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

#include <ogdf/graphalg/NodeColoringHalldorsson.h>

Inheritance diagram for ogdf::NodeColoringHalldorsson:

Classes
struct	SearchWrapperHalldorsson
	Wraps the recursive Halldórsson algorithm. More...

Public Member Functions
	NodeColoringHalldorsson ()
	The constructor. More...

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

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

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

virtual	~NodeColoringModule ()
	Destructor. More...

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

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

Private Member Functions
bool	halldorssonRecursive (const Graph &graph, List< node > &independentSet, int k, double alpha)
	Performs the recursive Halldorsson algorithm to find large independent sets. More...

void	performHalldorsson (const Graph &graph, List< node > &independentSet)
	Performs the Halldorsson algorithm for finding an independent set. More...

Private Attributes
SearchProcedure	m_searchProcedure

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

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

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

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. More...

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. More...

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. More...

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

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

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

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

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

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

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. More...

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. More...

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. More...

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. More...

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. More...

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

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

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

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

Detailed Description

Approximation algorithms for the node coloring problem in graphs.

This class implements the approximation given by Halldorsson which colors the graph by finding independent sets.

Definition at line 43 of file NodeColoringHalldorsson.h.

Constructor & Destructor Documentation

◆ NodeColoringHalldorsson()

ogdf::NodeColoringHalldorsson::NodeColoringHalldorsson ( )

inline

The constructor.

Initializes the search procedure with the linear search by default.

Definition at line 49 of file NodeColoringHalldorsson.h.

Member Function Documentation

◆ call()

virtual NodeColor ogdf::NodeColoringHalldorsson::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.

◆ halldorssonRecursive()

bool ogdf::NodeColoringHalldorsson::halldorssonRecursive	(	const Graph &	graph,
		List< node > &	independentSet,
		int	k,
		double	alpha
	)

private

Performs the recursive Halldorsson algorithm to find large independent sets.

Parameters

graph	The input graph
independentSet	The resulting independent set
k	Value, such that the graph is k-colorable
alpha	Control parameter for the proximity

Returns: If the given proximity can be reached for the given k-value

◆ performHalldorsson()

void ogdf::NodeColoringHalldorsson::performHalldorsson	(	const Graph &	graph,
		List< node > &	independentSet
	)

private

Performs the Halldorsson algorithm for finding an independent set.

This functions calls the recursive algorithm with varying parameters such that the biggest possible independent set will be found.

Parameters

graph	The input graph
independentSet	The resulting independent set

◆ setSearchProcedure()

void ogdf::NodeColoringHalldorsson::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 56 of file NodeColoringHalldorsson.h.

Member Data Documentation

◆ m_searchProcedure

SearchProcedure ogdf::NodeColoringHalldorsson::m_searchProcedure

private

Definition at line 64 of file NodeColoringHalldorsson.h.

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

include/ogdf/graphalg/NodeColoringHalldorsson.h

OpenGraph DrawingFramework

Classes

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ NodeColoringHalldorsson()

Member Function Documentation

◆ call()

◆ halldorssonRecursive()

◆ performHalldorsson()

◆ setSearchProcedure()

Member Data Documentation

◆ m_searchProcedure

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