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Unformatted text preview: 6.896 Sublinear Time Algorithms March 13, 2007 Lecture 11 Lecturer: Ronitt Rubinfeld Scribe: Christina Sauper 1 Estimating the Number of Connected Components Given a graph G ( V,E ) with max degree d and adjacency list representation and some , we want to give an additive estimate of the number of connected components to within n . 1.1 Main Idea Define: n u number of nodes in u s component, where u V Fact 1 For any connected component A V : X u A 1 n u = X u A 1 | A | = 1 In addition, there are u V 1 n u connected components. Determining this value exactly takes O ( n 2 ) time, but we will estimate the sum and the values of n u . Define: n u min nodes in u s component , 2 c = X u V 1 n u Fact 2 The error in estimating 1 n u is small. 1 n u- 1 n u 2 Either n u = n u or n u > n u = 2 . In the latter case, 2 = 1 n u 1 n u 0. Therefore, the error is small, at most 2 ....
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This note was uploaded on 04/02/2010 for the course CS 6.896 taught by Professor Ronittrubinfeld during the Fall '04 term at MIT.
- Fall '04