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Lecture4 - Lecture 4 Examples T(n 2T(n 2(n lg a n b nlg2 2...

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1 45 Examples n n n b a lg lg 2 2 T n T n n ( ) ( / ) ( ) 2 2 n n n T n n n ( )/ ( ) (lg ) ( ) ( lg ) 1 0 case 2 Strassen's matrix multiplication ( ) = ( / )+ ( T n T n n 7 2 2 ) a 7 n n b 2 lg lg Better than n 3 !!! n 2 ( ) case 1 n O n T n n 7 08 7 2 2 ( ) ( ) ( ) lg . lg 3 ( ) 4 ( /2) T n T n n 2 3 3 lg 4 case 3 ( ) ( ) n n T n n n  3 3 ( : need to check the additional condition 0 1 s.t. 4( /2) )   Note c n cn Lecture 4, Sept 30, 2010 46 Does the method always apply ? 2 2 Lower bound: 4 ( /2) case 1 ( ) T n n n   2 Exact Answer: ( lglg ) n n 2 ( ) 4 ( /2) /lg T n T n n n 2 2 Upper bound: 4 ( /2) case 2 ( lg ) T n n n n   2 2 lg 4 ( ), 0 /lg 1 (lg ), 0 lg ( ), 0 k O n n n n k n n n  
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