net.maizegenetics.analysis.gbs.neobio

Class Smawk

java.lang.Object

net.maizegenetics.analysis.gbs.neobio.Smawk

public class Smawk
extends Object

This class implement the SMAWK algorithm to compute column maxima on a totally monotone matrix as described.

This implementation derives from the paper of A.Aggarwal, M.Klawe, S.Moran, P.Shor, and R.Wilber, Geometric Applications of a Matrix Searching Algorithm, Algorithmica, 2, 195-208 (1987).

The matrix must be an object that implements the Matrix interface. It is also expected to be totally monotone, and the number of rows should be greater than or equals to the number of columns. If these conditions are not met, the the result is unpredictable and can lead to an ArrayIndexOutOfBoundsException.

computeColumnMaxima is the main public method of this class. It computes the column maxima of a given matrix, i.e. the rows that contain the maximum value of each column in O(n) (linear) time, where n is the number of rows. This method does not return the maximum values itself, but just the indexes of their rows.

Note that it is necessary to create an instance of this class to execute the computeColumnMaxima because it stores temporary data is that instance. To prevent problems with concurrent access, the computeColumnMaxima method is declared synchronized.

 // create an instance of Smawk
 Smawk smawk = new Smawk();

 // create an array to store the result
 int col_maxima = new int [some_matrix.numColumns()];

 // now compute column maxima
 smawk.computeColumnMaxima (some_matrix, col_maxima)
 

Note that the array of column maxima indexes (the computation result) must be created beforehand and its size must be equal to the number of columns of the matrix.

This implementation creates arrays of row and column indexes from the original array and simulates all operations (reducing, deletion of odd columns, etc.) by manipulating these arrays. The benefit is two-fold. First the matrix is not required to implement any of these this operations but only a simple method to retrieve a value at a given position. Moreover, it tends to be faster since it uses a manipulation of these small vectors and no row or column is actually deleted. The downside is, of course, the use of extra memory (in practice, however, this is negligible).

Note that this class does not contain a computeRowMaxima method, however, the computeColumnMaxima can easily be used to compute row maxima by using a transposed matrix interface, i.e. one that inverts the indexes of the valueAt method (returning [col,row] when [row,col] is requested) and swaps the number of rows by the number of columns, and vice-versa.

Another simpler method, naiveComputeColumnMaxima, does the same job without using the SMAWK algorithm. It takes advantage of the monotone property of the matrix only (SMAWK explores the stronger constraint of total monotonicity), and therefore has a worst case time complexity of O(n * m), where n is the number of rows and m is the number of columns. However, this method tends to be faster for small matrices because it avoids recursions and row and column manipulations. There is also a naiveComputeRowMaxima method to compute row maxima with the naive approach.

Author:

Sergio A. de Carvalho Jr.

See Also:

Matrix

Constructor Summary

Constructors

Constructor and Description
Smawk()

Method Summary

Modifier and Type	Method and Description
void	computeColumnMaxima(Matrix matrix, int[] col_maxima) Computes the column maxima of a given matrix.
static void	naiveComputeColumnMaxima(Matrix matrix, int[] col_maxima) This is a simpler method for calculating column maxima.
static void	naiveComputeRowMaxima(Matrix matrix, int[] row_maxima) This is a simpler method for calculating row maxima.
static void	printMatrix(Matrix matrix) Prints the contents of an object implementing the matrix interface in the standard output.

Methods inherited from class java.lang.Object

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

Constructor Detail

Smawk

public Smawk()

Method Detail

computeColumnMaxima

public void computeColumnMaxima(Matrix matrix,
                                int[] col_maxima)

Computes the column maxima of a given matrix. It first sets up arrays of row and column indexes to simulate a copy of the matrix (where all operations will be performed). It then calls the recursive protected computeColumnMaxima method.

The matrix is required to be an object that implements the Matrix interface. It is also expected to be totally monotone, and the number of rows should be greater than or equals to the number of columns. If it is not, the the result is unpredictable and can lead to an ArrayIndexOutOfBoundsException.

This method does not return the maximum values itself, but just the indexes of their rows. Note that the array of column maxima (the computation result) must be created beforehand and its size must be equal to the number of columns of the matrix.

To prevent problems with concurrent access, this method is declared synchronized.

Parameters:

matrix - the matrix that will have its column maxima computed

col_maxima - the array of column maxima (indexes of the rows containing maximum values of each column); this is the computation result

See Also:

computeColumnMaxima(int[])

naiveComputeColumnMaxima

public static void naiveComputeColumnMaxima(Matrix matrix,
                                            int[] col_maxima)

This is a simpler method for calculating column maxima. It does the same job as computeColumnMaxima, but without complexity of the SMAWK algorithm.

The matrix is required to be an object that implements the Matrix interface. It is also expected to be monotone. If it is not, the result is unpredictable but, unlike computeColumnMaxima, it cannot lead to an ArrayIndexOutOfBoundsException.

This method does not return the maximum values itself, but just the indexes of their rows. Note that the array of column maxima (the computation result) must be created beforehand and its size must be equal to the number of columns of the matrix.

It takes advantage of the monotone property of the matrix only (SMAWK explores the stronger constraint of total monotonicity), and therefore has a worst case time complexity of O(n * m), where n is the number of rows and m is the number of columns. However, this method tends to be faster for small matrices because it avoids recursions and row and column manipulations.

Parameters:

matrix - the matrix that will have its column maxima computed

col_maxima - the array of column maxima (indexes of the rows containing maximum values of each column); this is the computation result

See Also:

naiveComputeRowMaxima(net.maizegenetics.analysis.gbs.neobio.Matrix, int[])

naiveComputeRowMaxima

public static void naiveComputeRowMaxima(Matrix matrix,
                                         int[] row_maxima)

This is a simpler method for calculating row maxima. It does not use the SMAWK algorithm.

The matrix is required to be an object that implements the Matrix interface. It is also expected to be monotone. If it is not, the result is unpredictable but, unlike computeColumnMaxima, it cannot lead to an ArrayIndexOutOfBoundsException.

This method does not return the maximum values itself, but just the indexes of their columns. Note that the array of row maxima (the computation result) must be created beforehand and its size must be equal to the number of columns of the matrix.

It takes advantage of the monotone property of the matrix only (SMAWK explores the stronger constraint of total monotonicity), and therefore has a worst case time complexity of O(n * m), where n is the number of rows and m is the number of columns. However, this method tends to be faster for small matrices because it avoids recursions and row and column manipulations.

Parameters:

matrix - the matrix that will have its row maxima computed

row_maxima - the array of row maxima (indexes of the columns containing maximum values of each row); this is the computation result

See Also:

naiveComputeColumnMaxima(net.maizegenetics.analysis.gbs.neobio.Matrix, int[])

printMatrix

public static void printMatrix(Matrix matrix)

Prints the contents of an object implementing the matrix interface in the standard output. It can be used for debugging.

Parameters:

matrix - a matrix