l14 - 6.896 Sublinear Time Algorithms March 22, 2007...

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Unformatted text preview: 6.896 Sublinear Time Algorithms March 22, 2007 Lecture 14 Lecturer: Ronitt Rubinfeld Scribe: Huy Ngoc Nguyen 1 First order properties testing: First order graph property is a property that can be expressed in the following form: u 1 , u 2 , ....u k v 1 , v 2 , ....v l R ( u 1 , ...., u k , v 1 , ....., v l ) | {z } may include , , or other logical operations ) In this lecture, we will show a special case of the following theorem. Theorem 1 : Alon, Fischer, Krivilevich and Szegedy All first order properties of , type are testable in adjacent matrix model with queries number indepen- dent of n. In fact, recent results have given characterizations of the graph properties testable in constant time in the adjacency matrix representation, though we will not cover those proofs in lecture. For example, such properties include all monotone graph properties. 1.1 -free testing In this lecture, we will consider a case of first order property testing, free : u 1 , u 2 , u 3 R ( u 1 , u 2 , u 3 ) = ( u 1 u 2 u 2 u 3 u 1 u 3 ) Definition 1 G is -far from -free if we must add/delete at least n 2 edges to make it -free....
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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.

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l14 - 6.896 Sublinear Time Algorithms March 22, 2007...

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