Algorithms (Contd.)

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

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

Building a web search engine

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

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

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

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, …

Ranking by Popularity

• The web is a collection of links– A document’s 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.

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?

How does string matching work?

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

State machine – looking for abcdRead a Read b Read c

Read d

Other

Other

Other

Sa Sb ScSd

OK

What happens if input is abccadbacabcd?

Sa Sb Sc Sd Sa Sb Sa Sa Sb Sa Sb Sc Sd OK

State machine – looking for abcdRead a Read b Read c

Read d

Other

Other

Other

Sa Sb ScSd

OK

What happens if input is abcabcd?

Sa Sb Sc Sd Sa Sa Sa Sa

State machine – looking for abcd

Read a Read b Read c

Read d

Other

OtherOther

Sa Sb ScSd

OK

Read a Read a

Read a

Larger search challenges

• Allow strings to have don’t 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

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

Distributed Algorithms

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

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 PC’s. 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

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

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

PCs on a Campus

• Loosely coupled on a local-area-network

• PCs do other things some of the time

• When free cycles are available, they’re used

• Many more machines, but less of each machine available

Workstation Network at GoogleFront end100 machines called www.google.com

Searching machines Retrieving machines

Fit 40-80 machines in a 7’x2’x3’ rack

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@Home project built to do this

SETI@Home

• Receive data from Arecibo– 35 Gbytes per day by snail mail

• Break into Work Units– .25 Mbyte each, so 140,000 WU’s per day

• WU takes 20 hours to process

• Need about 117,000 dedicated machines to process one day

SETI@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@HomeStats

Medical/Biological Applications

• Peer-to-Peer Medicine• Cancer Research• …