Notes on algorithms with use in bioinformatics and computational biology:
WABI 2013: http://algo2013.inria.fr/wabi.shtml
Concepts and categories
Big O notation: http://rob-bell.net/2009/06/a-beginners-guide-to-big-o-notation/
Examples of dynamic programming algorithms:
- Needleman-Wunschm algorithm
- Smith-Waterman algorithm
- Sankoff algorithm
- Viterbi algorithm
Identifying K-mer clumps:
Dynamic programming algorithm to perform global sequence alignment. Also referred to as the "optimal matching algorithm". Introduced in 1970.
In general parlance, a Needleman-Wunsch type algorithm refers to a global alignment algorithm that takes quadratic time for a linear or affine gap penalty.
Smith Waterman algorithm:
Dynamic programming algorithm for local sequence alignment. Introduced in 1981. Can be considered a variation of the Needleman-Wunsch algorithm. Guaranteed to find the optimal local alignment with respect to the scoring system used.
See also http://seqanswers.com/forums/showthread.php?t=25305 for a discussion on implementing SW.
Also called "block-sorting compression". String transformation algorithm used in data compression. Transforms a character string by permuting the order of the character, to increase the number of character repeats.
Used by the sequence alignment program BWA.
From Wikipedia: "The Viterbi algorithm is a dynamic programming algorithm for finding the most likely sequence of hidden states – called the Viterbi path – that results in a sequence of observed events, especially in the context of Markov information sources and hidden Markov models."
Baum-Welch algorithm (Baum-Welch expectation maximization):
Invented by Leonard E. Baum and Lloyd R. Welch, the Baum-Welch algorithm is used to estimate the unknown parameters of a Hidden Markov Model (HMM).
L. E. Baum, T. Petrie, G. Soules, and N. Weiss, "A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains", Ann. Math. Statist., vol. 41, no. 1, pp. 164–171, 1970.
Fast Fourier Transform: http://en.wikipedia.org/wiki/Fast_Fourier_transform
An introduction to bioinformatics algorithms: http://bix.ucsd.edu/bioalgorithms/
Commentary and reviews
Algorithms in bioinformatics: http://www.springer.com/computer/bioinformatics/book/978-3-642-40452-8