cs246: page selection. junghoo "john" cho (ucla computer science) 2 page selection...

CS246: Page Selection

Junghoo "John" Cho (UCLA Computer Science) 2

Page Selection

• Infinite # of pages on the Web– E.g., infinite pages from a calendar site

• How to select the pages to download?

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Challenges Due to Infinity

• What does Web coverage mean?– 8 billion vs 20 billion

• How much should I download?– 8 billion? 100 billion?– How much have I covered?– When can I stop?

• How to maximize coverage?– How can we define coverage?


RankMass

• Web coverage weighted by PageRank• Q: Why PageRank?• A:

– Primary ranking metric for search results– User’s visit probability under random surfer model

PageRank

• A page is important if it is pointed by many important pages

• PR(p) = PR(p1)/c1 + … + PR(pk)/ck

pi : page pointing to p, ci : number of links in pi

• PageRank of p is the sum of PageRanks of its parents

• One equation for every page– N equations, N unknown variables

PageRank: Random Surfer Model

• The probability of a Web surfer to reach a page after many clicks, following random links

Random Click

Damping Factor and Trust Score

• Users do not always follow link– They get distracted and “jump” to other pages

– d: Damping factor. Probability to follow links.– ti: Trust score. Non-zero only for the pages that

user trusts and jumps to.

• “TrustRank”, “Personalized PageRank”

ij

jji tdcpPRdpPR )1(/)()(


RankMass: Definition

• RankMass of DC:

– Assuming personalized PageRank• Now what? How can we use it for the

crawling problem?

Ci Dp

iC pPRDRM )()(

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Two Crawling Challenges

• Coverage guarantee:– Given , make sure we download at least 1-

• Crawling efficiency:– For a given |DC|, pick DC such that RM(DC) is the

maximum

1)( CDRM

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RankMass Guarantee

• Q: How can we provide RankMass guarantee when we stop?

• Q: How do we calculate RankMass without downloading the whole Web?

• Q: Any way to provide the guarantee without knowing the exact PageRank?


RankMass Guarantee

• We can’t compute the exact PageRank but can lower bound

• How? Let’s a start with a simple case

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Single Trusted Page

• t1=1 ; ti = 0 (i≠1)

• Always jump to p1 when bored

• NL(p1): pages reachable from p1 in L links

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Single Trusted Page

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Q: What is the probability to get to a page L links away from P1?


RankMass Lower Bound: Single Trusted Page

• Assuming the trust vector T(1), the sum of the PageRank values of all L-neighbors of p1 is at least dL+1 close to 1

)(

1

1

1)Pr(pNp

Li

Li

dp

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PageRank Linearity

• Let be PageRank vector . based on trust vector

,That is

• , Then for any

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kij

jjkik tdcpPRdpPR )1(/)()(

)()1()()( 213 iii pPRwpPRwpPR

][ kik tT

213 )1( TwwTT

)]([ ikk pPRPR


RankMass Lower Bound: General Case

• The RankMass of the L-neighbors of the group of all trusted pages G, NL(G), is at least dL+1 close to 1. That is:

• Q: Given the result, how should we download for RankMass guarantee?

)(

11)(GNp

Li

Li

dpPR

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The L-Neighbor Crawler

1. L := 02. N[0] = {pi| ti > 0} // Start with trusted pages3. While ( < dL+1)

1. Download all uncrawled pages in N[L]2. N[L + 1] = {all pages linked to by a page in N[L]}3. L = L + 1

• Essentially, a BFS (Breadth-First Search) crawling algorithm

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Crawling Efficiency

• For a given |DC|, pick DC such that RM(DC) is the maximum

• Q: Can we use L-Neighbor?• A:

– L-Neighbor simple, but we need to further prioritize certain pages over others

– Page level prioritization.

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Page Level Prioritization

• Q: What page should we download first to maximize RankMass?

• A: Pages with high PageRank• Q: How do we know high PageRank pages?• The idea:

– Calculate PageRank lower bound of undownloaded pages– Give high priority to high lower bound pages

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Calculating PageRank Lower Bound

• PR(p): Probability random surfer at p• Breakdown path by “interrupts”, jumps to a

trusted page• Sum up all paths that start with an interrupt,

jump to a trusted page and end with p

Interrupt Pj

(1-d) (tj) (d*1/3) (d*1/5) (d*1/3)(d*1/4) (d*1/3) (d*1/3)

P3P1 P2 P4 P5 Pi

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Calculating PageRank Lower Bound

• Q: What if we sum up the probabilities of the subsets of the paths to p?

• A: “lower bound” of PageRank p• Basic idea

– Start with the set of trusted pages G– Enumerate paths to a page p as we discover links– Sum up the probability of each discovered path to p

• Not every path needed. Only the ones that we have discovered so far


RankMass Crawler: High Level

• Dynamically update lower bound on PageRank– By enumerating paths to pages

• Download page with highest lower bound– Sum of downloaded lower bounds = RankMass

coverage

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RankMass Crawler• CRM = 0 // CRM: crawled RankMass• rmi = (1 − d)ti for each ti > 0

// rmi : RankMass (PageRank lower bound) of pi

• While (CRM < 1 − ):– Pick pi with the largest rmi.– Download pi if not downloaded yet

• CRM = CRM + rmi // we have downloaded pi

• For each pj linked to by pi: rmj = rmj + d/ci rmi// Update RankMass based on the discovered links from pi

• rmi = 0

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Experimental Setup

• HTML files only• Algorithms simulated over web graph• Crawled between Dec’ 2003 and Jan’ 2004• 141 millon URLs span over 6.9 million host

names• 233 top level domains.

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Metrics Of Evaluation

1. How much RankMass is actually collected during the crawl

2. How much RankMass is “known” to have been collected during the crawl

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L-Neighbor

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RankMass

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Algorithm Efficiency

Algorithm Downloads

required for

above 0.98%

guaranteed

RankMass

Downloads

required

for above

0.98% actual

RankMass

L-Neighbor 7 million 65,000

RankMass 131,072 27,939

Optimal 27,101 27,101

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Summary

• Web crawler and its challenges• Page selection problem• PageRank• RankMass guarantee• Computing PageRank lower bound• RankMass crawling algorithm• Any questions?

cs246: page selection. junghoo "john" cho (ucla computer science) 2 page selection...

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