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# l03 - 6.896 Sublinear Time Algorithms Lecture 3 Lecturer...

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6.896 Sublinear Time Algorithms February 13, 2007 Lecture 3 Lecturer: Ronitt Rubinfeld Scribe: Jeremy Hurwitz In this lecture, we will prove the correctness of the equality tester for L 1 . L 1 -Dist-Test ( p, q, ) m O (max( 2 , 4) n 2 3 log n ) S p m samples from p S q m samples from q S S p S q discard any element that appears less than (1 63 ) mn 2 3 times in S if S = ˆ p i number of times i appears in S p ˆ q i number of times i appears in S q fail if i S | ˆ p i ˆ q i | > m 8 define p as output of following process sample x p if x / S output x else output x U D define q similarly else p p , q q run T ( p , q , 2 n ) with O ( n 2 3 4 ) samples T is a tester described in the last lecture which passes p, q for which the L 2 distance is at most / 2 and fails p, q for which the L 2 distance is at least . We assume that the error probability is at most 1/6. 1 Useful Claims, Observations, and a Lemma We begin by proving a series of claims. We will then analyze the behavior of the algorithm.

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l03 - 6.896 Sublinear Time Algorithms Lecture 3 Lecturer...

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