#include <GraphColoring.h>

Inherited by ColPack::GraphColoringInterface.

Collaboration diagram for ColPack::GraphColoring:

Public Member Functions
double **	GetSeedMatrix (int ip1_SeedRowCount, int ip1_SeedColumnCount)
	Return the Seed matrix based on existing coloring. This Seed matrix is managed and freed by ColPack.
double **	GetSeedMatrix_unmanaged (int ip1_SeedRowCount, int ip1_SeedColumnCount)
	Same as GetSeedMatrix(), except that this Seed matrix is NOT managed by ColPack.
int	CheckQuickDistanceTwoColoring (int Verbose=0)
	Quick check to see if DistanceTwoColoring() ran correctly.
int	CheckDistanceTwoColoring (int Verbose=0)
	Check to see if DistanceTwoColoring() ran correctly.
int	CalculateVertexColorClasses ()
void	SetStringVertexColoringVariant (string s)
	GraphColoring ()
	~GraphColoring ()
virtual void	Clear ()
int	DistanceOneColoring ()
int	DistanceTwoColoring ()
int	NaiveStarColoring ()
int	RestrictedStarColoring ()
int	StarColoring ()
int	StarColoring (vector< int > &, vector< int > &, map< int, map< int, int > > &)
int	CheckStarColoring ()
int	AcyclicColoring ()
int	AcyclicColoring (vector< int > &, map< int, vector< int > > &)
int	AcyclicColoring_ForIndirectRecovery ()
int	CheckAcyclicColoring ()
int	TriangularColoring ()
int	ModifiedTriangularColoring ()
int	CheckTriangularColoring ()
string	GetVertexColoringVariant ()
int	GetVertexColorCount ()
void	GetVertexColors (vector< int > &output)
int	GetHubCount ()
int	GetSetCount ()
double	GetVertexColoringTime ()
double	GetVertexColoringCheckingTime ()
int	PrintVertexColors ()
int	FileVertexColors ()
int	PrintVertexColoringMetrics ()
int	FileVertexColoringMetrics ()
void	PrintVertexColorClasses ()
Protected Member Functions
void	Seed_init ()
void	Seed_reset ()
Protected Attributes
int	m_i_VertexColorCount
int	m_i_LargestColorClass
int	m_i_SmallestColorClass
int	m_i_LargestColorClassSize
int	m_i_SmallestColorClassSize
double	m_d_AverageColorClassSize
double	m_d_ColoringTime
double	m_d_CheckingTime
string	m_s_VertexColoringVariant
vector< int >	m_vi_VertexColors
vector< int >	m_vi_VertexColorFrequency
bool	seed_available
int	i_seed_rowCount
double **	dp2_Seed
Private Member Functions
int	FindCycle (int, int, int, int, vector< int > &, vector< int > &, vector< int > &)
int	UpdateSet (int, int, int, map< int, map< int, int > > &, vector< int > &, vector< int > &, vector< int > &)
int	SearchDepthFirst (int, int, int, vector< int > &)
int	CheckVertexColoring (string s_GraphColoringVariant)
Private Attributes
int	m_i_ColoringUnits

Detailed Description

class GraphColoring in group1.

Graph coloring is an assignment of consecutive integral numbers (each representing a color) to vertices, edges or faces or a combination of two or more of these objects of a graph such that it satisfes one or more constraints. The present version of ColPack provides methods for vertex coloring only. The minimum number of vertex colors required to color a graph is known as the chromatic number of the graph. The problem of finding the chromatic number for even a planar graph is NP-hard. ColPack features some of the most efficient approximation algorithms available to date for some of the vertex coloring problems.

Definition at line 38 of file GraphColoring.h.

Constructor & Destructor Documentation

ColPack::GraphColoring::GraphColoring ( )

Definition at line 239 of file GraphColoring.cpp.

References Clear(), and Seed_init().

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ColPack::GraphColoring::~GraphColoring ( )

Definition at line 248 of file GraphColoring.cpp.

References Clear(), and Seed_reset().

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Member Function Documentation

int ColPack::GraphColoring::AcyclicColoring ( )

Note: This function can not be used for recovery!

Definition at line 1441 of file GraphColoring.cpp.

References _FALSE, _TRUE, _UNKNOWN, CheckVertexColoring(), ColPack::DisjointSets::Count(), ColPack::DisjointSets::FindAndCompress(), FindCycle(), ColPack::GraphCore::m_ds_DisjointSets, m_i_ColoringUnits, m_i_VertexColorCount, ColPack::GraphCore::m_mimi2_VertexEdgeMap, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, ColPack::DisjointSets::SetSize(), STEP_DOWN, STEP_UP, ColPack::DisjointSets::UnionBySize(), and UpdateSet().

Referenced by ColPack::GraphColoringInterface::AcyclicColoring(), and ColPack::GraphColoringInterface::Coloring().

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int ColPack::GraphColoring::AcyclicColoring	(	vector< int > &	vi_Sets,
		map< int, vector< int > > &	mivi_VertexSets
	)

Note: Originally created for Hessian Indirect Recovery

Definition at line 2464 of file GraphColoring.cpp.

References _FALSE, _TRUE, _UNKNOWN, CheckVertexColoring(), ColPack::DisjointSets::FindAndCompress(), FindCycle(), ColPack::GraphCore::m_ds_DisjointSets, m_i_VertexColorCount, m_s_VertexColoringVariant, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, ColPack::DisjointSets::SetSize(), STEP_DOWN, STEP_UP, ColPack::DisjointSets::UnionBySize(), and UpdateSet().

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int ColPack::GraphColoring::AcyclicColoring_ForIndirectRecovery ( )

Note: Currently used for Hessian Indirect Recovery

Definition at line 1952 of file GraphColoring.cpp.

References _FALSE, _TRUE, _UNKNOWN, CheckVertexColoring(), ColPack::DisjointSets::FindAndCompress(), FindCycle(), ColPack::GraphCore::m_ds_DisjointSets, m_i_VertexColorCount, ColPack::GraphCore::m_mimi2_VertexEdgeMap, m_s_VertexColoringVariant, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, ColPack::DisjointSets::SetSize(), STEP_DOWN, STEP_UP, ColPack::DisjointSets::UnionBySize(), and UpdateSet().

Referenced by ColPack::GraphColoringInterface::AcyclicColoring_ForIndirectRecovery(), and ColPack::GraphColoringInterface::Coloring().

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int ColPack::GraphColoring::CalculateVertexColorClasses ( )

Reimplemented in ColPack::GraphColoringInterface.

Definition at line 188 of file GraphColoring.cpp.

References _FALSE, _TRUE, _UNKNOWN, m_d_AverageColorClassSize, m_i_LargestColorClass, m_i_LargestColorClassSize, m_i_SmallestColorClass, m_i_SmallestColorClassSize, m_i_VertexColorCount, m_s_VertexColoringVariant, m_vi_VertexColorFrequency, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

Referenced by PrintVertexColorClasses().

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int ColPack::GraphColoring::CheckAcyclicColoring ( )

Definition at line 3019 of file GraphColoring.cpp.

References _FALSE, ColPack::GraphCore::m_vi_Vertices, SearchDepthFirst(), and STEP_DOWN.

Referenced by CheckTriangularColoring().

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int ColPack::GraphColoring::CheckDistanceTwoColoring ( int Verbose = 0 )

Check to see if DistanceTwoColoring() ran correctly.

100% accurate but slow. For a quick check, use CheckQuickDistanceTwoColoring().

Return value:

1 when this function detects that DistanceTwoColoring() must have run INcorrectly.
0 means DistanceTwoColoring() must have run correctly.

Precondition: DistanceTwoColoring() has been run.

Parameter: int Verbose

If Verbose == 0, this function will silently return after the first error is detected.
If Verbose == 1, this function will print out the error message and return after the first error is detected.
If Verbose == 2, this function will print out all the errors and then return.

Definition at line 4023 of file GraphColoring.cpp.

References ColPack::GraphCore::m_vi_Edges, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

int ColPack::GraphColoring::CheckQuickDistanceTwoColoring ( int Verbose = 0 )

Quick check to see if DistanceTwoColoring() ran correctly.

Return value:

1 when this function detects that DistanceTwoColoring() must have run INcorrectly.
0 otherwise

IMPORTANT: This is the quick check so if CheckQuickDistanceTwoColoring() return 1, then DistanceTwoColoring() definitely ran INcorrectly. However, when CheckQuickDistanceTwoColoring() return 0, it doesn't mean that DistanceTwoColoring() ran correctly (it may, it may not). To be 100% sure, use CheckDistanceTwoColoring()

Precondition: DistanceTwoColoring() has been run.

Parameter: int Verbose

If Verbose == 0, this function only check and see if m_i_MaximumVertexDegree <= m_i_VertexColorCount + 1.
If Verbose == 1, this function will print out the vertex with m_i_MaximumVertexDegree where the error can be detected.
If Verbose == 2, this function will print out all the errors (violations) and then return.

Algorithm:

See if m_i_MaximumVertexDegree <= STEP_UP(m_i_VertexColorCount). If DistanceTwoColoring() ran correctly, this should be the case
If m_i_MaximumVertexDegree > STEP_UP(m_i_VertexColorCount), DistanceTwoColoring() ran INcorrectly and this function will go ahead and find the 2 vertices within distance-2 have the same color

Definition at line 3984 of file GraphColoring.cpp.

References ColPack::GraphCore::m_i_MaximumVertexDegree, m_i_VertexColorCount, ColPack::GraphCore::m_vi_Edges, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

int ColPack::GraphColoring::CheckStarColoring ( )

Definition at line 1311 of file GraphColoring.cpp.

References _TRUE, ColPack::GraphCore::m_s_InputFile, ColPack::GraphCore::m_vi_Edges, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

int ColPack::GraphColoring::CheckTriangularColoring ( )

Definition at line 3290 of file GraphColoring.cpp.

References CheckAcyclicColoring().

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int ColPack::GraphColoring::CheckVertexColoring ( string s_GraphColoringVariant ) [private]

Definition at line 166 of file GraphColoring.cpp.

References _FALSE, _TRUE, m_s_VertexColoringVariant, ColPack::GraphOrdering::m_s_VertexOrderingVariant, and ColPack::GraphOrdering::NaturalOrdering().

Referenced by AcyclicColoring(), AcyclicColoring_ForIndirectRecovery(), DistanceTwoColoring(), GetHubCount(), GetSetCount(), ModifiedTriangularColoring(), NaiveStarColoring(), RestrictedStarColoring(), StarColoring(), and TriangularColoring().

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void ColPack::GraphColoring::Clear ( ) [virtual]

Reimplemented from ColPack::GraphOrdering.

Reimplemented in ColPack::GraphColoringInterface.

Definition at line 256 of file GraphColoring.cpp.

References m_d_AverageColorClassSize, m_d_CheckingTime, m_d_ColoringTime, m_i_ColoringUnits, m_i_LargestColorClass, m_i_LargestColorClassSize, m_i_SmallestColorClass, m_i_SmallestColorClassSize, m_i_VertexColorCount, m_s_VertexColoringVariant, m_vi_VertexColorFrequency, and m_vi_VertexColors.

Referenced by GraphColoring(), and ~GraphColoring().

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int ColPack::GraphColoring::DistanceOneColoring ( )

Definition at line 287 of file GraphColoring.cpp.

References _TRUE, _UNKNOWN, m_i_VertexColorCount, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

Referenced by ColPack::GraphColoringInterface::Coloring(), ColPack::GraphColoringInterface::DistanceOneColoring(), and TriangularColoring().

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int ColPack::GraphColoring::DistanceTwoColoring ( )

Definition at line 355 of file GraphColoring.cpp.

References _TRUE, _UNKNOWN, CheckVertexColoring(), m_i_VertexColorCount, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

Referenced by ColPack::GraphColoringInterface::Coloring(), and ColPack::GraphColoringInterface::DistanceTwoColoring().

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int ColPack::GraphColoring::FileVertexColoringMetrics ( )

Definition at line 3693 of file GraphColoring.cpp.

References _TRUE, ColPack::StringTokenizer::GetLastToken(), m_d_ColoringTime, ColPack::GraphOrdering::m_d_OrderingTime, m_i_ColoringUnits, m_i_VertexColorCount, ColPack::GraphCore::m_s_InputFile, m_s_VertexColoringVariant, ColPack::GraphOrdering::m_s_VertexOrderingVariant, ColPack::GraphCore::m_vi_Edges, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

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int ColPack::GraphColoring::FileVertexColors ( )

Definition at line 3441 of file GraphColoring.cpp.

References _TRUE, ColPack::StringTokenizer::GetLastToken(), m_d_ColoringTime, ColPack::GraphOrdering::m_d_OrderingTime, m_i_ColoringUnits, m_i_VertexColorCount, ColPack::GraphCore::m_s_InputFile, m_s_VertexColoringVariant, ColPack::GraphOrdering::m_s_VertexOrderingVariant, m_vi_VertexColors, and STEP_UP.

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int ColPack::GraphColoring::FindCycle	(	int	i_Vertex,
		int	i_AdjacentVertex,
		int	i_DistanceOneVertex,
		int	i_SetID,
		vector< int > &	vi_CandidateColors,
		vector< int > &	vi_FirstVisitedOne,
		vector< int > &	vi_FirstVisitedTwo
	)			`[private]`

Definition at line 28 of file GraphColoring.cpp.

References _TRUE, _UNKNOWN, m_vi_VertexColors, and STEP_UP.

Referenced by AcyclicColoring(), and AcyclicColoring_ForIndirectRecovery().

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int ColPack::GraphColoring::GetHubCount ( )

Definition at line 3318 of file GraphColoring.cpp.

References _UNKNOWN, CheckVertexColoring(), and m_i_ColoringUnits.

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double ** ColPack::GraphColoring::GetSeedMatrix	(	int *	ip1_SeedRowCount,
		int *	ip1_SeedColumnCount
	)

Return the Seed matrix based on existing coloring. This Seed matrix is managed and freed by ColPack.

Precondition:

the Graph has been colored

Postcondition:

Size of the returned matrix is (*ip1_SeedRowCount) rows x (*ip1_SeedColumnCount) columns. (*ip1_SeedRowCount) == num of columns of the original matrix == GetVertexCount() (*ip1_SeedColumnCount) == num of colors used to color vertices == GetVertexColorCount().

Notes:

This Seed matrix is managed and automatically freed by ColPack when the Graph object is deleted. Therefore, the user should NOT attempt to free the Seed matrix again.

Reimplemented in ColPack::GraphColoringInterface.

Definition at line 3914 of file GraphColoring.cpp.

References dp2_Seed, i_seed_rowCount, m_i_VertexColorCount, m_vi_VertexColors, seed_available, and Seed_reset().

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double ** ColPack::GraphColoring::GetSeedMatrix_unmanaged	(	int *	ip1_SeedRowCount,
		int *	ip1_SeedColumnCount
	)

Same as GetSeedMatrix(), except that this Seed matrix is NOT managed by ColPack.

Notes:

This Seed matrix is NOT managed by ColPack. Therefore, the user should free the Seed matrix manually when the matrix is no longer needed.

Definition at line 3943 of file GraphColoring.cpp.

References m_i_VertexColorCount, and m_vi_VertexColors.

Referenced by ColPack::GraphColoringInterface::GenerateSeedHessian_unmanaged().

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int ColPack::GraphColoring::GetSetCount ( )

Definition at line 3332 of file GraphColoring.cpp.

References _UNKNOWN, CheckVertexColoring(), and m_i_ColoringUnits.

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int ColPack::GraphColoring::GetVertexColorCount ( )

Definition at line 3304 of file GraphColoring.cpp.

References m_i_VertexColorCount, and STEP_UP.

Referenced by ColPack::HessianRecovery::DirectRecover_CoordinateFormat(), ColPack::HessianRecovery::DirectRecover_RowCompressedFormat(), ColPack::HessianRecovery::DirectRecover_SparseSolversFormat(), main(), toFileC(), and toFileC_forColoringBasedOrdering().

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double ColPack::GraphColoring::GetVertexColoringCheckingTime ( )

Definition at line 3351 of file GraphColoring.cpp.

References m_d_CheckingTime.

double ColPack::GraphColoring::GetVertexColoringTime ( )

Definition at line 3345 of file GraphColoring.cpp.

References m_d_ColoringTime.

Referenced by toFileC(), and toFileC_forColoringBasedOrdering().

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string ColPack::GraphColoring::GetVertexColoringVariant ( )

Definition at line 3297 of file GraphColoring.cpp.

References m_s_VertexColoringVariant.

void ColPack::GraphColoring::GetVertexColors ( vector< int > & output )

Definition at line 3311 of file GraphColoring.cpp.

References m_vi_VertexColors.

Referenced by ColPack::HessianRecovery::DirectRecover_CoordinateFormat(), ColPack::HessianRecovery::DirectRecover_RowCompressedFormat(), ColPack::HessianRecovery::DirectRecover_SparseSolversFormat(), ColPack::HessianRecovery::IndirectRecover_CoordinateFormat(), ColPack::HessianRecovery::IndirectRecover_RowCompressedFormat(), ColPack::HessianRecovery::IndirectRecover_SparseSolversFormat(), main(), and toFileC_forColoringBasedOrdering().

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int ColPack::GraphColoring::ModifiedTriangularColoring ( )

Definition at line 3197 of file GraphColoring.cpp.

References _TRUE, _UNKNOWN, CheckVertexColoring(), ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, and STEP_UP.

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int ColPack::GraphColoring::NaiveStarColoring ( )

Definition at line 439 of file GraphColoring.cpp.

References _TRUE, _UNKNOWN, CheckVertexColoring(), m_i_VertexColorCount, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

Referenced by ColPack::GraphColoringInterface::NaiveStarColoring().

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void ColPack::GraphColoring::PrintVertexColorClasses ( )

Definition at line 3878 of file GraphColoring.cpp.

References _TRUE, CalculateVertexColorClasses(), m_d_AverageColorClassSize, m_i_LargestColorClass, m_i_LargestColorClassSize, m_i_SmallestColorClass, m_i_SmallestColorClassSize, m_i_VertexColorCount, ColPack::GraphCore::m_s_InputFile, m_s_VertexColoringVariant, ColPack::GraphOrdering::m_s_VertexOrderingVariant, m_vi_VertexColorFrequency, and STEP_UP.

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int ColPack::GraphColoring::PrintVertexColoringMetrics ( )

Definition at line 3621 of file GraphColoring.cpp.

References _TRUE, m_d_ColoringTime, ColPack::GraphOrdering::m_d_OrderingTime, m_i_ColoringUnits, m_i_VertexColorCount, ColPack::GraphCore::m_s_InputFile, m_s_VertexColoringVariant, ColPack::GraphOrdering::m_s_VertexOrderingVariant, ColPack::GraphCore::m_vi_Edges, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

Referenced by main().

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int ColPack::GraphColoring::PrintVertexColors ( )

Definition at line 3357 of file GraphColoring.cpp.

References _TRUE, ColPack::StringTokenizer::GetLastToken(), m_d_ColoringTime, ColPack::GraphOrdering::m_d_OrderingTime, m_i_ColoringUnits, m_i_VertexColorCount, ColPack::GraphCore::m_s_InputFile, m_s_VertexColoringVariant, ColPack::GraphOrdering::m_s_VertexOrderingVariant, m_vi_VertexColors, and STEP_UP.

Referenced by main().

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int ColPack::GraphColoring::RestrictedStarColoring ( )

Definition at line 544 of file GraphColoring.cpp.

References _TRUE, _UNKNOWN, CheckVertexColoring(), m_i_VertexColorCount, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

Referenced by ColPack::GraphColoringInterface::Coloring(), and ColPack::GraphColoringInterface::RestrictedStarColoring().

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int ColPack::GraphColoring::SearchDepthFirst	(	int	i_RootVertex,
		int	i_ParentVertex,
		int	i_Vertex,
		vector< int > &	vi_TouchedVertices
	)			`[private]`

Definition at line 96 of file GraphColoring.cpp.

References _TRUE, ColPack::GraphCore::m_s_InputFile, ColPack::GraphCore::m_vi_Edges, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

Referenced by CheckAcyclicColoring().

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void ColPack::GraphColoring::Seed_init ( ) [protected]

Definition at line 3966 of file GraphColoring.cpp.

References dp2_Seed, i_seed_rowCount, and seed_available.

Referenced by GraphColoring().

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void ColPack::GraphColoring::Seed_reset ( ) [protected]

Definition at line 3973 of file GraphColoring.cpp.

References dp2_Seed, free_2DMatrix(), i_seed_rowCount, and seed_available.

Referenced by GetSeedMatrix(), ~GraphColoring(), and ColPack::GraphColoringInterface::~GraphColoringInterface().

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void ColPack::GraphColoring::SetStringVertexColoringVariant ( string s )

Definition at line 4063 of file GraphColoring.cpp.

References m_s_VertexColoringVariant.

Referenced by toFileC_forColoringBasedOrdering().

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int ColPack::GraphColoring::StarColoring	(	vector< int > &	vi_StarHubMap,
		vector< int > &	vi_EdgeStarMap,
		map< int, map< int, int > > &	mimi2_VertexEdgeMap
	)

Definition at line 978 of file GraphColoring.cpp.

References _FALSE, _TRUE, _UNKNOWN, m_i_ColoringUnits, m_i_VertexColorCount, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

int ColPack::GraphColoring::StarColoring ( )

Definition at line 633 of file GraphColoring.cpp.

References _TRUE, _UNKNOWN, CheckVertexColoring(), m_i_VertexColorCount, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, m_vi_VertexColors, ColPack::GraphCore::m_vi_Vertices, STEP_DOWN, and STEP_UP.

Referenced by ColPack::GraphColoringInterface::Coloring(), and ColPack::GraphColoringInterface::StarColoring().

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int ColPack::GraphColoring::TriangularColoring ( )

Definition at line 3055 of file GraphColoring.cpp.

References _FALSE, _TRUE, CheckVertexColoring(), DistanceOneColoring(), m_i_VertexColorCount, ColPack::GraphCore::m_vi_Edges, ColPack::GraphOrdering::m_vi_OrderedVertices, ColPack::GraphCore::m_vi_Vertices, ColPack::GraphOrdering::SmallestLastOrdering(), STEP_DOWN, and STEP_UP.

Referenced by ColPack::GraphColoringInterface::TriangularColoring().

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int ColPack::GraphColoring::UpdateSet	(	int	i_Vertex,
		int	i_AdjacentVertex,
		int	i_DistanceOneVertex,
		map< int, map< int, int > > &	mimi2_VertexEdgeMap,
		vector< int > &	vi_FirstSeenOne,
		vector< int > &	vi_FirstSeenTwo,
		vector< int > &	vi_FirstSeenThree
	)			`[private]`