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4.10. How efficient is this algorithm?
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We have seen the principle of an iterative algorithm in two paths for aligning and comparing two sequences of characters, here DNA sequences. And we understoodwhy the iterative version is much more efficient than the recursive version. But, how efficient is reallythis iterative algorithm? You remember that in order to measure the efficiency of algorithms, the computer scientists do not use any mean of measuring the time or any other thing. They evaluate the number of timethe main operation inside the algorithm is executed. In the caseof this Needleman and Wunsch algorithm which has been published 40 years ago, the operation which is critical is the comparisonbetween two letters of a pair of letters. It's easy, if you look at the algorithm, to find that the number of comparison is of the order of N multiplied by M with N and M being the lengths of the sequences. We say that the algorithmic complexity of this algorithm is quadratic. What does it mean? It means thatif the lengths of the sequences double, the execution time will be multiplied by four. It's easy to see. First, you have two sequences of lengths N and M. You double the length of the first sequence and you double the length of the fourth sequence since the number of comparison is the result of the multiplication of these two values, you see that of course you multiply the execution time by four.
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4.6. A path is optimal if all its sub-paths are optimal
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4.9. Recursion can be avoided: an iterative version
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4.4. Aligning sequences is an optimization problem
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4.7. Alignment costs
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4.2. Why gene/protein sequences may be similar?
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4.5. A sequence alignment as a path
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4.8. A recursive algorithm
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4.3. Measuring sequence similarity
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4.8. A recursive algorithm
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