Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology

Author: Dan Gusfield
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by anonymous   2017-08-20

1) You should look at using a suffix tree data structure.

Suffix Tree

This data structure can be built in O(N * log N) time
(I think even in O(N) time using Ukkonen's algorithm)
where N is the size/length of the input string.
It then allows for solving many (otherwise) difficult
tasks in O(M) time where M is the size/length of the pattern.

So even though I didn't try your particular problem, I am pretty sure that
if you use a suffix tree and a smart formulation of your problem, then the
problem can be solved by using a suffix tree (in reasonable O time).

2) A very good book on these (and related) subjects is this one:

Algorithms on Strings, Trees and Sequences

It's not really easy to read though unless you're well-trained in algorithms.
But OK, reading such things is the only way to get well-trained ;)

3) I suggest you have a quick look at this algorithm too.

Aho-Corasick Algorithm

Even though, I am not sure but... this one might be somewhat
off-topic with respect to your particular problem.

by anonymous   2017-08-20

The most fundamental data structure used in bioinformatics is string. There are also a whole range of different data structures representing strings. And algorithms like string matching are based on the efficient representation/data structures.

A comprehensive work on this is Dan Gusfield's Algorithms on Strings, Trees and Sequences

by anonymous   2017-08-20

Suffix tree related algorithms are useful here.

One is described in Algorithms on Strings, Trees and Sequences by Dan Gusfield (Chapter 9.6). It uses a combination of divide-and-conquer approach and suffix trees and has time complexity O(N log N + Z) where Z is the number of substring repetitions.

The same book describes simpler O(N2) algorithm for this problem, also using suffix trees.