GrB_Info ktruss_graphblas // compute the k-truss of a graph
(
GrB_Matrix *p_C, // output k-truss subgraph, C
GrB_Matrix A, // input adjacency matrix, A, not modified
const int64_t k, // find the k-truss, where k >= 3
int64_t *p_nsteps // # of steps taken
)
{
//--------------------------------------------------------------------------
// check inputs
//--------------------------------------------------------------------------
// ensure k is 3 or more
if (k < 3) return (GrB_INVALID_VALUE) ;
if (p_C == NULL || p_nsteps == NULL) return (GrB_NULL_POINTER) ;
//--------------------------------------------------------------------------
// initializations
//--------------------------------------------------------------------------
GrB_Info info ;
GxB_SelectOp supportop = NULL ;
GrB_Index n ;
GrB_Matrix C = NULL ;
OK (GrB_Matrix_nrows (&n, A)) ;
OK (GrB_Matrix_new (&C, GrB_INT64, n, n)) ;
// select operator
int64_t support = (k-2) ;
OK (GxB_SelectOp_new (&supportop, support_function, GrB_INT64)) ;
// last_cnz = nnz (A)
GrB_Index cnz, last_cnz ;
OK (GrB_Matrix_nvals (&last_cnz, A)) ;
//--------------------------------------------------------------------------
// find the k-truss of A
//--------------------------------------------------------------------------
double tmult = 0 ;
double tsel = 0 ;
for (int64_t nsteps = 1 ; ; nsteps++)
{
//----------------------------------------------------------------------
// C<C> = C*C
//----------------------------------------------------------------------
GrB_Matrix Cin = (nsteps == 1) ? A : C ;
double t1 = omp_get_wtime ( ) ;
OK (GrB_mxm (C, Cin, NULL, GxB_PLUS_LAND_INT64, Cin, Cin, NULL)) ;
double t2 = omp_get_wtime ( ) ;
printf ("C<C>=C*C time: %g\n", t2-t1) ;
tmult += (t2-t1) ;
//----------------------------------------------------------------------
// C = C .* (C >= support)
//----------------------------------------------------------------------
OK (GxB_select (C, NULL, NULL, supportop, C, &support, NULL)) ;
double t3 = omp_get_wtime ( ) ;
printf ("select time: %g\n", t3-t2) ;
tsel += (t3-t2) ;
//----------------------------------------------------------------------
// check if the k-truss has been found
//----------------------------------------------------------------------
OK (GrB_Matrix_nvals (&cnz, C)) ;
if (cnz == last_cnz)
{
printf ("ktruss_grb done: tmult %g tsel %g\n", tmult, tsel) ;
(*p_C) = C ; // return the output matrix C
(*p_nsteps) = nsteps ; // return # of steps
OK (GrB_free (&supportop)) ; // free the select operator
return (GrB_SUCCESS) ;
}
last_cnz = cnz ;
}
}
GrB_Info read_matrix // read a double-precision or boolean matrix
(
GrB_Matrix *A_output, // handle of matrix to create
FILE *f, // file to read the tuples from
bool make_symmetric, // if true, return A as symmetric
bool no_self_edges, // if true, then remove self edges from A
bool one_based, // if true, input matrix is 1-based
bool boolean, // if true, input is GrB_BOOL, otherwise GrB_FP64
bool pr // if true, print status to stdout
)
{
int64_t len = 256 ;
int64_t ntuples = 0 ;
double x ;
GrB_Index nvals ;
//--------------------------------------------------------------------------
// set all pointers to NULL so that FREE_ALL can free everything safely
//--------------------------------------------------------------------------
GrB_Matrix C = NULL, A = NULL, B = NULL ;
GrB_Descriptor dt1 = NULL, dt2 = NULL ;
GrB_UnaryOp scale2_op = NULL ;
//--------------------------------------------------------------------------
// allocate initial space for tuples
//--------------------------------------------------------------------------
size_t xsize = ((boolean) ? sizeof (bool) : sizeof (double)) ;
GrB_Index *I = malloc (len * sizeof (int64_t)), *I2 = NULL ;
GrB_Index *J = malloc (len * sizeof (int64_t)), *J2 = NULL ;
void *X = malloc (len * xsize) ;
bool *Xbool ;
double *Xdouble ;
void *X2 = NULL ;
if (I == NULL || J == NULL || X == NULL)
{
// out of memory
if (pr) printf ("out of memory for initial tuples\n") ;
FREE_ALL ;
return (GrB_OUT_OF_MEMORY) ;
}
Xbool = (bool *) X ;
Xdouble = (double *) X ;
//--------------------------------------------------------------------------
// read in the tuples from stdin, one per line
//--------------------------------------------------------------------------
// format warnings vary with compilers, so read in as double
double i2, j2 ;
while (fscanf (f, "%lg %lg %lg\n", &i2, &j2, &x) != EOF)
{
int64_t i = (int64_t) i2 ;
int64_t j = (int64_t) j2 ;
if (ntuples >= len)
{
I2 = realloc (I, 2 * len * sizeof (int64_t)) ;
J2 = realloc (J, 2 * len * sizeof (int64_t)) ;
X2 = realloc (X, 2 * len * xsize) ;
if (I2 == NULL || J2 == NULL || X2 == NULL)
{
if (pr) printf ("out of memory for tuples\n") ;
FREE_ALL ;
return (GrB_OUT_OF_MEMORY) ;
}
I = I2 ; I2 = NULL ;
J = J2 ; J2 = NULL ;
X = X2 ; X2 = NULL ;
len = len * 2 ;
Xbool = (bool *) X ;
Xdouble = (double *) X ;
}
if (one_based)
{
i-- ;
j-- ;
}
I [ntuples] = i ;
J [ntuples] = j ;
if (boolean)
{
Xbool [ntuples] = (x != 0) ;
}
else
{
Xdouble [ntuples] = x ;
}
ntuples++ ;
}
//--------------------------------------------------------------------------
// find the dimensions
//--------------------------------------------------------------------------
if (pr) printf ("ntuples: %.16g\n", (double) ntuples) ;
int64_t nrows = 0 ;
int64_t ncols = 0 ;
for (int64_t k = 0 ; k < ntuples ; k++)
{
nrows = MAX (nrows, I [k]) ;
ncols = MAX (ncols, J [k]) ;
}
nrows++ ;
ncols++ ;
if (pr) printf ("nrows %.16g ncols %.16g\n",
(double) nrows, (double) ncols) ;
//--------------------------------------------------------------------------
// prune self edges
//--------------------------------------------------------------------------
// but not if creating the augmented system aka a bipartite graph
double tic [2], t1 ;
simple_tic (tic) ;
if (no_self_edges && ! (make_symmetric && nrows != ncols))
{
int64_t ntuples2 = 0 ;
for (int64_t k = 0 ; k < ntuples ; k++)
{
if (I [k] != J [k])
{
// keep this off-diagonal edge
I [ntuples2] = I [k] ;
J [ntuples2] = J [k] ;
if (boolean)
{
Xbool [ntuples2] = Xbool [k] ;
}
else
{
Xdouble [ntuples2] = Xdouble [k] ;
}
ntuples2++ ;
}
}
ntuples = ntuples2 ;
}
t1 = simple_toc (tic) ;
if (pr) printf ("time to prune self-edges: %12.6f\n", t1) ;
//--------------------------------------------------------------------------
// build the matrix, summing up duplicates, and then free the tuples
//--------------------------------------------------------------------------
GrB_Type xtype ;
GrB_BinaryOp xop, xop2 ;
if (boolean)
{
xtype = GrB_BOOL ;
xop = GrB_LOR ;
xop2 = GrB_FIRST_BOOL ;
}
else
{
xtype = GrB_FP64 ;
xop = GrB_PLUS_FP64 ;
xop2 = GrB_FIRST_FP64 ;
}
simple_tic (tic) ;
GrB_Info info ;
OK (GrB_Matrix_new (&C, xtype, nrows, ncols)) ;
if (boolean)
{
OK (GrB_Matrix_build (C, I, J, Xbool, ntuples, xop)) ;
}
else
{
OK (GrB_Matrix_build (C, I, J, Xdouble, ntuples, xop)) ;
}
t1 = simple_toc (tic) ;
if (pr) printf ("time to build the graph with GrB_Matrix_build: %12.6f\n",
t1) ;
#ifdef TEST_SETELEMENT
{
// This is just for testing performance of GrB_setElement and comparing
// with GrB_build. It is not needed if this function is used in
// production.
// setElement will be just about as fast as build (perhaps 10% to 50%
// more time) with non-blocking mode. If blocking mode is enabled,
// setElement will be extremely and painfully slow since the matrix is
// rebuilt every time a single entry is added.
simple_tic (tic) ;
OK (GrB_Matrix_new (&B, xtype, nrows, ncols)) ;
for (int64_t k = 0 ; k < ntuples ; k++)
{
// B (I[k], J[k]) = X [k]
GrB_Matrix_setElement (B, X [k], I [k], J [k]) ;
}
// force completion of B
GrB_Matrix_nvals (&nvals, B) ;
double t2 = simple_toc (tic) ;
if (pr) printf ("time to build the graph with GrB_setElement:"
" %12.6f\n", t2) ;
GrB_free (&B) ;
}
#endif
free (I) ; I = NULL ;
free (J) ; J = NULL ;
free (X) ; X = NULL ;
//--------------------------------------------------------------------------
// construct the descriptors
//--------------------------------------------------------------------------
// descriptor dt2: transpose the 2nd input
OK (GrB_Descriptor_new (&dt2)) ;
OK (GrB_Descriptor_set (dt2, GrB_INP1, GrB_TRAN)) ;
// descriptor dt1: transpose the 1st input
OK (GrB_Descriptor_new (&dt1)) ;
OK (GrB_Descriptor_set (dt1, GrB_INP0, GrB_TRAN)) ;
//--------------------------------------------------------------------------
// create the output matrix
//--------------------------------------------------------------------------
if (make_symmetric)
{
//----------------------------------------------------------------------
// ensure the matrix is symmetric
//----------------------------------------------------------------------
if (pr) printf ("make symmetric\n") ;
if (nrows == ncols)
{
//------------------------------------------------------------------
// A = (C+C')/2
//------------------------------------------------------------------
if (pr) printf ("A = (C+C')/2\n") ;
double tic [2], t ;
simple_tic (tic) ;
OK (GrB_Matrix_new (&A, xtype, nrows, nrows)) ;
OK (GrB_eWiseAdd (A, NULL, NULL, xop, C, C, dt2)) ;
OK (GrB_free (&C)) ;
if (boolean)
{
*A_output = A ;
A = NULL ;
}
else
{
OK (GrB_Matrix_new (&C, xtype, nrows, nrows)) ;
OK (GrB_UnaryOp_new (&scale2_op, scale2, xtype, xtype)) ;
OK (GrB_apply (C, NULL, NULL, scale2_op, A, NULL)) ;
OK (GrB_free (&A)) ;
OK (GrB_free (&scale2_op)) ;
*A_output = C ;
C = NULL ;
}
t = simple_toc (tic) ;
if (pr) printf ("A = (C+C')/2 time %12.6f\n", t) ;
}
else
{
//------------------------------------------------------------------
// A = [0 C ; C' 0], a bipartite graph
//------------------------------------------------------------------
// no self edges will exist
if (pr) printf ("A = [0 C ; C' 0], a bipartite graph\n") ;
double tic [2], t ;
simple_tic (tic) ;
int64_t n = nrows + ncols ;
OK (GrB_Matrix_new (&A, xtype, n, n)) ;
GrB_Index I_range [3], J_range [3] ;
I_range [GxB_BEGIN] = 0 ;
I_range [GxB_END ] = nrows-1 ;
J_range [GxB_BEGIN] = nrows ;
J_range [GxB_END ] = ncols+nrows-1 ;
// A (nrows:n-1, 0:nrows-1) += C'
OK (GrB_assign (A, NULL, xop2, // or NULL,
C, J_range, GxB_RANGE, I_range, GxB_RANGE, dt1)) ;
// A (0:nrows-1, nrows:n-1) += C
OK (GrB_assign (A, NULL, xop2, // or NULL,
C, I_range, GxB_RANGE, J_range, GxB_RANGE, NULL)) ;
// force completion; if this statement does not appear, the
// timing will not account for the final build, which would be
// postponed until A is used by the caller in another GraphBLAS
// operation.
GrB_Matrix_nvals (&nvals, A) ;
t = simple_toc (tic) ;
if (pr) printf ("time to construct augmented system: %12.6f\n", t) ;
*A_output = A ;
// set A to NULL so the FREE_ALL macro does not free *A_output
A = NULL ;
}
}
else
{
//----------------------------------------------------------------------
// return the matrix as-is
//----------------------------------------------------------------------
if (pr) printf ("leave A as-is\n") ;
*A_output = C ;
// set C to NULL so the FREE_ALL macro does not free *A_output
C = NULL ;
}
//--------------------------------------------------------------------------
// success: free everything except the result, and return it to the caller
//--------------------------------------------------------------------------
FREE_ALL ;
if (pr) printf ("\nMatrix from file:\n") ;
GxB_print (*A_output, pr ? GxB_SHORT : GxB_SILENT) ;
return (GrB_SUCCESS) ;
}
GrB_Info random_matrix // create a random double-precision matrix
(
GrB_Matrix *A_output, // handle of matrix to create
bool make_symmetric, // if true, return A as symmetric
bool no_self_edges, // if true, then do not create self edges
int64_t nrows, // number of rows
int64_t ncols, // number of columns
int64_t nedges, // number of edges
int method, // method to use: 0:setElement, 1:build,
bool A_complex // if true, create a Complex matrix
)
{
GrB_Matrix Areal = NULL, Aimag = NULL, A = NULL ;
*A_output = NULL ;
GrB_Index *I = NULL, *J = NULL ;
double *X = NULL ;
GrB_Info info ;
if (make_symmetric)
{
nrows = MAX (nrows, ncols) ;
ncols = MAX (nrows, ncols) ;
}
//--------------------------------------------------------------------------
// create a Complex matrix
//--------------------------------------------------------------------------
if (A_complex)
{
// Areal = real random matrix
OK (random_matrix (&Areal, make_symmetric, no_self_edges, nrows,
ncols, nedges, method, false)) ;
// Aimag = real random matrix
OK (random_matrix (&Aimag, make_symmetric, no_self_edges, nrows,
ncols, nedges, method, false)) ;
// A = Areal + imag(Aimag)
OK (GrB_Matrix_new (&A, Complex, nrows, ncols)) ;
OK (GrB_apply (A, NULL, NULL, Complex_complex_real, Areal,
NULL)) ;
OK (GrB_apply (A, NULL, Complex_plus, Complex_complex_imag, Aimag,
NULL)) ;
*A_output = A ;
A = NULL ;
FREE_ALL ;
return (GrB_SUCCESS) ;
}
//--------------------------------------------------------------------------
// create a real double matrix (GrB_FP64)
//--------------------------------------------------------------------------
OK (GrB_Matrix_new (&A, GrB_FP64, nrows, ncols)) ;
if (method == 0)
{
//----------------------------------------------------------------------
// use GrB_Matrix_setElement: no need to allocate tuples
//----------------------------------------------------------------------
// This is just about as fast as the GrB_Matrix_build method with
// non-blocking mode (about 10% more time, regardless of the problem
// size). This is mainly because setElement doesn't know how many
// tuples will eventually be added, so it must dynamically reallocate
// its internal storage. In constrast, the arrays I, J, and X are a
// fixed, known size and are not reallocated as tuples are added.
// Note how simple this code is, below. A user application can use
// setElement without having to create its own I,J,X tuple lists. It
// can create the tuples in any order. The code is simpler, and the
// performance penalty is neglible.
// With blocking mode, setElement is EXTREMELY slow, since the matrix
// is rebuilt on every iteration. In this case, it is easily a 1,000
// or even a million times slower than using build when the matrix is
// very large. Don't attempt to do this with large matrices with
// blocking mode enabled. Actual run time could increase from 1 minute
// to 1 year (!) in the extreme case, with a matrix that can be
// generated on a commodity laptop.
for (int64_t k = 0 ; k < nedges ; k++)
{
GrB_Index i = simple_rand_i ( ) % nrows ;
GrB_Index j = simple_rand_i ( ) % ncols ;
if (no_self_edges && (i == j)) continue ;
double x = simple_rand_x ( ) ;
// A (i,j) = x
OK (GrB_Matrix_setElement (A, x, i, j)) ;
if (make_symmetric)
{
// A (j,i) = x
OK (GrB_Matrix_setElement (A, x, j, i)) ;
}
}
}
else
{
//----------------------------------------------------------------------
// use GrB_Matrix_build: allocate initial space for tuples
//----------------------------------------------------------------------
// This method is harder for a user application to use. It is slightly
// faster than the setElement method. Its performance is not affected
// by the mode (blocking or non-blocking).
int64_t s = ((make_symmetric) ? 2 : 1) * nedges + 1 ;
I = malloc (s * sizeof (GrB_Index)) ;
J = malloc (s * sizeof (GrB_Index)) ;
X = malloc (s * sizeof (double )) ;
if (I == NULL || J == NULL || X == NULL)
{ // out of memory
FREE_ALL ;
return (GrB_OUT_OF_MEMORY) ;
}
//----------------------------------------------------------------------
// create the tuples
//----------------------------------------------------------------------
int64_t ntuples = 0 ;
for (int64_t k = 0 ; k < nedges ; k++)
{
GrB_Index i = simple_rand_i ( ) % nrows ;
GrB_Index j = simple_rand_i ( ) % ncols ;
if (no_self_edges && (i == j)) continue ;
double x = simple_rand_x ( ) ;
// A (i,j) = x
I [ntuples] = i ;
J [ntuples] = j ;
X [ntuples] = x ;
ntuples++ ;
if (make_symmetric)
{
// A (j,i) = x
I [ntuples] = j ;
J [ntuples] = i ;
X [ntuples] = x ;
ntuples++ ;
}
}
//----------------------------------------------------------------------
// build the matrix
//----------------------------------------------------------------------
OK (GrB_Matrix_build (A, I, J, X, ntuples, GrB_SECOND_FP64)) ;
free (I) ;
free (J) ;
free (X) ;
}
*A_output = A ;
return (GrB_SUCCESS) ;
}