Created: *Sun 21 Sep 2009*

Last modified:
*
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**Assigned:**
Wed 23 Sep 2009

**Due:**
Wed 30 Sep 2009

## Instructions

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

- 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

Problem | 01 | 02 | 03 | 04 |
05 | 06 | 07 | 08 | 09 | ... |

Credit | RC | RC | RC | EC | RC |
RC | NA | RC | RC | ... |

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.

- 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.

- Problem 1.29
- 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.

- Problem 2.4 - Show your work.
- Problem 2.5 a, c, e - Use the master theorem.
- Problem 2.5 g, h, i - Show your work.
- 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