neobio.alignment
Class SmithWaterman

java.lang.Object
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  +--neobio.alignment.PairwiseAlignmentAlgorithm
        |
        +--neobio.alignment.SmithWaterman

public class SmithWaterman

extends PairwiseAlignmentAlgorithm

This class implement the classic local alignment algorithm (with linear gap penalty function) due to T.F.Smith and M.S.Waterman (1981).

This algorithm is very similar to the NeedlemanWunsch algorithm for global alignment. The idea here also consists of building an (n+1 x m+1) matrix M given two sequences A and B of sizes n and m, respectively. However, unlike in the global alignment case, every position M[i,j] in the matrix contains the similarity score of suffixes of A[1..i] and B[1..j].

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

 M[0,0] = M[0,j] = M[i,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])             }
 

Note that, here, all cells in the first row and column are set to zero. The best local alignment score is the highest value found anywhere in the matrix.

Just like in global alignment case, this algorithm has quadratic space complexity because 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 position of the highest score until a cell of value zero is reached. This step is performed by the buildOptimalAlignment method, and its time complexity is linear on the size of the alignment.

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 local alignment problem, see the CrochemoreLandauZivUkelson algorithm. For global alignment, see the NeedlemanWunsch algorithm.

Author:

Sergio A. de Carvalho Jr.

See Also:

NeedlemanWunsch, CrochemoreLandauZivUkelson, CrochemoreLandauZivUkelsonLocalAlignment, CrochemoreLandauZivUkelsonGlobalAlignment

Field Summary

protected int[][]	matrix The dynamic programming matrix.
protected int	max_col Indicate the column of where an optimal local alignment can be found in the matrix.
protected int	max_row Indicate the row of where an optimal local alignment can be found in the matrix..
protected CharSequence	seq1 The first sequence of an alignment.
protected CharSequence	seq2 The second sequence of an alignment.

Fields inherited from class neobio.alignment.PairwiseAlignmentAlgorithm

alignment, APPROXIMATE_MATCH_TAG, GAP_CHARACTER, GAP_TAG, MATCH_TAG, MISMATCH_TAG, score, score_computed, scoring, sequences_loaded, use_match_tag

Constructor Summary

SmithWaterman()

Method Summary

protected PairwiseAlignment	buildOptimalAlignment() Builds an optimal local alignment between the loaded sequences.
protected void	computeMatrix() Computes the dynamic programming matrix.
protected PairwiseAlignment	computePairwiseAlignment() Builds an optimal local alignment between the loaded sequences after computing the dynamic programming matrix.
protected int	computeScore() Computes the score of the best local alignment between the two sequences using the scoring scheme previously set.
protected void	loadSequencesInternal(java.io.Reader input1, java.io.Reader input2) Loads sequences into CharSequence instances.
protected void	unloadSequencesInternal() Frees pointers to loaded sequences and the dynamic programming matrix so that their data can be garbage collected.

Methods inherited from class neobio.alignment.PairwiseAlignmentAlgorithm

getPairwiseAlignment, getScore, loadSequences, max, max, max, scoreDeletion, scoreInsertion, scoreSubstitution, setScoringScheme, unloadSequences, useMatchTag

Methods inherited from class java.lang.Object

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

Field Detail

seq1

protected CharSequence seq1

The first sequence of an alignment.

seq2

protected CharSequence seq2

The second sequence of an alignment.

matrix

protected int[][] matrix

The dynamic programming matrix. Each position (i, j) represents the best score between a suffic of the firsts i characters of seq1 and a suffix of the first j characters of seq2.

max_row

protected int max_row

Indicate the row of where an optimal local alignment can be found in the matrix..

max_col

protected int max_col

Indicate the column of where an optimal local alignment can be found in the matrix.

Constructor Detail

SmithWaterman

public SmithWaterman()

Method Detail

loadSequencesInternal

protected void loadSequencesInternal(java.io.Reader input1,
                                     java.io.Reader input2)
                              throws java.io.IOException,
                                     InvalidSequenceException

Loads sequences into CharSequence instances. In case of any error, an exception is raised by the constructor of CharSequence (please check the specification of that class for specific requirements).

Specified by:

loadSequencesInternal in class PairwiseAlignmentAlgorithm

Parameters:

input1 - Input for first sequence

input2 - Input for second sequence

Throws:

java.io.IOException - If an I/O error occurs when reading the sequences

InvalidSequenceException - If the sequences are not valid

See Also:

CharSequence

unloadSequencesInternal

protected void unloadSequencesInternal()

Frees pointers to loaded sequences and the dynamic programming matrix so that their data can be garbage collected.

Specified by:

unloadSequencesInternal in class PairwiseAlignmentAlgorithm

See Also:

PairwiseAlignmentAlgorithm.unloadSequences()

computePairwiseAlignment

protected PairwiseAlignment computePairwiseAlignment()
                                              throws IncompatibleScoringSchemeException

Builds an optimal local alignment between the loaded sequences after computing the dynamic programming matrix. It calls the buildOptimalAlignment method after the computeMatrix method computes the dynamic programming matrix.

Specified by:

computePairwiseAlignment in class PairwiseAlignmentAlgorithm

Returns:

an optimal pairwise alignment between the loaded sequences

Throws:

IncompatibleScoringSchemeException - If the scoring scheme is not compatible with the loaded sequences.

See Also:

computeMatrix(), buildOptimalAlignment()

computeMatrix

protected void computeMatrix()
                      throws IncompatibleScoringSchemeException

Computes the dynamic programming matrix.

Throws:

IncompatibleScoringSchemeException - If the scoring scheme is not compatible with the loaded sequences.

buildOptimalAlignment

protected PairwiseAlignment buildOptimalAlignment()
                                           throws IncompatibleScoringSchemeException

Builds an optimal local alignment between the loaded sequences. Before it is executed, the dynamic programming matrix must already have been computed by the computeMatrix method.

Returns:

an optimal local alignment between the loaded sequences

Throws:

IncompatibleScoringSchemeException - If the scoring scheme is not compatible with the loaded sequences.

See Also:

computeMatrix()

computeScore

protected int computeScore()
                    throws IncompatibleScoringSchemeException

Computes the score of the best local alignment between the two sequences using the scoring scheme previously set. This method calculates the similarity value only (doesn't build the whole matrix so the alignment cannot be recovered, however it has the advantage of requiring O(n) space only).

Specified by:

computeScore in class PairwiseAlignmentAlgorithm

Returns:

the score of the best local alignment between the loaded sequences

Throws:

IncompatibleScoringSchemeException - If the scoring scheme is not compatible with the loaded sequences.

See Also:

PairwiseAlignmentAlgorithm.getScore()