Introduction to Algorithms
November 27, 2002
Massachusetts Institute of Technology
6.046J/18.410J
Professors Erik Demaine and Shafi Goldwasser
Handout 25
Problem Set
This is a
makeup
problem set, only for students who are missing several problems. It is due to
your TA on
Monday, December 2.
Mark the top of each sheet with your name, the course number, the problem number, your
recitation section, the date, and the names of any students with whom you collaborated.
Each problem should be done on a separate sheet (or sheets) of threehole punched paper.
You will often be called upon to “give an algorithm” to solve a certain problem. Your writeup
should take the form of a short essay. A topic paragraph should summarize the problem you are
solving and what your results are. The body of your essay should provide the following:
1. A description of the algorithm in English and, if helpful, pseudocode.
2. At least one worked example or diagram to show more precisely how your algorithm works.
3. A proof (or indication) of the correctness of the algorithm.
4. An analysis of the running time of the algorithm.
Remember, your goal is to communicate. Graders will be instructed to take off points for convo
luted and obtuse descriptions.
Problem
1.
Suppose you are given a set
of
tasks, where task
requires
units of pro
cessing time to complete, once it has started. You have one computer on which to run these tasks,
and the computer can run only one task at a time.
A
schedule
assigns which tasks to run during what times on the computer. For any schedule, let
denote the
completion time
of task , that is, the time at which task
completes processing. Your
goal is to find a schedule that minimizes the average completion time, that is, one that minimizes
(a)
Suppose there are two tasks with
and
. Consider (1) the schedule in
which task 1 runs first, followed by task 2 and (2) the schedule in which task 2 runs
first, followed by task 1. In each case, state the values of
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 Spring '09
 Naver
 Algorithms, Analysis of algorithms, Erik Demaine, average completion time

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