org.cicirello.permutations.distance

Class InterchangeDistance

java.lang.Object

org.cicirello.permutations.distance.InterchangeDistance

All Implemented Interfaces:

NormalizedPermutationDistanceMeasurer, NormalizedPermutationDistanceMeasurerDouble, PermutationDistanceMeasurer, PermutationDistanceMeasurerDouble

public final class InterchangeDistance
extends Object

Interchange Distance:

Interchange distance is the minimum number of swaps necessary to transform one permutation into the other.

Interchange distance is computed efficiently by counting the number of permutation cycles between the permutations. A permutation cycle of length k is transformed into k fixed points with k − 1 swaps (a fixed point is a cycle of length 1).

Runtime: O(n), where n is the permutation length.

Computing Interchange distance using cycle lengths is described in:
V.A. Cicirello, "The Permutation in a Haystack Problem and the Calculus of Search Landscapes," IEEE Transactions on Evolutionary Computation, 20(3):434-446, June 2016.

Since:

1.0

Constructor Summary

Constructors

Constructor and Description
InterchangeDistance() Constructs the distance measurer as specified in the class documentation.

Method Summary

Modifier and Type	Method and Description
int	distance(Permutation p1, Permutation p2) Measures the distance between two permutations.
double	distancef(Permutation p1, Permutation p2) Measures the distance between two permutations
int	max(int length) Computes the maximum possible distance between permutations of a specified length.
double	maxf(int length) Computes the maximum possible distance between permutations of a specified length.
double	normalizedDistance(Permutation p1, Permutation p2) Measures the distance between two permutations, normalized to the interval [0.0, 1.0].

Methods inherited from class java.lang.Object

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

Constructor Detail

InterchangeDistance

public InterchangeDistance()

Constructs the distance measurer as specified in the class documentation.

Method Detail

distance

public int distance(Permutation p1,
                    Permutation p2)

Measures the distance between two permutations.

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2

max

public int max(int length)

Computes the maximum possible distance between permutations of a specified length.

Parameters:

length - Permutation length.

Returns:

the maximum distance between a pair of permutations of the specified length.

distancef

public final double distancef(Permutation p1,
                              Permutation p2)

Measures the distance between two permutations

Specified by:

distancef in interface PermutationDistanceMeasurerDouble

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2

maxf

public final double maxf(int length)

Computes the maximum possible distance between permutations of a specified length.

Specified by:

maxf in interface NormalizedPermutationDistanceMeasurerDouble

Parameters:

length - Permutation length.

Returns:

the maximum distance between a pair of permutations of the specified length.

normalizedDistance

public final double normalizedDistance(Permutation p1,
                                       Permutation p2)

Measures the distance between two permutations, normalized to the interval [0.0, 1.0].

Specified by:

normalizedDistance in interface NormalizedPermutationDistanceMeasurerDouble

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2 normalized to the interval [0.0, 1.0]