Algorithms (Contd.)

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Algorithms (Contd.)
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How do we describe algorithms?

• Pseudocode
• Combines English, simple code constructs
• Works with various types of primitives
• Could be - /
• Could be more complex operations
• Describes how data is organized
• Describes operations on the data
• Is meant to be higher level than programming

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Searching with indices (pseudocode)

• Build the indices
• Do this by going through the list and determining
  where department names change
• Store the results in an array called Indices
• Search the indices
• Do a binary search on the array Indices
• Do this by comparing to the middle element
• Then use binary search to compare to the upper
  half
• Or use binary search to compare to the lower half

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Building a web search engine

• Crawl/spider the web
• Organize the results for fast query processing
• Process queries

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Crawl the web

• Every month use networking to go to as many
  reachable web pages as you can
• 10B pages, 10 Kbytes/page, so 100 terabytes
• Can compress an average page to 3Kbytes
• Numeracy
• To crawl 10B pages in 100 days
• Crawl 100M pages per day
• Crawl 4M pages per hour
• Crawl 1,000 pages per second

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Organize the results

• Put into alphabetical order
• Build indices for faster lookup
• Make multiple copies so that searching can
  proceed in parallel.
• When you update, you rebuild the indices

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Process search queries

• Look up indices
• Look up words/phrases
• Advertiser can buy a word or phrase
• This search gives you internal addresses of web
  pages
• Look them up to build results page
• Ranking results content match, popularity, price
  paid by advertisers,

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Ranking by Popularity

• The web is a collection of links
• A documents importance is determined by
• How many pages point to it
• How important those pages are
• Used for determining
• How often to crawl a page
• How to order pages presented.

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Content Relevance

• Simple string matching
• Does the document/string contain the word
  computer?
• More complex string matching
• Did the word computer occur before or after the
  word science?
• Did it appear within 10 words of the word science?

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How does string matching work?

• State machines ?
• Move along states as long as you keep matching
• Back off when you miss a match

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State machine looking for abcd
Read a
What happens if input is abccadbacabcd?
Sa Sb Sc Sd Sa Sb Sa Sa Sb Sa Sb Sc Sd OK
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State machine looking for abcd
Read a
What happens if input is abcabcd?
Sa Sb Sc Sd Sa Sa Sa Sa
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State machine looking for abcd
Read a
Read a
Read b
Read c
Sd
Sa
Sb
Sc
Read a
Other
Read a
Read d
Other
OK
Other
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Larger search challenges

• Allow strings to have dont cares
• Starts with a and ends with e
• Has come number of copies of the substring ab
• Finding strings similar to but not the same as
  your string
• For spelling corection

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Algorithms -- summary

• Methods for solving problems
• Understand at a high level
• Make sure your reasoning is correct
• Worry about efficiency in situations where that
  matters
• Write as pseudocode

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Distributed Algorithms
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Distributed computing

• Key idea
• Buying 1000 machines of speed x is significantly
  cheaper than buying one machine of speed 1000x
• No one person has to buy all 1000 machines A lot
  of computational, communication and storage
  resources already in place and can be harvested
  for bigger things
• Key challenge
• Making the machines work together for effective
  speedup. Communication between machines is a key
  challenge.
• Approaches
• Find problems that can be distributed easily

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Distributed problems

• Problems that can use decentralized computing
• Weather prediction
• Weather in a location is most affected by weather
  nearby
• Movie generation
• Individual frames can be generated separately
• Google search engine
• 10,000s PCs. all of them cheap, many of them
  identical
• Can answer over 100,000,000 queries per day in ½
  sec or less each
• Looking for the origin of the universe
• Can be localized like weather prediction
• File swapping and access (distributed storage)
• Looking for extra terrestrial intelligence
• Content caching and distribution

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Distributed computers

• Scales of distributed computing
• Cluster-in-a-room hundreds of machines
• All dedicated to the task
• PCs on a campus thousands of machines
• Using spare cycles
• SETI cluster millions of machines
• Screen saver situation

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Cluster in a Room

• Machines are dedicated to the network
• All machines run similar software
• Problem is divided into pieces
• Each piece is assigned to a machine in the
  cluster
• Problem pieces should be loosely linked
• Computation is faster than communication

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PCs on a Campus

• Loosely coupled on a local-area-network
• PCs do other things some of the time
• When free cycles are available, theyre used
• Many more machines, but less of each machine
  available

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Workstation Network at Google
Retrieving machines
Searching machines
Fit 40-80 machines in a 7x2x3 rack
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SETI

• Telescope at Arecibo, PR collects data
• Data is processed in real time by fast machines
• But, no one looks for weak signals
• Too costly
• SETI_at_Home project built to do this

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SETI_at_Home

• Receive data from Arecibo
• 35 Gbytes per day by snail mail
• Break into Work Units
• .25 Mbyte each, so 140,000 WUs per day
• WU takes 20 hours to process
• Need about 117,000 dedicated machines to process
  one day

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SETI_at_Home

• Get individual users to download software
• Machine idle and screen saver runs software
• Download WU
• Compute
• When finished send back result
• Database at Berkeley reassembles results
• Progress to date -- Seti_at_HomeStats

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Medical/Biological Applications

• Peer-to-Peer Medicine
• Cancer Research