In the sequence alignment problem, suppose you knew that the input strings were relatively similar, in the sense that there is an optimal alignment that uses at most k gaps, where k is much smaller than the lengths m and n of the strings. Show how to compute the NW score in O((m+n)k) time.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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 In the sequence alignment problem, suppose you knew that the input strings were relatively similar, in the sense that there is an optimal alignment that uses at most k gaps, where k is much smaller than the lengths m and n of the strings. Show how to compute the NW score in O((m+n)k) time.

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