# CS4800 09F: Homework 03

Created: Sun 21 Sep 2009

Assigned: Wed 23 Sep 2009
Due: Wed 30 Sep 2009

## Instructions

1. Please review the course syllabus and make sure that you understand the course policies for grading, late homework, and academic honesty.

2. On the first page of your solution write-up, you must make explicit which problems are to be graded for "regular credit", which problems are to be graded for "extra credit", and which problems you did not attempt. Please use a table something like the following

Problem01020304 0506070809...
CreditRCRCRCECRC RCNARCRC...

where "RC" is "regular credit", "EC" is "extra credit", and "NA" is "not applicable" (not attempted). Failure to do so will result in an arbitrary set of problems being graded for regular credit, no problems being graded for extra credit, and a five percent penalty assessment.

3. You must also write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.

## Problems

Required: Do any 5 of the following 6 problems.
Points: Problems are worh 20 point each.
Unless otherwise indicated, problems are from Algorithms by Dasgupta, Papadimitriou, and Vazirani.

1. Problem 1.29
2. Read the Wikipedia article on Bloom filters:
http://en.wikipedia.org/wiki/Bloom_filter
and then consider what happens if you fix the length of the bit array at m bits, but you allow the number of hash functions, k, to vary.
a. What goes wrong in the extreme limit when k becomes large?
b. What goes wrong in the extreme limit when k becomes 1?

Thanks to Prof. Gene Cooperman for this problem.

3. Problem 2.4 - Show your work.
4. Problem 2.5 a, c, e - Use the master theorem.
5. Problem 2.5 g, h, i - Show your work.
6. Problem 2.13

### Switch to:

Harriet Fell
College of Computer Science, Northeastern University
360 Huntington Avenue #340 WVH,
Boston, MA 02115
Email: fell@ccs.neu.edu
Phone: (617) 373-2198 / Fax: (617) 373-5121
The URL for this document is: http://www.ccs.neu.edu/home/fell/CS4800/F09/Homework/hw.03.html