Module org.jgrapht.core

Package org.jgrapht.alg.color

Class ChordalGraphColoring<V,E>

java.lang.Object

org.jgrapht.alg.color.ChordalGraphColoring<V,E>

Type Parameters:

V - the graph vertex type.

E - the graph edge type.

All Implemented Interfaces:

VertexColoringAlgorithm<V>

public class ChordalGraphColoring<V,E>
extends Object
implements VertexColoringAlgorithm<V>

Calculates a minimum vertex coloring for a chordal graph. A chordal graph is a simple graph in which all cycles of four or more vertices have a chord. A chord is an edge that is not part of the cycle but connects two vertices of the cycle. To compute the vertex coloring, this implementation relies on the ChordalityInspector to compute a perfect elimination order. The vertex coloring for a chordal graph is computed in $\mathcal{O}(|V| + |E|)$ time. All the methods in this class are invoked in a lazy fashion, meaning that computations are only started once the method gets invoked.

Nested Class Summary

Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.VertexColoringAlgorithm

VertexColoringAlgorithm.Coloring<V>, VertexColoringAlgorithm.ColoringImpl<V>

Field Summary

Fields

Modifier and Type	Field	Description
private final ChordalityInspector<V,E>	chordalityInspector
private VertexColoringAlgorithm.Coloring<V>	coloring
private final Graph<V,E>	graph

Constructor Summary

Constructors

Constructor	Description
ChordalGraphColoring(Graph<V,E> graph)	Creates a new ChordalGraphColoring instance.
ChordalGraphColoring(Graph<V,E> graph, ChordalityInspector.IterationOrder iterationOrder)	Creates a new ChordalGraphColoring instance.

Method Summary

Modifier and Type	Method	Description
VertexColoringAlgorithm.Coloring<V>	getColoring()	Returns a minimum vertex coloring of the inspected graph.
List<V>	getPerfectEliminationOrder()	Returns the perfect elimination order used to create the coloring (if one exists).
private Set<V>	getPredecessors(Map<V,Integer> vertexInOrder, V vertex)	Returns the predecessors of vertex in the order defined by map.
private Map<V,Integer>	getVertexInOrder(List<V> vertexOrder)	Returns a map containing vertices from the vertexOrder mapped to their indices in vertexOrder.
private void	lazyComputeColoring()	Lazily computes the coloring of the graph.

Methods inherited from class java.lang.Object

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

Field Details

graph

private final Graph<V,E> graph

chordalityInspector

private final ChordalityInspector<V,E> chordalityInspector

coloring

private VertexColoringAlgorithm.Coloring<V> coloring

Constructor Details

ChordalGraphColoring

public ChordalGraphColoring(Graph<V,E> graph)

Creates a new ChordalGraphColoring instance. The ChordalityInspector used in this implementation uses the default MaximumCardinalityIterator iterator.

Parameters:

graph - graph

ChordalGraphColoring

public ChordalGraphColoring(Graph<V,E> graph,
 ChordalityInspector.IterationOrder iterationOrder)

Creates a new ChordalGraphColoring instance. The ChordalityInspector used in this implementation uses either the MaximumCardinalityIterator iterator or the LexBreadthFirstIterator iterator, depending on the parameter iterationOrder.

Parameters:

graph - graph

iterationOrder - constant which defines iterator to be used by the ChordalityInspector in this implementation.

Method Details

lazyComputeColoring

private void lazyComputeColoring()

Lazily computes the coloring of the graph.

getVertexInOrder

private Map<V,Integer> getVertexInOrder(List<V> vertexOrder)

Returns a map containing vertices from the vertexOrder mapped to their indices in vertexOrder.

Parameters:

vertexOrder - a list with vertices.

Returns:

a mapping of vertices from vertexOrder to their indices in vertexOrder.

getPredecessors

private Set<V> getPredecessors(Map<V,Integer> vertexInOrder,
 V vertex)

Returns the predecessors of vertex in the order defined by map. More precisely, returns those of vertex, whose mapped index in map is less then the index of vertex.

Parameters:

vertexInOrder - defines the mapping of vertices in graph to their indices in order.

vertex - the vertex whose predecessors in order are to be returned.

Returns:

the predecessors of vertex in order defines by map.

getColoring

public VertexColoringAlgorithm.Coloring<V> getColoring()

Returns a minimum vertex coloring of the inspected graph. If the graph isn't chordal, returns null. The number of colors used in the coloring equals the chromatic number of the input graph.

Specified by:

getColoring in interface VertexColoringAlgorithm<V>

Returns:

a coloring of the graph if it is chordal, null otherwise.

getPerfectEliminationOrder

public List<V> getPerfectEliminationOrder()

Returns the perfect elimination order used to create the coloring (if one exists). This method returns null if the graph is not chordal.

Returns:

the perfect elimination order used to create the coloring, or null if graph is not chordal.