Hongjun Song Computer Science The University of Memphis Googling Hongjun Song Computer Science The University of Memphis COMP 7100: Computers in the Information society

Some searches... “David Evans” “Dave Evans” “idiot” “lawn lighting” Tomorrow at 6pm (but google doesn’t know 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 Crawler activeURLs = [ “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 pages Will take very long to get a good view of the web Will annoy web server admins downloadPage and extractLinks must be very robust

Crawling Crawler activeURLs = [ “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 Crawler activeURLs = [ “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 distributing finding aliens?

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

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 Index Word 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?

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 multiplication is 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 Searching First Letter Items 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) Finding a good H is difficult 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 [<“aardvark”, 1024235>, ... ] 1 [<“aaa”, 224155>, ..., <“zzz”, 29543> ] ... nbins – 1 [<“abba”, 25583>, ..., <“zeit”, 50395> ]

Google’s Reverse Index (From 1998 paper...may have changed some since then) WordId ndocs pointer 00000000 3 00000001 15 ... 16777215 105 Inverted Barrels: 41 GB (1998) Lexicon: 293 MB (1998)

Inverted Barrels 7630486927 23 ... docid (27 bits) nhits (5 bits) hits (16 bits each) 7630486927 23 ... plain hit: capitalized: 1 bit font size: 3 bits position: 12 bits first 4095 chars, everything else extra info for anchors, titles (less position bits)

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

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 Model Initialize all page ranks = 0 p = select a random URL for 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 ranks How 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) Google in 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

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 Ready to go become the next google?

Charge Before becoming the next Google, you need to finish COMP7100.