CLOUD COMPUTING PROJECT. By: - Manish Motwani - Devendra Singh Parmar - Ashish Sharma

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1 CLOUD COMPUTING PROJECT By: - Manish Motwani - Devendra Singh Parmar - Ashish Sharma

2 Instructor: Prof. Reddy Raja Mentor: Ms M.Padmini To Implement PageRank Algorithm using Map-Reduce for Wikipedia and verify it for smaller data-sets

3 Motivation Introduction to Algorithm PageRank Equation Analysis Brief Description of Project Module1 Module2 Module3 Applications

4 -> Need for PageRank: The Search engines store billions of web pages which overall contain trillions of web url links. So, there is a need for an algorithm that gives the most relevant pages specific to a query. -> Need for Distributed Environment ( Map-Reduce and Distributed Storage) Trillions of links implies huge data storage required. (if each url requires 0.5K, then we need over 400TB just to store URLs!) Large data set implies large computations

5 Motivation Introduction to Algorithm PageRank Equation Analysis Brief Description of Project Module1 Module2 Module3 Applications

6 PageRank is a link analysis algorithm, named after Larry Page, used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the Worldwide Web, with the purpose of "measuring" its relative importance within the set The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).

7 Google figures that when one page links to another page, it is effectively casting a vote for the other page. The more votes that are cast for a page, the more important the page must be. Also, the importance of the page that is casting the vote determines how important the vote itself is. Google calculates a page's importance from the votes cast for it. How important each vote is also taken into account when a page's PageRank is calculated.

8 Motivation Introduction to Algorithm PageRank Equation Analysis Brief Description of Project Module1 Module2 Module3 Applications

9 Simple Iterative Algorithm For kth iteration PageRank of ith page is given by: Here,

10 Problems: Sinks or Dangling Pages Cycles Solution:

11 Solution for Cycles and If a random surfer gets bored Here d is known as damping factor. It represents the probability, at any step, that the person will continue surfing. The value of d is typically kept 0.85

12

13 In a simpler way:- a page's PageRank = 0.15 /N * (a "share" of the PageRank of every page that links to it) "share" = the linking page's PageRank divided by the number of outbound links on the page. And N= the number of documents in collection The equation of PageRank shows clearly how a page's PageRank is arrived at. But what isn't immediately obvious is that it can't work if the calculation is done just once.

14 Motivation Introduction to Algorithm PageRank Equation Analysis Brief Description of Project Module1 Module2 Module3 Applications

15 Input: Data Set containing multiple records where each record contains the Url of the Page(from Url) followed by the url of a page to which it is pointing to(tourl). FromUrl Wiki_Votes.txt ToUrl

16 Output: The output file consist of records containing the url of the page(from Url), the page rank value of the page(prvalue) and the list of urls to which the page points to(tourllist). FinalOutput.txt fromurl PRValue ToUrlList

17 Web Graph Module1: Converter Converter Module2: PageRank Calculator PageRank Calculator Iterate until convergence... Module3: Output Analyzer Output Analyzer Search Engine Create Index

18 Motivation Introduction to Algorithm PageRank Equation Analysis Brief Description of Project Module1 Module2 Module3 Applications

19 FromUrl PRValue List: Converter (Initializing with PR= 1/N )

20 Self Loops: -handled by checking the FromUrl with ToUrl before sending it to the reduce function Dangling Pages: -handled by initializing their PRValue with 1/N and the List of ToUrls is left blank.

21 Motivation Introduction to Algorithm PageRank Equation Analysis Brief Description of Project Module1 Module2 Module3 Applications

22 PageRank Calculator (User can give Precision)

23 Map: Input: index.html PRValue OutList: < 1.html 2.html... > Output 1. Output for each outlink: key: 1.html value: PRValue/ ListLength 2. ToUrl itself (Vote Share) key: index.html value: <OutList> Reduce Input: Key: 1.html Value: Value: Value : UrlList <OutLink> Output: Key: 1.html Value: <new pagerank> <OutList> 1.html 2.html... Start with the initial PageRank and Outlinks of a document. PR( x) (1 d) N d n i i 1 C( ti ) PR( t )

24 Map: Input: index.html PRValue OutList: < 1.html 2.html... > Output 1. Output for each outlink: key: 1.html value: PRValue/ ListLength 2. ToUrl itself (Vote Share) key: index.html value: <OutList> Reduce Input: Key: 1.html Value: Value: Value : UrlList <OutLink> Output: Key: 1.html Value: <new pagerank> <OutList> 1.html 2.html... For each Outlink, output the PageRank s share of the Inlinks, and List of outlinks. PR( x) (1 d) N d n i i 1 C( ti ) PR( t )

25 Map: Input: index.html PRValue OutList: < 1.html 2.html... > Output 1. Output for each outlink: key: 1.html value: PRValue/ ListLength 2. ToUrl itself (Vote Share) key: index.html value: <OutList> Reduce Input: Key: 1.html Value: Value: Value : UrlList <OutLink> Output: Key: 1.html Value: <new pagerank> <OutList> 1.html 2.html... Now the reducer has a Url of document, all the inlinks to that document and their corresponding PageRank s share and List of outlinks. PR( x) (1 d) N d n i i 1 C( ti ) PR( t )

26 Map: Input: index.html PRValue OutList: < 1.html 2.html... > Output 1. Output for each outlink: key: 1.html value: PRValue/ ListLength 2. ToUrl itself (Vote Share) key: index.html value: <OutList> Reduce Input: Key: 1.html Value: Value: Value : UrlList <OutLink> Output: Key: 1.html Value: <new pagerank> <OutList> 1.html 2.html... Compute the new PageRank and output in the same format as the input. PR( x) (1 d) N d n i i 1 C( ti ) PR( t )

27 Map: Input: index.html PRValue OutList: < 1.html 2.html... > Output 1. Output for each outlink: key: 1.html value: PRValue/ ListLength 2. ToUrl itself (Vote Share) key: index.html value: <OutList> Reduce Input: Key: 1.html Value: Value: Value : UrlList <OutLink> Output: Key: 1.html Value: <new pagerank> <OutList> 1.html 2.html... Now iterate until convergence (determined by the precision value). PR( x) (1 d) N d n i i 1 C( ti ) PR( t )

28 Suppose we have 2 pages, A and B, which link to each other, and neither have any other links of any kind. This is what happens:- Step 1: Calculate A's PageRank from the value of its inbound links Step 2: Calculate B's PageRank from the value of its inbound links we can't work out A's PageRank until we know B's PageRank, and we can't work out B's PageRank until we know A's PageRank. Thus the PageRank of A and B will be inaccurate.

29 This problem is overcome by repeating the calculations many times. Each time produces slightly more accurate values. In fact, total accuracy can never be achieved because the calculations are always based on inaccurate values. The number of iterations should be sufficient to reach a point where any further iterations wouldn't produce enough of a change to the values to matter. => Use delta function which will keep track of changes in the PageRank of all the pages and if the change in PageRank of all the pages is less than the value specified by the user the iterations can be stopped.

30 Motivation Introduction to Algorithm PageRank Equation Analysis Brief Description of Project Module1 Module2 Module3 Applications

31 Input Analyzer ( If user want Top 3) Output

32 Motivation Introduction to Algorithm PageRank Equation Analysis Brief Description of Project Module1 Module2 Module3 Applications Questions

33 A simple model of Search Engine. (Implemented) The application utilizes: 1. The PageRank calculated by the PageRank Calculator 2. The output generated by a map-reduce module that finds out the number of times a pattern (as per the user s query) matches in each of the files present in data set. And outputs: The list of pages which are relevant to the query made in the order of their importance. (DEMO)

34 Other Applications: PageRank-based mechanism to rank knowledge items used in E-Learning. GeneRank (based on PageRank) ranks the genes analyzed in the microarray to see the relationship between the cell s function and gene expression. Can be used to sort the items present in the side menu in various blogs and sites depending on their importance.

35 ( research paper by Brin and Page) calculated

36 Questions

37 Thank You

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