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Web Algorithmics

Web Algorithmics. Web Search Engines. Goal of a Search Engine. Retrieve docs that are “relevant” for the user query Doc : file word or pdf, web page, email, blog, e-book,... Query : paradigm “bag of words” Relevant ?!?. The Web: Language and encodings: hundreds…

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Web Algorithmics

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  1. Web Algorithmics Web Search Engines

  2. Goal of a Search Engine Retrieve docs that are “relevant” for the user query • Doc: file word or pdf, web page, email, blog, e-book,... • Query: paradigm “bag of words” Relevant ?!?

  3. The Web: Language and encodings:hundreds… Distributed authorship: SPAM, format-less,… Dynamic: in one year 35% survive, 20% untouched The User: Query composition: short (2.5 terms avg) and imprecise Query results: 85% users look at just one result-page Several needs: Informational, Navigational, Transactional Two main difficulties Extracting “significant data” is difficult !! Matching “user needs” is difficult !!

  4. Evolution of Search Engines • First generation-- use only on-page, web-text data • Word frequency and language • Second generation-- use off-page, web-graph data • Link (or connectivity) analysis • Anchor-text (How people refer to a page) • Third generation-- answer “the need behind the query” • Focus on “user need”, rather than on query • Integrate multiple data-sources • Click-through data 1995-1997 AltaVista, Excite, Lycos, etc 1998: Google Google, Yahoo, MSN, ASK,……… Fourth generation  Information Supply [Andrei Broder, VP emerging search tech, Yahoo! Research]

  5. +$ -$

  6. This is a search engine!!!

  7. Wolfram Alpha

  8. Clusty

  9. Yahoo! Correlator

  10. Web Algorithmics The structure of a Search Engine

  11. ? Page archive Crawler Web Page Analizer Indexer Query resolver Ranker Control text auxiliary Structure The structure Query

  12. Generating the snippets !

  13. The big fight: find the best ranking...

  14. Ranking: Google vs Google.cn

  15. Problem: Indexing • Consider Wikipedia En: • Collection size ≈ 10 Gbytes • # docs ≈4 * 106 • #terms in total > 1 billion(avg term len = 6 chars) • #terms distinct = several millions • Which kind of data structure do we build to support word-based searches ?

  16. DB-based solution: Term-Doc matrix #docs ≈ 4M #terms > 1M Space ≈ 4Tb ! 1 if play contains word, 0 otherwise

  17. 2 4 6 10 32 1 2 3 5 8 13 21 34 Current solution: Inverted index • A term like Calpurnia may use log2 N bits per occurrence • A term like the should take about 1 bit per occurrence Brutus the Calpurnia 13 16 Currently they get 13% original text

  18. Gap-coding for postings • Sort the docIDs • Store gaps between consecutive docIDs: • Brutus: 33, 47, 154, 159, 202 … 33, 14, 107, 5, 43 … Two advantages: • Space: store smaller integers (clustering?) • Speed: query requires just a scan

  19. g-code for integer encoding Length-1 • v > 0 and Length = log2 v +1 e.g., v=9 represented as <000,1001>. • g-code for v takes 2 log2 v +1 bits (ie. factor of 2 from optimal) • Optimal for Pr(v) = 1/2v2, and i.i.d integers

  20. Rice code (simplification of Golomb code) [q times 0s] 1 Log k bits • It is a parametric code: depends on k • Quotient q=(v-1)/k, and the rest is r= v – k * q – 1 • Useful when integers concentrated around k • How do we choose k ? • Usually k  0.69 * mean(v) [Bernoulli model] • Optimal for Pr(v) = p (1-p)v-1, where mean(v)=1/p, and i.i.d ints

  21. PForDelta coding Use b (e.g. 2) bits to encode 128 numbers or create exceptions 3 42 2 3 3 1 1 … 3 3 23 1 2 11 10 11 11 01 01 … 11 11 01 10 42 23 a block of 128 numbers Translate data: [base, base + 2b-1]  [0,2b-1] Encode exceptions: ESC or pointers Choose b to encode 90% values, or trade-off: b waste more bits, b more exceptions

  22. Interpolative coding D = 1 1 1 2 2 2 2 4 3 1 1 1 M = 1 2 3 5 7 9 11 15 18 19 20 21 lo=9+1=10, hi=21, num=6 lo=1, hi=9-1=8, num=5 • Recursive coding  preorder traversal of a balanced binary tree • At every step we know (initially, they are encoded): • num= |M| = 12, Lidx=1, low= 1, Ridx=12, hi= 21 • Take the middle element: h= (Lidx+Ridx)/2=6  M[6]=9, • left_size= h – Lidx = 5, right_size= Ridx-h = 6 • low+left_size =1+5 = 6 ≤ M[h] ≤ hi– right_size=(21 – 6)= 15 • We can encode 9 in log2 (15-6+1) = 4 bits

  23. 2 4 6 13 32 1 2 3 5 8 13 21 34 Query processing • Retrieve all pages matching the query Brutus the Caesar 4 13 17

  24. 2 4 6 13 32 1 2 3 5 8 13 21 34 Some optimization Best order for query processing ? • Shorter lists first… Brutus The Calpurnia 4 13 17 Query: BrutusANDCalpurniaANDThe

  25. Phrase queries • Expand the posting lists with word positions • to: • 2:1,17,74,222,551;4:8,16,190,429,433;7:13,23,191; ... • be: • 1:17,19; 4:17,191,291,430,434;5:14,19,101; ... • Larger space occupancy,  5÷8% on Web

  26. 2 4 6 13 32 1 2 3 5 8 13 21 34 Query processing • Retrieve all pages matching the query • Order pages according to various scores: • Term position & freq (body, title, anchor,…) • Link popularity • User clicks or preferences Brutus the Caesar 4 13 17

  27. ? Page archive Crawler Web Page Analizer Indexer Query resolver Ranker Control text auxiliary Structure The structure Query

  28. Web Algorithmics Text-based Ranking (1° generation)

  29. æ ö n = ç ÷ idf log where nt = #docs containing term t n = #docs in the indexed collection è ø t n t A famous “weight”: tf-idf = tf Frequency of term t in doc d = #occt / |d| t,d Vector Space model

  30. Postulate: Documents that are “close together” in the vector space talk about the same things. Euclidean distance sensible to vector length !! Easy to Spam A graphical example t3 cos(a)= v w / ||v|| * ||w|| d2 d3 Sophisticated algos to find top-k docs for a query Q d1 a t1 d5 t2 d4 The user query is a very short doc

  31. Approximate top-k results • Preprocess: Assign to each term, its m best documents • Search: • If |Q| = q terms, merge their preferred lists ( mq answers). • Compute COS between Q and these docs, and choose the top k. Need to pick m>k to work well empirically. Now SE use tf-idf PLUS PageRank (PLUS other weights)

  32. Web Algorithmics Link-based Ranking (2° generation)

  33. Query-independent ordering • First generation: using link counts as simple measures of popularity. • Undirected popularity: • Each page gets a score given by the number of in-links plus the number of out-links (es. 3+2=5). • Directed popularity: • Score of a page = number of its in-links (es. 3). Easy to SPAM

  34. Second generation: PageRank • Each link has its own importance!! • PageRank is • independent of the query • many interpretations…

  35. Any node d 1-d Neighbors Basic Intuition…

  36. Principal eigenvector Google’s Pagerank Fixed value B(i) : set of pages linking to i. #out(i): number of outgoing links from i.

  37. Any node d “In the steady state” each page has a long-term visit rate - use this as the page’s score. 1-d Neighbors Three different interpretations • Graph (intuitive interpretation) • Co-citation • Matrix (easy for computation) • Eigenvector computation or a linear system solution • Markov Chain (useful to prove convergence) • a sort of Usage Simulation

  38. Pagerank: use in Search Engines • Preprocessing: • Given graph of links, build matrix L • Compute its principal eigenvector r • r[i] is the pagerank of page i We are interested in the relative order • Query processing: • Retrieve pages containing query terms • Rank them by their Pagerank The final order is query-independent

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