UMBC CMSC441, Design & Analysis of Algorithms, Fall 1999, Section 0101
Project: Select versus Quicksort
The report for this project is due November 11, 1999. You will also be
asked to submit the source code for your programs online (details
will be given later).
After reading the description of the linear-time Select algorithm,
Professor X made the following statement:
This algorithm is so complicated that if you were to implement it in real
life it would be really slow. Even though the theoretical analysis gives
it a O(n) running time, it will probably be faster to just use Quicksort.
The purpose of your project is to either support or refute Professor X's
For this project you will implement the following algorithms to find the
median element in an array.
We fully expect that the randomized selection algorithm will the fastest of
the three --- it will be used to check the other two algorithms.
- The deterministic linear time Select algorithm given
in Chapter 10 of the textbook.
- The randomized selection algorithm given in Chapter 10 of the
- Using randomized Quicksort to first sort the set of numbers, then
picking the middle element of the sorted array.
In order for this to be a fair comparison, you must make each algorithm as
fast as you can. The following is a minimal list of issues that you
should address to make your implementation run as fast as possible:
Other implementation issues will come up as you write your programs. You
must document in your report the steps you have taken to make the
implementations as fast as you can.
- The Select algorithm in the textbook groups the items into
segments of 5 items each. The number 5 was chosen purely for analysis
purposes. Segments of 7, 9, 11, ... would also work. You should run
experiments to determine the optimal segment size.
- The textbook does not describe exactly what happens when you
recursively call Select to find the median of the medians (Step 3,
page 190). You should not copy the medians of the segments into a
new array. This is unnecessary and wastes a lot of time. Your
implementation of Select should be flexible enough that you can use
it to find the median of an array from one index to another considering
only every k-th item.
- For small arrays it will be faster to use Insertion Sort to sort
the items. You should run some experiments to find the optimal size to
switch over to insertion sort and use this in your running time trials.
For this project you must use "real" data. Both Quicksort and the
randomized selection algorithm will use a pseudo-random number generator on
your system. It is not a fair experiment to also use this generator to
produce your data. Furthermore, your arrays must be large enough to be
meaningful. Your arrays should contain at least tens of thousands of
items. Hundreds of thousands is preferable. Your experiments should
include several trials for each size.
The internet is a useful source of ``random'' data. For example, you can
download text or images and treat every four bytes as a 32-bit integer.
Alternatively you can treat the binary code of an application (e.g.,
Microsoft Word) as a sequence of integers. Your report should fully
document how you obtained the data for testing and give some indication of
why you think this is a fair way to test your implementations.
You should report your results as a technical report of roughly 5 to 10
pages. The report counts as 20% of the project grade. The report will be
graded on its quality, not its length. A good report should present your
case clearly and convincingly. The English will be judged according to the
standards of a term paper submitted in a liberal arts course. Grammar
The report should contain the following parts:
- Abstract: An abstract is a short description of the contents
of the report. The abstract should be written in the third
person and should not be longer than half a page.
- Introduction: Describe the project, your approach and summarize the
conclusions. A person who understands computer science but has not read
this project description should understand this section.
- Implementation: Document how you implemented the algorithms.
Report how the implementation issues described above were addressed.
- Experiments: Describe how you generated the data, which experiments
you performed, how the running times were collected, etc. Report the
timing results of your experiments in tables and graphs. The purpose of
this section is to give enough information for the reader to repeat your
- Conclusion: State and justify your conclusions. Between Select
and Quicksort, which algorithm is faster? Do you think your conclusions
valid in general or just for the data and systems that you used?
Your project will be graded on 5 parts weighted equally.
Note that coding is only one part of this project. You will not do well
if you simply turned in 3 working programs. You must leave sufficient
time after you code to test the code, run your experiments and write up
- Report: The report will be graded according to presentation, as described
- Implementation: This portion of the project grade depends on how
well you implemented each algorithm. See the implementation issues
- Data: The quality of the data used in your experiments count for
20% of your grade. If you have doubts about your approach in collecting
data, ask your instructor well before the project deadline.
- Correctness: The implementation, reporting and experimental
methodology should conform to this project description.
- Conclusion: You will not be graded on the statement of your
conclusion, but on how convincing your conclusions are.
1 Nov 1999 22:23:36 EST
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