Approximation algorithms for the node coloring problem in graphs. More...

#include <ogdf/graphalg/NodeColoringBergerRompel.h>

Inheritance diagram for ogdf::NodeColoringBergerRompel:

Classes
struct	SearchWrapperBergerRompel
	Wraps the parameterized Berger&Rompel algorithm. More...

Public Types
enum class	BruteForceProcedure { trivialColoring , sequentialColoringSimple , sequentialColoringDegree , johnsonColoring , wigdersonColoring , pooled }
	Declares the procedure dealing with the brute force coloring. More...

Public Types inherited from ogdf::NodeColoringModule
using	NodeColor = unsigned int
	Data type of the node colors.

enum class	RamseyProcedure { smallestIndex , smallestDegree , largestDegree , extremalDegree }
	Declares the procedure of finding nodes in Ramsey's algorithm. More...

enum class	SearchProcedure { linearSearch , binarySearch , wigdersonSearch }
	Declares the search procedures. More...

Public Member Functions
	NodeColoringBergerRompel ()
	The constructor.

virtual NodeColor	call (const Graph &graph, NodeArray< NodeColor > &colors, NodeColor start=0) override
	The actual algorithm call.

void	setAlpha (double alpha)
	Sets the parameter alpha which controls the accuracy of the algorithm.

void	setBruteForceProcedure (BruteForceProcedure bruteForceProcedure)
	Sets the brute force procedure.

void	setSearchProcedure (SearchProcedure searchProcedure)
	Sets the search procedure to find the smallest possible parameter k such as the graph is k-colorable.

Public Member Functions inherited from ogdf::NodeColoringModule
	NodeColoringModule ()
	Default constructor.

virtual	~NodeColoringModule ()
	Destructor.

virtual bool	checkColoring (const Graph &graph, const NodeArray< NodeColor > &colors) const
	Checks if the given node coloring is valid.

virtual void	preprocessGraph (Graph &graph) const
	Preprocesses a graph so that a coloring algorithm can be applied.

Private Member Functions
bool	bergerRompelParameterized (const Graph &graph, NodeArray< NodeColor > &colors, NodeColor &color, int k, double alpha)

Private Attributes
double	m_alpha

BruteForceProcedure	m_bruteForceProcedure

NodeColoringJohnson	m_johnsonColoring

SearchProcedure	m_searchProcedure

NodeColoringSequential	m_sequentialColoring

NodeColoringSimple	m_simpleColoring

NodeColoringWigderson	m_wigdersonColoring

Additional Inherited Members
Protected Member Functions inherited from ogdf::NodeColoringModule
template<class CONTAINER >
bool	checkIndependentSet (const Graph &graph, const CONTAINER &nodes) const
	Checks if subgraph induced by the given nodes forms an independent set.

virtual void	cliqueRemoval (const Graph &graph, List< node > &independentSet) const
	Applies the clique removal algorithm for finding a large independent set in a given graph.

virtual void	createBuckets (const Graph &graph, int size, Array< Array< node > > &buckets) const
	Creates a partitioning of the node set into buckets of a given size.

virtual int	getMaximumDegreeNode (const Graph &graph, node &maxDegreeNode) const
	Searches for a maximum degree node in the graph.

virtual int	getMaximumDegreeNodes (const Graph &graph, List< node > &maxDegreeNodes) const
	Searches for all nodes with maximum degree in the graph.

virtual NodeColor	getMaximumNodeColor (NodeArray< NodeColor > &colors)
	Calculates the maximum node color index used in a certain node coloring.

virtual int	getMinimumDegreeNode (const Graph &graph, node &minDegreeNode) const
	Searches for a minimum degree node in the graph.

virtual int	getMinimumDegreeNodes (const Graph &graph, List< node > &minDegreeNodes) const
	Searches for all nodes with minimum degree in the graph.

int	getNeighborDegrees (const node &v) const
	Calculates the sum of neighbor nodes degrees for a given node v.

template<class LISTITERATOR >
void	getNeighbors (const Graph &graph, LISTITERATOR nodes, List< node > &neighbors) const
	Calculates the set of neighbors Y for a given set of nodes X.

template<class LISTITERATOR >
void	getNeighborsComplement (const Graph &graph, LISTITERATOR nodes, List< node > &complementNeighbors) const
	Calculates the set of complement neighbors Y for a given set of nodes X.

template<class LISTITERATOR >
void	mergeNodeLists (const Graph &graph, LISTITERATOR firstList, LISTITERATOR secondList, List< node > &mergedList) const
	Merges two lists of nodes and deletes the duplicates.

virtual void	ramseyAlgorithm (const Graph &graph, List< node > &clique, List< node > &independentSet) const
	Performs the Ramsey algorithm for finding heuristically large cliques and independents sets in a graph.

virtual void	reverseNodeTable (const Graph &graphOrig, const Graph &graphNew, const NodeArray< node > &orig2New, NodeArray< node > &new2Orig) const
	Reverses the mapping between the nodes sets of a graph and a subgraph.

int	searchBinary (SearchWrapper *searchWrapper, int start, int end) const
	Performs a binary search in a specified range with a given oracle.

int	searchLinear (SearchWrapper *searchWrapper, int start, int end) const
	Performs a linear search in a specified range with a given oracle.

int	searchWigderson (SearchWrapper *searchWrapper) const
	Performs a the search procedure specified by Wigderson.

Protected Attributes inherited from ogdf::NodeColoringModule
RamseyProcedure	m_ramseyProcedure
	The RamseyProcedure to be used to select nodes.

Detailed Description

Approximation algorithms for the node coloring problem in graphs.

This class implements the approximation given by Berger&Rompel which colors the graph by finding independent sets.

Definition at line 49 of file NodeColoringBergerRompel.h.

Member Enumeration Documentation

◆ BruteForceProcedure

enum class ogdf::NodeColoringBergerRompel::BruteForceProcedure

strong

Declares the procedure dealing with the brute force coloring.

Enumerator
trivialColoring	Uses trivial coloring, i.e. colors each node with a different color.
sequentialColoringSimple	Uses sequential coloring with the trivial node permutation.
sequentialColoringDegree	Uses sequential coloring with the nodes sorted decreasing by their degree.
johnsonColoring	Uses Johnson's coloring algorithm.
wigdersonColoring	Uses Wigderson's coloring algorithm.
pooled	Pools all nodes from the recursion anchor and then applies sequential coloring.

Definition at line 54 of file NodeColoringBergerRompel.h.

Constructor & Destructor Documentation

◆ NodeColoringBergerRompel()

ogdf::NodeColoringBergerRompel::NodeColoringBergerRompel ( )

inline

The constructor.

Initializes the search procedure with the binary-search by default. The parameter alpha is initialized with 1.0 by default.

Definition at line 68 of file NodeColoringBergerRompel.h.

Member Function Documentation

◆ bergerRompelParameterized()

bool ogdf::NodeColoringBergerRompel::bergerRompelParameterized	(	const Graph &	graph,
		NodeArray< NodeColor > &	colors,
		NodeColor &	color,
		int	k,
		double	alpha
	)

private

◆ call()

virtual NodeColor ogdf::NodeColoringBergerRompel::call	(	const Graph &	graph,
		NodeArray< NodeColor > &	colors,
		NodeColor	start = `0`
	)

overridevirtual

The actual algorithm call.

Parameters

graph	The graph for which the node coloring will be calculated.
colors	The resulting node coloring.
start	The first color index which will be used.

Returns: The number of colors used by the node coloring.

Implements ogdf::NodeColoringModule.

◆ setAlpha()

void ogdf::NodeColoringBergerRompel::setAlpha ( double alpha )

inline

Sets the parameter alpha which controls the accuracy of the algorithm.

A higher value of alpha results in a better approximation ratio. Also, the running time increases with alpha.

Parameters

alpha The control parameter alpha

Definition at line 100 of file NodeColoringBergerRompel.h.

◆ setBruteForceProcedure()

void ogdf::NodeColoringBergerRompel::setBruteForceProcedure ( BruteForceProcedure bruteForceProcedure )

inline

Sets the brute force procedure.

Parameters

bruteForceProcedure The desired brute force coloring procedure

Definition at line 90 of file NodeColoringBergerRompel.h.

◆ setSearchProcedure()

void ogdf::NodeColoringBergerRompel::setSearchProcedure ( SearchProcedure searchProcedure )

inline

Sets the search procedure to find the smallest possible parameter k such as the graph is k-colorable.

Parameters

searchProcedure The desired search procedure

Definition at line 82 of file NodeColoringBergerRompel.h.

Member Data Documentation

◆ m_alpha

double ogdf::NodeColoringBergerRompel::m_alpha

private

Definition at line 115 of file NodeColoringBergerRompel.h.

◆ m_bruteForceProcedure

BruteForceProcedure ogdf::NodeColoringBergerRompel::m_bruteForceProcedure

private

Definition at line 114 of file NodeColoringBergerRompel.h.

◆ m_johnsonColoring

NodeColoringJohnson ogdf::NodeColoringBergerRompel::m_johnsonColoring

private

Definition at line 111 of file NodeColoringBergerRompel.h.

◆ m_searchProcedure

SearchProcedure ogdf::NodeColoringBergerRompel::m_searchProcedure

private

Definition at line 113 of file NodeColoringBergerRompel.h.

◆ m_sequentialColoring

NodeColoringSequential ogdf::NodeColoringBergerRompel::m_sequentialColoring

private

Definition at line 110 of file NodeColoringBergerRompel.h.

◆ m_simpleColoring

NodeColoringSimple ogdf::NodeColoringBergerRompel::m_simpleColoring

private

Definition at line 109 of file NodeColoringBergerRompel.h.

◆ m_wigdersonColoring

NodeColoringWigderson ogdf::NodeColoringBergerRompel::m_wigdersonColoring

private

Definition at line 112 of file NodeColoringBergerRompel.h.

The documentation for this class was generated from the following file:

include/ogdf/graphalg/NodeColoringBergerRompel.h

OpenGraph DrawingFramework

Classes

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ BruteForceProcedure

Constructor & Destructor Documentation

◆ NodeColoringBergerRompel()

Member Function Documentation

◆ bergerRompelParameterized()

◆ call()

◆ setAlpha()

◆ setBruteForceProcedure()

◆ setSearchProcedure()

Member Data Documentation

◆ m_alpha

◆ m_bruteForceProcedure

◆ m_johnsonColoring

◆ m_searchProcedure

◆ m_sequentialColoring

◆ m_simpleColoring

◆ m_wigdersonColoring

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Graph Drawing
Framework