The Math Behind PageRank

anaesthetica writes "The American Mathematical Society is featuring an article with an in-depth explanation of the type of mathematical operations that power PageRank. Because about 95% of the text on the 25 billion pages indexed by Google consist of the same 10,000 words, determining relevance requires an extremely sophisticated set of methods. And because the links constituting the web are constantly changing and updating, the relevance of pages needs to be recalculated on a continuous basis."

Comments

10,000 words

[ambivalentduck]

But 9,000 of those words are slang for parts of the human anatomy.  Go figure.

Re:10,000 words

[MadAhab]

On the other hand: explain Gallagher and Carrot Top. "Apparently" they are funny, because they have "careers". Yet everyone with an actual sense of humor knows they are just waiting to unhinge their jaws and swallow you whole.

Re:10,000 words

[binaryacid]

Not directly related to this reply, but putting it here for visibility. Not self-promotion. Just would like to provide some useful reference:

The Anatomy of a Large-Scale Hypertextual Web Search Engine
http://infolab.stanford.edu/~backrub/google.html
- This paper tells you what PageRank really is, by the original author.

Efficient Computation of PageRank
http://dbpubs.stanford.edu:8090/pub/1999-31
- This paper tells you how they efficiently compute it

And as far as I know about information retrieval, the magic you see on Google today isn't primarily contributed by PageRank, since people fake it so much nowadays with domain farms.

PageRank doesn't seem to be based on keywords

[dada21]

I have sites with a PR of 6, and I can tell you that they got that way because of inbound links from other sites. In fact, when other sites dropped those links, my PR dropped (to 5, and even to 4). Getting more inbound links brought the PR back.

Think about those links, too. How often do you use common words in an HREF? I don't think there's a lot of weeding out of common words since the link to a site is usually either its name, or a description containing some important keywords.

I love seeing these technoscientists think they understand PageRank, but just like TimeCube, they're way, way off.

Re:PageRank doesn't seem to be based on keywords

[markov_chain]

There has been a PageRank paper out there since 2000 or so, so it's not exactly a secret how it works. Basically an initial set of relevant pages is pulled from the database and ranked by doing some computation on a connectivity matrix. The trick is to come up with a good initial set; and unless they managed to implement an all-knowing oracle they probably do it by doing a keyword search. Here's where the article summary makes sense; if most pages have the same keywords, a keyword search is going to come up with an awfully large initial set.

The article might have details, maybe someone who has actually read it can fill in :)

Re:PageRank doesn't seem to be based on keywords

[Anonymous Coward]

It's not secret.

Re:PageRank doesn't seem to be based on keywords

[kimvette]

You got the link wrong. Here is the correct URL.

Re:PageRank doesn't seem to be based on keywords

[zootm]

If you're referring to the article, it focuses on the "links" aspect when describing the PageRank algorithm. The summary on here is pretty misleading in that way.

Re:PageRank doesn't seem to be based on keywords

[Pollardito]

Think about those links, too. How often do you use common words in an HREF?

interestingly, it appears that Adobe Acrobat leads the list of results when you search for "here" on Google (you can download it here).

and who would have expected this

Re:PageRank doesn't seem to be based on keywords

[Raenex]

I'm behind on my Slashdot reading, but I wanted to offer you a supportive comment even if it isn't timely. You're right, the original poster only read the summary and got modded up for a stupid comment based on not RTFA.

That said, your comment contained more insult than explanation (yeah he didn't RFTA, but point out the discrepancy in his argument). The more inflammatory your message, the less likely it will be considered. I know, it's tempting to flame, and I do it myself now and then, but not nearly as much as I've used to. It's amazing how much better a response you get by just sticking to the argument and not attacking the person, even if it means ignoring insults thrown your way.

Bad summary

[Knights who say 'INT]

The article specifically says the PageRank eigenvector is only recalculated once a month, approximately. Even though Google uses some clever numerics to calculate the eigenvectors to a 25 billion by 25 billion matrix by iteration, it still takes several hours to finish.

Re:Bad summary

[The Zon]

Even though Google uses some clever numerics to calculate the eigenvectors to a 25 billion by 25 billion matrix by iteration, it still takes several hours to finish.

Please. I can do that on paper in, like, five minutes.

Re:Bad summary

[Firehed]

Several hours for 25b x 25b? Jeez, it took Slashdot the better part of a day to update the comment id field type in their database... 16.7m by 1. OSTG, we demand that the servers running Slashdot be upgraded to something that could actually withstand a Slashdotting!

Re:Bad summary

[trentblase]

Please, I can do that in my mind in, like, 5 seconds.

Re:Bad summary

[martin-boundary]

It's nowhere near like that. A web matrix is very sparse, so if you did a true 25Bx25B matrix power iteration, you'd be multiplying zero by zero a gazillion times. Optimization is about not doing things you don't need to do, and optimizing PageRank is about figuring out clever ways to not do the full multiplication. Moreover, PageRank is calculated in parallel over a computer farm. Overall, you can expect a single iteration to take on the order of an hour, and you can expect around 50-80 iterations before Google gives up and says it's converged. You can also try and reuse the previous "converged" PageRank vector to cut down on the 50-80 iterations after you've crawled new pages.

If google used a single computer to do all the work, and truly did 80*25B^2 operations, they'd be morons.

Re:Bad summary

[Patent-Monkey]

Interestingly, Google does a lot of reindexing using existing searches and then builds upon a search listing and a page indexing review. For example in US Patent 6,526,440, "The search engine obtains an initial set of relevant documents by matching a user's search terms to an index of a corpus. A re-ranking component in the search engine then refines the initially returned document rankings so that documents that are frequently cited in the initial set of relevant documents are preferred over documents that are less frequently cited within the initial set."

I agree that they are doing a lot of things to avoid computational load.

Re:Bad summary

[sasdrtx]

42

Nouns maybe?

[Bryansix]

It seems like it would be the nouns, pronouns, etc. that Google should be paying attention to. Who cares about all the verbs, adjectives, etc. that just muddy the indexing waters?

Re:Nouns maybe?

[kramulous]

I believe that a race is on at the moment for semantic searching. Not only nouns, verbs etc, but whether the phases are subjective or objective. I know a blog search company that is working on this. They wanted to borrow some of my code.

Re:Nouns maybe?

[abshnasko]

Searching for pill and the pill should yield very different results. Yes nouns are more important, but articles and other words cannot be disregarded.

Re:Nouns maybe?

[WaXHeLL]

RTFA please. It deals with determining relevance, not the optimal method of indexing pages.

In regards to your comment:
Verbs play an extremely important role when dealing with relevancy based on phrases.

The small snippet that was posted was just cut and pasted from the opening hook of the article. It just leads into a mathematical discussion how to sort through the thousands of results that are returned.

Re:Nouns maybe?

[gfody]

The is a stop word and will most likely be excluded from your search term.

Re:Nouns maybe?

[WaXHeLL]

It's not entirely excluded.

An index of "the pill" and "pill" are two different queries becuase matching the whole phrase will get you more relevant results. This is built into the code that interprets queries (this is completely different from PageRank, which deals with cross linking between sites to get the highest probability of relevance -- AFTER the query is interpreted and a set of pages is generated). Almost all search engines work that way.

Re:Nouns maybe?

[svindler]

So if I want to look for dwarf throwing I'll have to wade through all dwarf related pages because throwing is not relevant for the pagerank?

Re:Nouns maybe?

[Bryansix]

I actually thought about that after I posted. I know all the words are important for indexing. I'm just saying that looking at keywords and placing more importance on those is a part of the mix too. Those keywords are almost always nouns.

A bit late?

[kramulous]

I read about this some time ago ... I think the paper was entitled "The 10 billion dollar Eignvector: The math behind google" or something to that effect. Sorry, but I've got a new laptop and cannot find the exact title. It was an excellent introduction for beginner computational scientists for an application of the eigenvector. I forget the American University responsible.

Re:A bit late?

[mochan_s]

Here's the bibtex reference.

@article{bryan:569,
author = {Kurt Bryan and Tanya Leise},
collaboration = {},
title = {The $25,000,000,000 Eigenvector: The Linear Algebra behind Google},
publisher = {SIAM},
year = {2006},
journal = {SIAM Review},
volume = {48},
number = {3},
pages = {569-581},
keywords = {linear algebra; PageRank; eigenvector; stochastic matrix},
url = {http://link.aip.org/link/?SIR/48/569/1},
doi = {10.1137/050623280}
}

Re:A bit late?

[kramulous]

Cheers for that. Helpful.

Kind regards

I joke a lot on Slashdot, but serious question

[CrazyJim1]

I skimmed the article and didn't find what I wanted to find. If you make a webpage that you want ranked high, what do you do? Do you make 100 geocities accounts and provide links to your main website, or what? I'm just wondering this out of curiosity, not out of need.

Re:I joke a lot on Slashdot, but serious question

[Larry Lightbulb]

At a very basic level a sites page rank is a reflection on how much other sites think it's relevent, and is based on how important the sites are that link to it. Get a link from the BBC, CNN, or somewhere like that and it's worth thousands or millions of links from Geocities sites.

Re:I joke a lot on Slashdot, but serious question

[mojodamm]

That's kinda what I thought at first as well, but looking over the lower two-thirds of the article, I started to get a different impression. They talked about a 'strong web' idea, where if your webpage is disconnected from the 'main' web and set up in a sort of 'secondary web' with just your Geocities accounts, for instance, linking to it, then the actual websites that interconnected within your site matrix would rank a 0 overall.

Not sure if this is correct or not, just the impression that I got from what little of the TFA I could skim at work...

Re:I joke a lot on Slashdot, but serious question

[x_MeRLiN_x]

That wouldn't work, because they'd all be coming from the same domain.

Re:I joke a lot on Slashdot, but serious question

[Anonymous Brave Guy]

The underlying idea behind page rank is pretty well-exposed at this point, and is described in TFA. Essentially, it's a big set of simultaneous equations: each incoming link to your page gets a score that is roughly the rank of the source page divided by the number of outgoing links on that page, and then the rank of your page is roughly the sum of the scores of all incoming links.

Various fudge factors are introduced along the way. For example, if you break Google's rules about displaying the same content to bots as to humans, you can get slapped right down. More subtly, newly registered domains take a modest hit for a while. More nobody-knows-ly, Google's handling of redirects is unclear: information about exactly what adjustments are made is pretty scarce, and there's a lot of conjecture around. One thing that's pretty certain is that they penalise for duplicate content, which is why some webmasters do apparently unnecessary things like redirecting http://www.theircompany.com/ to http://theircompany.com/ or vice versa.

So, if you want to get a page with a high rank yourself, then ideally you need would get many established, highly-ranked pages to link to your page and no others. In your example, all those Geocities sites wouldn't help a lot, because (a) they'd have negligible rank themselves, and (b) they'd be penalised for being new and lose some of that negligible rank before they even started. Many times negligible is still negligible, and so would be your target page's rank. OTOH, get a few links from university sites, big news organisations and the like, and your rank will suddenly be way up there. Alternatively, get a grass-roots movement going where a gazillion individuals with small personal sites link to you, and the cumulative effect will kick in.

Re:I joke a lot on Slashdot, but serious question

[TheLink]

"if you break Google's rules about displaying the same content to bots as to humans"

I notice many sites that do that and don't get slapped down - esp subscription sites. And seems Google doesn't cache those, so its probably collusion.

You see the keywords and paragraphs in the search, but click on it you get a login page.

They should have to pay a special rate be marked differently from the other search results. It's a waste of time otherwise.

Re:I joke a lot on Slashdot, but serious question

[linhux]

If those 100 geocities pages each have a PageRank of 0 (which they would if they aren't linked to from other high-ranking pages), their total contribution to your main page PageRank will be 0.

Re:I joke a lot on Slashdot, but serious question

[oni]

I notice many sites that do that and don't get slapped down - esp subscription sites.

I wonder, if I changed my useragent to be whatever the googlebot reports itself to be - would I get by the registration screen on websites like the NYTimes??

Re:I joke a lot on Slashdot, but serious question

[kimvette]

No, because they check the IP you're coming from as well now - they grew wise to user agent spoofing years ago.

Google for the "bugmenot" Firefox extension.

Re:I joke a lot on Slashdot, but serious question

[l0cust]

Thanks for the informative post. I have one question though. How does it help find the relevant information unless that information just happens to be on a popular page too? What I mean to say is that the idea behind grading/filtering systems like PageRank is to provide the most relevant information about the thing you are trying to search on the net. Now suppose Mr. A is looking for some obscure Indian text written in Sanskrit and Mr. B has (recently or not) put up a website with that text as one of the contents but its not a popular blogsite, nor a mainstream ebook source site etc. And there are a gazillion hugely popular sites out there which mention that particular text while talking about a totally different book or text.

So it means the only way that Mr. A will come across Mr. B's website is if he kept on looking for 100s of result pages or if he just chanced upon it via something he read about earlier. Doesn't it defeat the purpose of making the searches more relevant, specially since lots of webmasters actively use PageRanking system to get better ranking on the search index. Where does that leave the people with worthwhile content but not much popular backing?

(I would like to clear that I am not trying to knock this system or anything, I am just curious about the implications for small-but-good-content website owners)

Re:I joke a lot on Slashdot, but serious question

[XorNand]

As pointed out, the Times site isn't fooled, but there are a good many out there that are fooled. Sometimes if you ever do a Google search, one of the results will contain a keyword or two. However, when you click on the link, you'll find yourself redirected to a subscription page. Useragent spoofing can frequently show you the same page that Google indexed.

If you're a FF user, grab the Useragent Switcher extension and add in a UA of "Mozilla/5.0 (compatible; googlebot/2.1; +http://www.google.com/bot.html)". You'll then be two clicks away from seeing what was previously registration-only.

Re:I joke a lot on Slashdot, but serious question

[jZnat]

Googlebot doesn't use the same IP address all the time (several servers running Googlebot I'd imagine), so filtering based on IP addresses would be infeasible (at least according to Google).

Re:I joke a lot on Slashdot, but serious question

[suggsjc]

Here is an email with associated response I received from Google on roughly this topic.

This is a very general question. I'm creating a website. It is going to be a blogging platform. Obviouslly, the content of the site(s) is the most important thing. I've already started making the content of my site dynamic in the sense that I tailor it to the requesting agent (via the user-agent header). My intention for doing this is to make sure that the content renders correctly for *any* browser that accesses the site. I've built the site modularly, so tailoring the content to the requesting agent isn't a big deal. However that leads me to my question(s) and the reason I am emailing you? FYI, I have no ulterior motives for being able to tailor my content, other than making sure that the user get the most usefull information.

That said. When a "bot" (ie your crawler) accesses my site. I'm going to treat it like I would a mobile browser. I'm going to give the minimal markup and the css will be very simple. I'm going to make sure that my content comes before my navigation, advertisements, etc in the source.

My real question is does the fact that I'm presenting you the content of my site differently from other browsers make a difference? If so, (then again my reasoning is to make sure that my users get the correct content) how do I prevent this from hurting me in your rankings? If not, then how do you protect yourself from other sites taking advantage of this "hole"? Meaning I could make my site appear legit when I knew your bots were crawling me, but give "alternate" content when real users were visiting.

Last question. Do you have any idea when your ads will work correctly with xhtml?

Hope you weren't expecting a straightforward answer (like I was), because here is what I got back

Hello Jonathon,

Thanks for your email about the website you're creating.

First, since you asked when our program will support XHTML, I wanted to
let you know that we're unable to say if we'll support XHTML pages in the
future.

While the AdSense team isn't able to answer your questions about your
site's ranking in the Google search index, I'd recommend visiting
http://www.google.com/support/webmasters . I also wanted to let you know
that our advertising programs are independent of our search results.
Participation in AdWords and AdSense doesn't affect inclusion or ranking
in the Google search index.

I've also included answers to some of the most common questions AdSense
publishers have asked.

How can I improve my site's ranking?
Answer:
http://www.google.com/support/w ebmasters/bin/answer.py?answer=34432&hl=en_US

H ow do I add my site to Google's search results?
Answer:
http://www.google.com/support/w ebmasters/bin/answer.py?answer=34397&hl=en_US

M y site is no longer included in the search results. What happened?
Answer:
http://www.google.com/support/ webmasters/bin/answer.py?answer=34443&hl=en_US

Why doesn't my site show up for a specific keyword?
Answer:
http://www.google.com/support/w ebmasters/bin/answer.py?answer=34434&hl=en_US

F or additional questions, I'd encourage you to visit the AdSense Help
Center (http://www.google.com/adsense_help), our complete resource center
for all AdSense topics. Alternatively, feel free to post your question on
the forum just for AdSense publishers: the AdSense Help Group
(http://groups.google.com/group/adsense-hel p).

Sincerely,

Jake
The Google AdSense Team

Re:I joke a lot on Slashdot, but serious question

[Jotii]

Still, Google has a few IP-ranges which are only for Google.

Re:I joke a lot on Slashdot, but serious question

[Hyperspite]

If you read the entire article carefully, they deal with that by changing the way they search through the web. Instead of following every link, they assign a probability of .85 to following it. This makes their eigenvectors have nonzero entries because the search can jump out of the strong web and get back on track (if the random number falls into the .15 category it goes to a random indexed page from the entire internet). So yea, making a web of geocities accounts wouldn't do much more than you'd think it should - and thank god, because MySpace would pwn the internet otherwise :P

Re:I joke a lot on Slashdot, but serious question

[cvos]

a webpage that you want ranked high, what do you do? Do you make 100 geocities accounts and provide links to your main website No this would definitely not work. The reason is that 100 new geocities websites would have a value of 0 so using the PageRank algorithm you would effectively have 100 links X 0 PR. Incoming links only have a positive impact if they have weight independent of other websites. This is why it is so crucial to have your own website in the oldest dataset possible. It takes a long time for websites created in 1995 to disappear.

Does PageRank count?

[matr0x_x]

As a self proclaimed SEO expert - I honestly don't believe PageRank counts nearly as much as it did a few years ago! You'll find lots of PR5 sites ahead in the SERPS of PR9 sites!

Re:Does PageRank count?

[Trieuvan]

The pagerank that's reported from toolbar is really old. Google never want to let you know the real number or it will be easy to spam ...

Re:Does PageRank count?

[dbmasters]

PageRank is worthless in terms of SEO. What it can do is tell you if there is a problem, if you have a PR of 0 or 1 or something, but thinking it somehow affects your SERPs is a dillusion far to many people fall in to. Concentrate on SERPs, not PR, ASAP for SEO on the WWW.

Re:Does PageRank count?

[Anonymous Coward]

Concentrate on SERPs, not PR, ASAP for SEO on the WWW

I searched on Google but I cannot find what "on", "not", "for" and "the" mean...

Re:Does PageRank count?

[HalfBrown]

The pagerank that's reported from toolbar is really old.

I think that at least part of this is indicative of the "Google Sandbox" (if you believe it exists). I've noticed, with the Google Toolbar in IE and FireFox, that some sites seem to have stagnant PR's (even with noticable increases/decreases of traffic), but others move along in a relatively sistent manner.

Just my 2 cents.

Old guys bully new comers.

[eat bugs]

I asked some math website to put a link to http://www.mathpotd.org/ Math Problem of the Day -- they don't bother to do so. They know the math and use it.

Pagerank

[Skythe]

Because about 95% of the text on the 25 billion pages indexed by Google consist of the same 10,000 words, determining relevance requires an extremely sophisticated set of methods.

They use a set of nested if-else statements
*ducks*

Here it is... Google's PageRank formula

[Reverend99]

SELECT advertiser, description, link, adcost
FROM tblAdvertisers
WHERE adword LIKE %searchstring%
ORDER BY adcost

Re:Here it is... Google's PageRank formula

[8ball629]

I'd be mad if I were advertising...

Shouldn't it be "ORDER BY adcost DESC"?

Re:Here it is... Google's PageRank formula

[kaizenfury7]

Interesting, I never knew the formula was

#1064 - You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '%searchstring% LIMIT 0, 30' at line 1

Re:Pagerank is cool

[silentounce]

Interestingly enough, google thinks so, too.

Of course, yahoo has its own opinion.
 
Although, altavista seems to almost agree. Check the second non-advertised result.
 
I do find this amusing though. Third place, how humble.
 
I didn't expect such interesting results. The site with the search term in its url was tops for av and yahoo, but not google. Yahoo ranked the wiki entry above google, but av reversed that decision, google of course thought itself was more important than the wiki. Google's own reference site was number one in its own search and near the top in the other two, but pagerank.net wasn't even in the top 10 for google's search. I'm not sure what conclusions can be drawn from all that, but it is definitely food for thought.

you forgot..

[gfody]

ORDER BY adcost DESC

Re:you forgot..

[Reverend99]

Yeah... you and the sans-humor moderator who called this "Flamebait" should get together. I'm sure you'd make a match made in anal heaven.

Re:The two that matter

[Anonymous Coward]

There's only two that really reflect the power of Pagerank: Click here.
About 1.2 billion pages, and surprise surprise, Acrobat Reader tops the list, followed by a who's who of internet applications and plugins. But around result #30 it gets a bit more interesting, and when you're a few dozen pages in, "new patterns begin to emerge."

And to explain why not to use "click here", I found this buried on page 45. Thanks for the proof pudding guys, it's delicious.

OK, but...

[indigest]

The algorithms behind PageRank are no secret. Why not just read about them from the source?

"The Who" vs the who

[kenb215]

It seems that in searching "The Who", only that exact phrase is returned, but when searching the who, both words are searched, i.e. "the" appears as if it is being searched like a normal word here. If you try searching for the best, "the" is counted when used as part of the phrase "the best", but appears not to be counted when it appears by itself. The Google algorithm is apparently a lot more complicated than the usual explanations are.

Only three articles about Google on one page?

[colourmyeyes]

I think we can get four or five tomorrow.

Thanks for all the replies

[CrazyJim1]

I now have a nice basic understanding of Google page ranking system. Thats all I was asking for.

evolution

[drDugan]

Great article.

The character of online content is changing now rapidly. We used to be in an Internet where mostly only the site provider determined the content on the pages they served (/. being a notable, early exception). Now, with the rise of "2.0" systems, user-generated content, and empowerment of the individual - the content being served on many sites is coming into sites from wide groups, and being moderated and curated by those groups.

So... a thought: as user-submitted and group-moderated content continues to rise on the Internet - the main premise behind PageRank system will change. To remain relevant, Google will need to continue to evolve how they do their rankings to match the structure of data in the online world. Will/Can they?

Re:evolution

[the_womble]

I could not disagree more. Most of the sort of information people search for is not user generated: when did you last do a Google search for which a slasdot comment was the appropriate answer?

The only exception that I can think of (form my searches) are forums that have answers to software problems. Google seems to have no problem finding these for me.

Re:evolution

[Vintermann]

Sometimes you want to search through your old posts. Not all sites let you do that (slashdot does if you pay up, I think), and often forums are even norobots space.

Re:evolution

[drDugan]

The meme that Google helps us find all the information is a huge marketing Spin.

Compared to "exactly the information you want, when and how you want it" - Google sucks. It is better that anything else now, but it still is not anywhere close to really solving the information access problem generally.

It's the World' s Largest Matrix Computation

[MadMagician]

For a different, somewhat more technical, but more succint discussion, Cleve Moler [of Matlab fame] wrote another view of this topic, about 5 years ago.

The math is the same, of course, but two points of view may provide a greater sense of perspective. So to speak. And Cleve is always worth listening to.

Re:It's the World' s Largest Matrix Computation

[jfengel]

Actually, I'm not so sure it's the largest matrix computation. Weather and nuclear bomb simulations are done with matrix algebra, and it wouldn't surprise me to discover that they do some months-long calculations with even larger matrices.

Re:Pagerank is cool

[ben there...]

I do find this amusing though. Third place, how humble.

What I found interesting about that link was the description listed for google's entry:

Google - 11:54pm
Enables users to search the Web, Usenet, and images. Features include PageRank, caching and translation of results, and an option to find similar pages.
www.google.com/ - 5k - Dec 5, 2006 - Cached - Similar pages

Where did they get that text from? It's not anywhere to be found in the source. Did they cheat? Or are they just tricky?

Other google technologies

[quakehead3]

Pigeon Rank: http://www.google.com/technology/pigeonrank.html

Re:Pagerank is cool

[McDutchie]

Where did they get that text from? It's not anywhere to be found in the source. Did they cheat? Or are they just tricky?

They got it from the Google category at the Open Directory Project at dmoz.org, mirrored at directory.google.com. Google is a user of dmoz.org data but has completely de-emphasized that as of late.

It's actually against the dmoz license agreement to use their data without a link back to the source, but nobody seems to care.

Re:Pagerank is cool

[flood6]

Whenever possible, Google uses the DMOZ description for the snippet shown in the results.

Re: [OT] for whoever runs mathpotd

[eat bugs]

A system error caused the problem. It didn't insist it be 1/3 -- it was because choice B (which didn't correspond to any choice) was given as the correct answer. The website support has corrected the problem.

Re:Shameless plug for my uni

[CptPicard]

Frankly, any university with a CS program worth anything will have students take a linear algebra course in math as the first thing. It's a good weed-out-the-weak excercise early on, gets you up to speed with university level mathematics, and the stuff in itself comes in handy, for example in computer graphics. Being good at manipulating matrices has a lot of use in algorithmics too.

Please, try to impress me about Stanford some other way once you've progressed further ;-)

Re:Pagerank is cool

[krishn_bhakt]

Things change with key word "search engine"... MSN is 1st! [ http://www.google.com/search?hl=en&lr=&q=search+en gine ]

Re:Shameless plug for my uni

[Anonymous Coward]

Blah. Ugly red clothes... Go Bears!

Re:Pagerank is Broken

[RegularFry]

Why does that make PageRank broken? That's not the problem it tries to solve. Google might be broken for slavishly adhering to PageRank, but that's a different matter entirely...

Re:Shameless plug for my uni

[retiarius]

shameless math plug(s) from my alma mater:

          - cal berkeley leads stanford in william lowell putnam competition fellows

          - as for killer math events

                            stanford had streleski (v.i.z. wikipedia)
                            but berkeley topped him with kaczynski (!)

seriously, best wishes for the cardinals shepherding
the putman team under prof. vakil last saturday.

Interesting Appendix: Page and Brin on Advertising

[jbourj]

One of the references for the article is http://infolab.stanford.edu/pub/papers/google.pdf" >The Anatomy of a Large-Scale Hypertextual Web Serach Engine published in Computer Networks and ISDN Systems. At the end of the paper, they have a very interesting appendix: "Advertising and Mixed Motives"

Currently, the predominant business model for commercial search engines is advertising. The goals of the advertising business model do not always correspond to providing quality search to users. For example, in our prototype search engine one of the top results for cellular phone is "The Effect of Cellular Phone Use Upon Driver Attention", a study which explains in great detail the distractions and risk associated with conversing on a cell phone while driving. This search result came up first because of its high importance as judged by the PageRank algorithm, an approximation of citation importance on the web [Page, 98]. It is clear that a search engine which was taking money for showing cellular phone ads would have difficulty justifying the page that our system returned to its paying advertisers. For this type of reason and historical experience with other media [Bagdikian 83], we expect that advertising funded search engines will be inherently biased towards the advertisers and away from the needs of the consumers.

Since it is very difficult even for experts to evaluate search engines, search engine bias is particularly insidious. A good example was OpenText, which was reported to be selling companies the right to be listed at the top of the search results for particular queries [Marchiori 97]. This type of bias is much more insidious than advertising, because it is not clear who "deserves" to be there, and who is willing to pay money to be listed. This business model resulted in an uproar, and OpenText has ceased to be a viable search engine. But less blatant bias are likely to be tolerated by the market. For example, a search engine could add a small factor to search results from "friendly" companies, and subtract a factor from results from competitors. This type of bias is very difficult to detect but could still have a significant effect on the market. Furthermore, advertising income often provides an incentive to provide poor quality search results. For example, we noticed a major search engine would not return a large airline's homepage when the airline's name was given as a query. It so happened that the airline had placed an expensive ad, linked to the query that was its name. A better search engine would not have required this ad, and possibly resulted in the loss of the revenue from the airline to the search engine. In general, it could be argued from the consumer point of view that the better the search engine is, the fewer advertisements will be needed for the consumer to find what they want. This of course erodes the advertising supported business model of the existing search engines. However, there will always be money from advertisers who want a customer to switch products, or have something that is genuinely new. But we believe the issue of advertising causes enough mixed incentives that it is crucial to have a competitive search engine that is transparent and in the academic realm.

Why doesn't Brin get some credit??

[moeinvt]

??

Seems unfair that something Brin and Page developed together would bear only one of their names.

"Page-rank"

??

Re:Popularity != Quality

[namco]

Porn has no quality (just cheese ;p) and is very popular! I'd love to see pageranking's on those every month!

Pages that don't exist anymore

[namco]

I've seen links on google searches that don't exist anymore but were ranked highly when they DID exist and still exist in the top 10 of the query. What happens to those? Do they stay at their ranking till they get overtaken by other more popular pages on the same search? Get their ranking slowly reduced because they don't exist?

Re:Pagerank is cool

[MotF Bane]

Use the Google search, try for "best search engine". They don't list themselves. Then go try Yahoo search, try for "best search engine"....