Models for Inexact Matching

In this lecture we consider four variants of biologically motivated inexact matching problems:

Problem 2.1   Global Alignment
INPUT: Two strings S and Tof roughly the same length.
QUESTION: What is the difference (or similarity) between the two?

Problem 2.2   Local Alignment
INPUT: Two strings S and T.
QUESTION: What is the maximum similarity (minimum difference) between a substring of S and a substring of T? What are these most similar substrings?

Problem 2.3   Ends free-space alignment
INPUT: Two strings Sand T of different length.
QUESTION: What is the maximum similarity between substrings of s and T, respectively? where at least one of these substrings must be a prefix of the original string and one (not necessary ly the other) must be a suffix?

Problem 2.4   Gap penalty
INPUT: Two strings S and T of different length.
QUESTION: Defining a gap as any maximal, consecutive run of spaces in a single string of a given alignment, and the length of a gap as the number of indel operations on it ^2.1, What is the similarity between the two strings, given a weight function for gaps (depending on their lengths)?