Single Machine Environment
The single machine environment is the easiest machine environment. However, that doesnt
mean all scheduling problems in this environment are easy! Moreover, the design of algorithms
for the single machine environment g

Chapter 3
Computational complexity
3.1
Algorithm runtime and Big-O notation
Measuring the precise runtime of an algorithm can be a daunting task. For example, consider
the following algorithm for adding two m n matrices
Algorithm 3: Adding two matrices
in

CO 454 - Homework assignment 4
Spring 15
Page 1
CO 454 - Spring 15
Homework assignment #4: (Due on Monday, June 29th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: Textbook, your CO454 c

CO 454 - Homework assignment 1
Spring 15
Page 1
CO 454 - Spring 15
Homework assignment #1: (Due on Wednesday, May 20th)
(7 points)
Question 1
(a) (5 points) Show that, if for every j J, fj : R+ R is a non-decreasing function, then
wj fj (Cj )
jJ
and max f

CO 454 - Homework assignment 5
Spring 15
Page 1
CO 454 - Spring 15
Homework assignment #5: (Due on Friday, July 10th)
Question 1 (16 points)
Consider the following set of jobs:
Jobs 1 2 3 4 5 6 7
pj
8 1 3 2 2 4 2
Find the optimal schedules for (P |pmtn|Cm

CO 454 - Homework assignment 3
Spring 15
Page 1
CO 454 - Spring 15
Homework assignment #3: (Due on Friday, June 5th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: Textbook, your CO454 co

CO 454 - Homework assignment 3
Spring 15
Page 1
CO 454 - Spring 15
Homework assignment #3: (Due on Friday, June 5th)
Question 1 (20 points)
Consider the problem (1|prec|fmax ), where fj : R+ R, j J are nondecreasing functions and
fmax := maxjJ fj (Cj ). G

C&O 454 Scheduling Spring 2016
Assignment 4
Due: Wed, Jul 6 in class before lecture
Bonus problem: Due by Mon, Jul 11
Write your name and ID# clearly, and underline your last name. Acknowledge all collaborators.
Unless otherwise stated, all algorithms sho

C&O 454 Scheduling Spring 2016
Assignment 3
Due: Mon, Jun 27 in class before lecture
Write your name and ID# clearly, and underline your last name. Acknowledge all collaborators.
Unless otherwise stated, all algorithms should be accompanied with a proof o

C&O 454: Scheduling
Practice Questions
Problem 1:
(a) Dene what is meant by NP, an NP-hard problem, and an NP-complete problem. (Your denition can
refer to the notion of a polynomial-time algorithm, and a polynomial-time reduction denoted by P ,
but you m

C&O 454: Scheduling
Practice Questions
Problem 1:
(a) Dene what is meant by NP, an NP-hard problem, and an NP-complete problem. (Your denition can
refer to the notion of a polynomial-time algorithm, and a polynomial-time reduction denoted by P ,
but you m

C&O 454 Scheduling Spring 2013
Assignment 2
Due: Thur, Jun 6, in class before lecture
Bonus problem: Due by Tue, Jun 11
Write your name and ID# clearly, and underline your last name.
Unless otherwise stated, all algorithms should be accompanied
with a pro

C&O 454 Scheduling Spring 2013
Assignment 1
Due: Thu, May 30 in class before lecture
Write your name and ID# clearly, and underline your last name.
Unless otherwise stated, all algorithms should be accompanied
with a proof of correctness and a brief analy

Scheduling Algorithms
David Karger, Massachusetts Institute of Technology
Cli Stein, Dartmouth College
Joel Wein, Polytechnic University
1 Introduction
Scheduling theory is concerned with the optimal allocation of scarce resources to activities over
time.