l2 - 6.896 Sublinear Time Algorithms September 14, 2004...

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Unformatted text preview: 6.896 Sublinear Time Algorithms September 14, 2004 Lecture 2 Lecturer: Ronitt Rubinfeld Scribe: Akshay Patil 1 L a s t T i m e Types of approximation Optimization problems - standard (saw the notion of -additive and -multiplicative relative ap- proximations). Decision problems - saw example of monotone sequences 2 Definition of Property Tester 2.1 Decision Problems Define a language P to be a class of inputs that have a certain property. examples: class of allowable graphs (e.g. connected, bipartite, has large cut) class of allowable sequences (e.g. monotonic increasing integers) class of allowable functions, represented by input/output tables (e.g. homomorphisms) 2.1.1 Behavior of a decision algorithm for P A ( x ) : x P pass x P fail 2.2 Representation/Model Representation is very important with respect to distance functions. Also important is how we access the input. Most common is the random access model. In this model, accessing each of the following would count as 1 step: i th bit of a string function value f ( i ) the i, j th entry of a matrix 2.3 Distance function In order to define a property tester, it is important to define a notion of distance from having a property....
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l2 - 6.896 Sublinear Time Algorithms September 14, 2004...

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