This file contains the algorithm for listing all cliques according to the algorithm of Tomita et al. (TCS 2006). More...

#include <limits.h>
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include "misc.h"
#include "LinkedList.h"
#include "MemoryManager.h"
#include "tomita_algorithm.h"

Functions
long	listAllMaximalCliquesMatrix (char *adjacencyMatrix, LinkedList cliques, int numVertices)
	List all maximal cliques in a given graph using the algorithm by Tomita et al. (TCS 2006).
int	findBestPivotNonNeighborsMatrix (int *pivotNonNeighbors, int numNonNeighbors, char *adjacencyMatrix, int vertexSets, int *vertexLookup, int size, int beginX, int beginP, int beginR)
	Computes the vertex v in P union X that has the most neighbors in P, and places P \ {neighborhood of v} in an array. These are the vertices to consider adding to the partial clique during the current recursive call of the algorithm.
void	moveToRMatrix (int vertex, int vertexSets, int vertexLookup, char *adjacencyMatrix, int pBeginX, int pBeginP, int pBeginR, int pNewBeginX, int pNewBeginP, int *pNewBeginR)
	Move a vertex to the set R, and update the sets P and X.
void	moveFromRToXMatrix (int vertex, int vertexSets, int vertexLookup, int pBeginX, int pBeginP, int *pBeginR)
	Move a vertex from the set R to the set X, and update all necessary pointers and arrays of neighbors in P.
void	listAllMaximalCliquesMatrixRecursive (long cliqueCount, LinkedList cliques, LinkedList partialClique, char adjacencyMatrix, int vertexSets, int *vertexLookup, int size, int beginX, int beginP, int beginR)
	Recursively list all maximal cliques containing all of all vertices in R, some vertices in P and no vertices in X.

Detailed Description

This file contains the algorithm for listing all cliques according to the algorithm of Tomita et al. (TCS 2006).

Author:: Darren Strash (first name DOT last name AT gmail DOT com)

See GPL 3.0 here

See the algorithm's description in http://dx.doi.org/10.1016/j.tcs.2006.06.015

This is a recursive backtracking algorithm that maintains three sets of vertices, R, a partial clique, P, the common neighbors of vertices in R that are candidates to add to the partial clique, and X, the set of common neighbors of R that have been listed in a maximal clique with R already.

The algorithm recursively adds vertices to R from P, then updates the sets P and X to be the new common neighbors of R and recurses. When P and X are empty, R is a maximal clique, and is reported.

Updating the sets P and X is done by testing if the vertices in P (X) have thee new vertex v added to R as a neighbor, by looking up the edge in the adjacency matrix. Neighbors of v remain in their respective sets.

Function Documentation

int findBestPivotNonNeighborsMatrix	(	int **	pivotNonNeighbors,
		int *	numNonNeighbors,
		char **	adjacencyMatrix,
		int *	vertexSets,
		int *	vertexLookup,
		int	size,
		int	beginX,
		int	beginP,
		int	beginR
	)

Computes the vertex v in P union X that has the most neighbors in P, and places P \ {neighborhood of v} in an array. These are the vertices to consider adding to the partial clique during the current recursive call of the algorithm.

Parameters:

	pivotNonNeighbors	An intially unallocated pointer, which will contain the set P \ {neighborhood of v} when this function completes.
	numNonNeighbors	A pointer to a single integer, which has been preallocated, which will contain the number of elements in pivotNonNeighbors.
	adjacencyMatrix	The input graph in adjacency matrix format.
	vertexSets	An array containing sets of vertices divided into sets X, P, R, and other.
	vertexLookup	A lookup table indexed by vertex number, storing the index of that vertex in vertexSets.
	size	The number of vertices in the graph.
	beginX	The index where set X begins in vertexSets.
	beginP	The index where set P begins in vertexSets.
	beginR	The index where set R begins in vertexSets.

long listAllMaximalCliquesMatrix	(	char **	adjacencyMatrix,
		LinkedList *	cliques,
		int	numVertices
	)

List all maximal cliques in a given graph using the algorithm by Tomita et al. (TCS 2006).

Parameters:

	adjacencyMatrix	An input graph in the adjacency matrix format.
	cliques	A linked list of cliques to return. (only available when compiled with RETURN_CLIQUES_ONE_BY_ONE defined)
	numVertices	The number of vertices in the graph.

Returns:: the number of maximal cliques of the input graph.

void listAllMaximalCliquesMatrixRecursive	(	long *	cliqueCount,
		LinkedList *	cliques,
		LinkedList *	partialClique,
		char **	adjacencyMatrix,
		int *	vertexSets,
		int *	vertexLookup,
		int	size,
		int	beginX,
		int	beginP,
		int	beginR
	)

Recursively list all maximal cliques containing all of all vertices in R, some vertices in P and no vertices in X.

Parameters:

	cliqueCount	A pointer to the number of maximal cliques computed thus far.
	cliques	A linked list of cliques to return. (only available when compiled with RETURN_CLIQUES_ONE_BY_ONE defined)
	partialClique	A linked list storing R, the partial clique for this recursive call.
	adjacencyMatrix	The input graph in adjacency matrix format.
	vertexSets	An array containing sets of vertices divided into sets X, P, R and other.
	vertexLookup	A lookup table indexed by vertex number, storing the index of that vertex in vertexSets.
	size	The number of vertices in the graph.
	beginX	The index where set X begins in vertexSets.
	beginP	The index where set P begins in vertexSets.
	beginR	The index where set R begins in vertexSets.

void moveFromRToXMatrix	(	int	vertex,
		int *	vertexSets,
		int *	vertexLookup,
		int *	pBeginX,
		int *	pBeginP,
		int *	pBeginR
	)			`[inline]`

Move a vertex from the set R to the set X, and update all necessary pointers and arrays of neighbors in P.

Parameters:

	vertex	The vertex to move from R to X.
	vertexSets	An array containing sets of vertices divided into sets X, P, R, and other.
	vertexLookup	A lookup table indexed by vertex number, storing the index of that vertex in vertexSets.
	pBeginX	The index where set X begins in vertexSets.
	pBeginP	The index where set P begins in vertexSets.
	pBeginR	The index where set R begins in vertexSets.

void moveToRMatrix	(	int	vertex,
		int *	vertexSets,
		int *	vertexLookup,
		char **	adjacencyMatrix,
		int *	pBeginX,
		int *	pBeginP,
		int *	pBeginR,
		int *	pNewBeginX,
		int *	pNewBeginP,
		int *	pNewBeginR
	)			`[inline]`

Move a vertex to the set R, and update the sets P and X.

Parameters:

	vertex	The vertex to move to R.
	vertexSets	An array containing sets of vertices divided into sets X, P, R, and other.
	vertexLookup	A lookup table indexed by vertex number, storing the index of that vertex in vertexSets.
	adjacencyMatrix	An input graph in the adjacency matrix format.
	pBeginX	The index where set X begins in vertexSets.
	pBeginP	The index where set P begins in vertexSets.
	pBeginR	The index where set R begins in vertexSets.
	pNewBeginX	After function, contains the new index where set X begins in vertexSets after adding vertex to R.
	pNewBeginP	After function, contains the new index where set P begins in vertexSets after adding vertex to P.
	pNewBeginR	After function, contains the new index where set R begins in vertexSets after adding vertex to R.

src/tomita_algorithm.c File Reference

Functions

Detailed Description

Function Documentation