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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 k-1 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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