net.maizegenetics.analysis.gbs.neobio

Class NeedlemanWunsch

java.lang.Object

net.maizegenetics.analysis.gbs.neobio.PairwiseAlignmentAlgorithm

net.maizegenetics.analysis.gbs.neobio.NeedlemanWunsch

public class NeedlemanWunsch
extends PairwiseAlignmentAlgorithm

This class implements the classic global alignment algorithm (with linear gap penalty function) due to S.B.Needleman and C.D.Wunsch (1970).

It is based on a dynamic programming approach. The idea consists of, given two sequences A and B of sizes n and m, respectively, building an (n+1 x m+1) matrix M that contains the similarity of prefixes of A and B. Every position M[i,j] in the matrix holds the score between the subsequences A[1..i] and B[1..j]. The first row and column represent alignments with spaces.

Starting from row 0, column 0, the algorithm computes each position M[i,j] with the following recurrence:

 M[0,0] = 0
 M[i,j] = max { M[i,j-1]   + scoreInsertion (B[j]),
                M[i-1,j-1] + scoreSubstitution (A[i], B[j]),
                M[i-1,j]   + scoreDeletion(A[i])             }
 

In the end, the value at the last position (last row, last column) will contain the similarity between the two sequences. This part of the algorithm is accomplished by the computeMatrix method. It has quadratic space complexity since it needs to keep an (n+1 x m+1) matrix in memory. And since the work of computing each cell is constant, it also has quadratic time complexity.

After the matrix has been computed, the alignment can be retrieved by tracing a path back in the matrix from the last position to the first. This step is performed by the buildOptimalAlignment method, and since the path can be roughly as long as (m + n), this method has O(n) time complexity.

If the similarity value only is needed (and not the alignment itself), it is easy to reduce the space requirement to O(n) by keeping just the last row or column in memory. This is precisely what is done by the computeScore method. Note that it still requires O(n²) time.

For a more efficient approach to the global alignment problem, see the CrochemoreLandauZivUkelson algorithm. For local alignment, see the SmithWaterman algorithm.

Author:

Sergio A. de Carvalho Jr.

See Also:

SmithWaterman, CrochemoreLandauZivUkelson, CrochemoreLandauZivUkelsonLocalAlignment, CrochemoreLandauZivUkelsonGlobalAlignment

Constructor Summary

Constructors

Constructor and Description
NeedlemanWunsch()

Method Summary

Methods inherited from class net.maizegenetics.analysis.gbs.neobio.PairwiseAlignmentAlgorithm

getPairwiseAlignment, getScore, loadSequences, setScoringScheme, unloadSequences

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NeedlemanWunsch

public NeedlemanWunsch()