## Lecture 8: Universal Hashing, Perfect Hashing

recorded by: Massachusetts Institute of Technology, MIT

published: Feb. 10, 2009, recorded: October 2005, views: 39193

released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)

# Slides

# Related content

# Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our**to describe your request and upload the data.**

__ticket system__*Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.*

# Description

*"Hashing. Today we're going to do some amazing stuff with hashing. And, really, this is such neat stuff, it's amazing. We're going to start by addressing a fundamental weakness of hashing. And that is that for any choice of hash function There exists a bad set of keys that all hash to the same slot. OK. So you pick a hash function. We looked at some that seem to work well in practice, that are easy to put into your code. But whichever one you pick, there's always some bad set of keys. So you can imagine, just to drive this point home a little bit..."*

# See Also:

Download slides: mit6046jf05_leiserson_lec08_01.pdf (221.7 KB)

Download mit6046jf05_leiserson_lec08_01.m4v (Video - generic video source 166.9 MB)

Download mit6046jf05_leiserson_lec08_01.rm (Video - generic video source 127.1 MB)

Download mit6046jf05_leiserson_lec08_01.flv (Video 230.5 MB)

Download mit6046jf05_leiserson_lec08_01_320x240_h264.mp4 (Video 236.5 MB)

Download mit6046jf05_leiserson_lec08_01.wmv (Video 687.7 MB)

Download mit6046jf05_leiserson_lec08_01.mp3 (Audio lecture 16.7 MB)

# Link this page

Would you like to put a link to this lecture on your homepage?

Go ahead! Copy the HTML snippet !

## Reviews and comments:

Nodir, May 7, 2009 at 3:45 p.m.:Cool lecture.

But I have 2 points which I would want to understand:

- the constructed set of universal hash functions do not seem to be easily computable (namely, in O(1) time) or is it?

- in the proof of universality of dot-product hash functions: what happens when x=<x0,...,xr> and y=<y0,...,yr> differ in more than 1 digit?

RUBEN BUABA, June 18, 2009 at 12:10 a.m.:Wow, this is an excellent lecture.

Can I have more of your lectures on LSH?

Thanks.

Ruben Buaba

NCA&T State University

LK, December 8, 2011 at 10:17 a.m.:@Nodir:

- if the prime m is large, i.e. proportional to the size of the universe, then we can compute h in O(1), assuming that we can do constant size operations with such large numbers, which is reasonable. The cost is log_m(u).

- in the proof it is not assumed that x and y differs in exactly 1 digit, we only need that they differ in at least one digit and w.l.o.g. it is assumed that at index 0 they differ.

Gabriel, December 20, 2012 at 3:30 a.m.:I don't understand how the cardinality of a set can be a fraction, at the Universal hashing definition. Is it implying |H| = km ?

Miroslav Chomut, April 21, 2014 at 3:14 p.m.:Slide "Perfect Hashing" seems to contain error,

namely

h(14)=h(27)=1

h_31(14)=1

h_31(27)=2

is compressed (lossy compression) into

h_31(14)=h_31(27)=1

which is inconsistent with image, and would cause collision

Tomas Novella, August 21, 2016 at 2:40 p.m.:There's an error on the intro slide of perfect hashing. It reads h_31(14) = 1 = h_31(27) which is not true because the latter equals 2.

However the version on the blackboard is correct.

## Write your own review or comment: