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Unformatted text preview: Problem 2 0) Construction of the Algorithm Lets consider a function I such that I ( i ) = set of interesting loci covered by( a i ,b i ) and lets sort the set of restriction enzymes based on their I value and consider the n t h enzyme, then we know that we have two cases: either the enzyme n is within an optimal set O or its not. If enzyme n is not in the optimal set, then we can simply discard it and look at the smaller subset and find k other enzymes. However, if n is in the optimal set, then we add I(n) into our optimal set and look at the left over enzymes and find k1 other enzymes to use. This gives us the following definition of the optimum set of enzymes OPT ( n,k ) = max cardinality ( OPT ( n 1 ,k ) ,I ( n ) U OPT ( n 1 ,k 1)) if n 6 = 0 ,k 6 = 0 else 1) Algorithm 1. Create the I(i) table by going through all restriction enzymes and then iterating over all interesting loci to see which ones are part of I(i)....
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 Spring '08
 KLEINBERG
 Algorithms, Sort

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