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lecture21 - Outline COMPUTER SCIENCE 51 Spring 2009...

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4/28/2009 1 COMPUTER SCIENCE 51 Spring 2009 cs51.seas.harvard.edu Prof. Greg Morrisett Prof. Ramin Zabih Final lecture! Outline Two great clustering examples 21 st Century and 19 th Century Impossible programs Cows with guns Files and images 21 st Century clustering Walmart processes hundreds of millions of transactions per day Several petabytes (million gigabytes) Incredible source of information about what people buy There are clearly clusters in the data I.e., college students Finding common subsets is a great CS problem, related to clustering People who bought {A,B} also bought {C} 19 th Century clustering John Snow’s map of cholera outbreak Epidemiology, spatial statistics How did we know AIDS wasn’t airborne? Impossible programs CS51 has been about powerful methods to write programs Elegant programming tools Efficient algorithms But not all problems can be solved with a computer (obviously) Even well-specified computational problems are not always solvable Importance of impossibility Negative results serve as vital shortcuts Suppose someone claims to have code to solve an impossible problem You know that subroutine must be wrong No matter how complex or fashionable! Somewhat akin to conservation of energy in physics Perpetual motion machines cannot be patented See also: dimensional analysis
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4/28/2009 2 Pigeonhole principle Usually stated with pigeons and holes In honor of Greg, cows with guns http://www.youtube.com/watch?v=FQMbXvn2RNI If there are N cows and N-1 guns, you can’t assign each cow its own gun How to prove?
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