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Unformatted text preview: Algorithms – Sequence Alignment Sequence Alignment Design and Analysis of Algorithms Andrei Bulatov Algorithms – Sequence Alignment 82 The Sequence Alignment Problem Question: How similar two words are? Say “ ocurrance ” and “ occurrence ” They are similar, because one can be turned into another by few changes oc urr a nce oc c urr e nce Clearly, this can be done in many ways, say oc urr a nce oc c urr e nce Problem: Minimize the “number” of gaps and mismatches gap mismatch Algorithms – Sequence Alignment 83 Alignments Let and be two strings A matching is a set of ordered pairs, such that an element of each set occurs at most once. A matching is an alignment if there no crossing pairs: if (i,j) and (i’,j’) are in the matching and i < i’ then j < j’ o c u r r a n c e o c u r r e n c e c o c u r r a n c e o c u r r e n c e c m x x x X , , , 2 1 K = n y y y Y , , , 2 1 K = Algorithms – Sequence Alignment 84 The Problem Let M be an alignment between X and Y. Each position of X or Y that is not matched in M is called a gap . Each pair (i,j) ∈ M such that is called a mismatch The cost of M is given as follows: There is δ > 0, a gap penalty . For each gap in M we incur a cost of δ For each pair of letters p,q in the alphabet, there is a mismatch cost For each (i,j) ∈ M we pay the mismatch cost...
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 Fall '09
 Bulatov
 Algorithms, Graph Theory, Shortest path problem, Sequence alignment, Andrei Bulatov

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