Module org.cicirello.jpt

Package org.cicirello.permutations.distance

Class ReversalDistance

java.lang.Object

org.cicirello.permutations.distance.ReversalDistance

All Implemented Interfaces:

NormalizedPermutationDistanceMeasurer, NormalizedPermutationDistanceMeasurerDouble, PermutationDistanceMeasurer, PermutationDistanceMeasurerDouble

public final class ReversalDistance
extends Object
implements NormalizedPermutationDistanceMeasurer

Reversal Distance is the minimum number of subpermutation reversals necessary to transform one permutation into the other. This is an NP-Hard problem.

Our original motivation for implementing this required computing reversal distance from a target permutation for all permutations of that target. Therefore, we were going to exhaust all N! permutations of an N element list regardless of how we computed this.

Therefore, the approach taken in this implementation is to compute a lookup table with N! elements, one for each of the N! possible permutations. The lookup table maps permutations to distances. The distances are computed using a breadth first enumeration outward from the permutation [0, 1, ..., (N-1)]. The starting permutation is distance 0 from itself. The N*(N-1)/2 permutations that are derived by reversing a subpermutation are a distance of 1 from the initial permutation. And we continue in this manner, computing all that are a distance of 2, and then 3, etc.

The total cost of this is: O(N! * N^3) since each permutation has N^2 neighbors, generating a neighbor is linear cost, and there are N! permutations. Since our original application required computing distance for all N! permutations, the amortized cost (if your application also has that requirement) of computing distance is O(N^3).

We have not used this for N > 10. Warning: time to construct distance measure increases factorially.

Constructor Summary

Constructors

Constructor	Description
ReversalDistance()	Construct the distance measure.
ReversalDistance(int n)	Defines a distance measure for permutations of length n.

Method Summary

Modifier and Type	Method	Description
int	distance(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.

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.cicirello.permutations.distance.NormalizedPermutationDistanceMeasurer

maxf, normalizedDistance

Methods inherited from interface org.cicirello.permutations.distance.PermutationDistanceMeasurer

distancef

Constructor Details

ReversalDistance

public ReversalDistance()

Construct the distance measure. Default handles permutations of length n=5.

ReversalDistance

public ReversalDistance(int n)

Defines a distance measure for permutations of length n. n must be no greater than 12.

Parameters:

n - The length of the permutations supported.

Throws:

IllegalArgumentException - when n is greater than 12

Method Details

distance

public int distance(Permutation p1,
 Permutation p2)

Measures the distance between two permutations.

Specified by:

distance in interface PermutationDistanceMeasurer

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2

Throws:

IllegalArgumentException - if p1.length() is not equal to p2.length().

IllegalArgumentException - if length of the permutations is not equal to the the permutation length for which this was configured at time of construction.

max

public int max(int length)

Description copied from interface: NormalizedPermutationDistanceMeasurer

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

Specified by:

max in interface NormalizedPermutationDistanceMeasurer

Parameters:

length - Permutation length.

Returns:

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