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David Evanshttp://www.cs.virginia.edu/evans

CS150: Computer ScienceUniversity of VirginiaComputer Science

Class 38:Googling

2CS150 Fall 2005: Lecture 38: Googling Google

Some searches...

“David Evans”

“Dave Evans”

“idiot”

“lawn lighting” Tomorrow at 6pm (but google doesn’tknow that!)


Building a Web Search Engine

• Database of web pages– Crawling the web collecting pages and

links– Indexing them efficiently

• Responding to Searches– How to find documents that match a

query– How to rank the “best” documents


Crawling CrawleractiveURLs = [ “www.yahoo.com” ]while (len(activeURLs) > 0) : newURLs = [ ] for URL in activeURLs: page = downloadPage (URL) newURLs += extractLinks (page) activeURLs = newURLs

Problems:Will keep revisiting the same pagesWill take very long to get a good view of the webWill annoy web server adminsdownloadPage and extractLinks must be very robust


Crawling CrawleractiveURLs = [ “www.yahoo.com” ]visitedURLs = [ ]while (len(activeURLs) > 0) : newURLs = [ ] for URL in activeURLs: visitedURLs += URL page = downloadPage (URL) newURLs += extractLinks (page) -

visitedURLs activeURLs = newURLs

What is the complexity?


Distributed CrawleractiveURLs = [ “www.yahoo.com” ]visitedURLs = [ ]while (len(activeURLs) > 0) : newURLs = [ ] parfor URL in activeURLs: visitedURLs += URL page = downloadPage (URL) newURLs += extractLinks (page) -

visitedURLs activeURLs = newURLs

Is this as“easy” as distributingfinding aliens?








Building an Index

• What if we just stored all the pages?

Answering a query would be (size of the database)

(need to look at all characters in database)

For google: about 4 Billion pages (actual size is now considered a corporate secret) * 60 KB (average web page size) = ~184 Trillion

Linear is not nearly good enough when n is Trillions


Reverse IndexWord Locations

…

“David” [ …, http://www.cs.virginia.edu/~evans/index.html:12, …]

…

“Evans”

[ …, http://www.cs.virginia.edu/~evans/index.html:19, …]

…

What is time complexity of search now?


Best Possible Searching

• Searching Problem:– Input: a target key key, a list of n <key,

value> pairs, sorted by key using a comparison function cf

– Output: if key is in the list, the value associated with key; otherwise, not found

• What is the best possible solution to the general searching problem?


Recall Class 13:Sorting problem is Ω(n log n)

• There are n! possible orderings • Each comparison can eliminate at

best ½ of them• So, best possible sorting procedure is

Ω(log2n!)

• Sterling’s approximation: n! = Ω(nn)– So, best possible sorting procedure is

Ω(log (nn)) = Ω(n log n)Recall log multiplicationis normal addition:log mn = log m + log n


Searching Problem is (log n)

• It is (log n)– Each comparison can eliminate at best ½ of

all the elements from consideration• It is O (log n)

– We know a procedure that solves it in (log n)

• For google: n is the number of distinct words on the web (hundreds of millions?) (log n) is not good enough


Faster Searching?• The proof that searching is (log n) relied

on knowing that the best a comparison can do is eliminate ½ the entries

• Can we do better?– Without knowing anything about comparison:

no– With knowing about comparison: yes

• What if one comparison can eliminate O(n) of the entries?


Bin SearchingFirst

LetterItems

a [<“aardvark”, [http://www.aardvarksareus.com, …]>, … ]

b [ … ]

…

z [ …, <“zweitgeist”, […]>]def binsearch (key, table) : search (key, table[key[0]])

What is time complexity of binsearch?


Searching in O(1)

• To do better than (log n) the number of bins must scale with n– Average number of elements in a bin

must be O(1)– One comparison must eliminate O(n) of

the elements


Hash Tables

• Bin = H(key, number of bins)– H is a hash function – We’ve seen cryptographic hash functions

where H must be collision resistant– For this, we don’t need that just need H

must distribute the keys well across the bins

• Finding a good H is difficult– You can download google’s from

http://goog-sparsehash.sourceforge.net/


Google’s Lexicon• 1998: 14 million words (much more today)• Lookup word in H(word, nbins)• Maps to WordID

Key Words

0 [<“aardvark”, 1024235>, ... ]

1 [<“aaa”, 224155>, ..., <“zzz”, 29543> ]

... ...

nbins – 1 [<“abba”, 25583>, ..., <“zeit”, 50395> ]


Google’s Reverse Index

WordId

ndocs

pointer

00000000

3

00000001

15

...

16777215

105

(From 1998 paper...may have changed some since then)

Lexicon: 293 MB (1998)

InvertedBarrels:

41 GB (1998)


Inverted Barrelsdocid (27 bits) nhits (5

bits)hits (16 bits each)

7630486927

23

...

plain hit:capitalized: 1 bitfont size: 3 bitsposition: 12 bits first 4095 chars, everything else

extra info foranchors, titles(less position bits)








Finding the “Best” Documents

• Humans rate them– “Jerry and David’s Guide to the World

Wide Web” (became Yahoo!)

• Machines rate them– Count number of occurrences of keyword

• Easy for sites to rig this

– Machine language understanding not good enough

• Business Model– Whoever pays you the most is listed first


Random Walk ModelInitialize all page ranks = 0p = select a random URLfor as long as you feel like p.rank = p.rank + 1 p = select random link from Links (p)

Eventually, ranks measure probability a random websurfer would encounter a page

Problems with this?


Back Links

http://www.google.com/search?hl=en&lr=&q=link%3Awww.cs.virginia.edu%2F%7Eevans%2Findex.html&btnG=Search= 219 backlinks


Counting Back Links

• link:http://www.deainc.com/– 109 backlinks (hey, I should be first!)

• Back links are not a good measure– Most of mine are from my own pages

• But Google doesn’t know that (always)

– Some pages are more important than others


PageRank

Weight the back links by the popularity of the linking page

def PageRank (u): rank = 0 for b in BackLinks (u) rank = rank + PageRank (b) / Links (b) return rank

Would this work?


Converging PageRank

• Ranks of all pages depend on ranks of all other pages

• Keep recalculating ranks until they converge

def CalculatePageRanks (urls): initially, every rank is 1 for as many times as necessary calculate a new rank for each page (using old ranks of other pages) replace the old ranks with the new ranksHow do initial ranks effect results?

How many iterations are necessary?


PageRank• Crawlable web (1998): 150 million

pages, 1.7 Billion links• Database of 322 million links

– Converges in ~50 iterations

• Initialization matters– All pages = 1: very democratic, models

browser equally likely to start on random page

– www.yahoo.com = 1, ..., all others = 0• More like what Google probably uses


Query Work• To respond to 1 query (2002)

– Read 100 MB of data– 10s of Billions of CPU cycles

• Google in 2002:– 15,000 commodity PCs

• Racks of 88 2GB PCs, $278,000 each rack• Power: 10 MW-h/month ($1,500)

– If you have 15,000 PCs, there always be some with faults: load balancing, data partitioning






query– How to rank the “best” documentsReady to go become the next google?


Charge• Before becoming the next Google,

you need to finish PS8!• Tomorrow: 6pm, Lighting of the Lawn• Friday’s class:

– A few other neat things about Google– Guidelines for project presentations– Exam review – email me your topics and

questions

• Monday: project presentations