ECS124_Lecture4 - ECS 124 Theory and practice of...

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E ECS 124: Theory and practice of bioinformatics Lecture 4: Dynamic Programming and Local sequence alignment Instructor: Ilias Tagkopoulos [email protected] Offi K 3063 d GBSF 5313 Office: Kemper 3063 and GBSF 5313 4/13/2010 1 UC Davis
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Last time: # of alignments, complexity and global alignment # of alignments 10 8,097,452 ݊ ൅ ݎ ݊ ݊ ݎ ݊ ݎൌ0 20 ~2.6054e+014 100 ~2.0537e+075 4/13/2010 UC Davis 2
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Ali G h Alignment Graph We can calculate the maximum score (min distance) from (0 0) to any distance) from (0,0) to any node (i,j). What about this node? Do we have to calculate the total path ? Can you find a way to speed up the computation ? Computing distance from neighbor nodes only How many operations? Complexity? A case of dynamic programming 4/13/2010 UC Davis 3
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D i i Dynamic programming Dynamic programming is a case of “ divide and is a case of conquer ” where you can break down the problem to smaller sub problems, and compute them efficiently. Two conditions for dynamic programming: Existence of overlapping sub problems. Existence of optimal sub structure optimal sub structure . Overlapping sub problems : sub problem space is small, i.e. naively we would have to do the same computation multiple times Optimal sub structure : optimal global solution is the bi ti f ti l l l (i b bl ) combination of optimal local (i.e. sub problem) solution 4/13/2010 UC Davis 4
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D i i Dynamic programming Two categories: Top down approach : Saving previous results on run time (what is called “memoization”). Similar to run time (what is called memoization ). Similar to mapping, caching, lookup tables etc.
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