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/*****************************************************************************
* *
* Sparse-graph-specific auxiliary source file for version 2.8 of nauty. *
* *
* Copyright (2004-2022) Brendan McKay. All rights reserved. *
* Subject to waivers and disclaimers in nauty.h. *
* *
* CHANGE HISTORY *
* 26-Oct-04 : initial creation *
* 23-Nov-06 : dispatch uses targetcell_sg, not bestcell_sg *
* 8-Dec-06 : add adjacencies_sg() *
* 10-Nov-09 : remove types shortish and permutation *
* 14-Nov-09 : added copy_sg() *
* 11-May-10 : use sorttemplates.c for sorting procedures *
* 19-May-10 : add two *_tr procedures for traces. *
* 21-May-10 : fixes for nde,v fields becoming size_t *
* 23-May-10 : add sparsenauty() *
* 15-Jan-12 : add TLS_ATTR attributes *
* 17-Dec-15 : extend sortlists_sg() to sort weights *
* : add weights to copy_sg() and updatecan_sg() *
* 11-Mar-16 : add cleanup_sg(). This can be used in the cleanup *
* field of the dispatch vector to sort the lists of the *
* canonical graph, but isn't there by default. *
* 15-Oct-19 : fix static declaration of snwork[] *
* 6-Apr-21 : increase work space in sparsenauty() *
* 16-Nov-22 : fix an error in the Traces utility comparelab_tr() *
* *
*****************************************************************************/
#define TMP
/* #define ONE_WORD_SETS not sure about this! See notes.txt. */
#include "nausparse.h"
/* macros for hash-codes: */
#define MASH(l,i) ((((l) ^ 065435) + (i)) & 077777)
/* : expression whose long value depends only on long l and int/long i.
Anything goes, preferably non-commutative. */
#define CLEANUP(l) ((int)((l) % 077777))
/* : expression whose value depends on long l and is less than 077777
when converted to int then short. Anything goes. */
#if MAXM==1
#define M 1
#else
#define M m
#endif
#define ACCUM(x,y) x = (((x) + (y)) & 077777)
static const int fuzz1[] = {037541,061532,005257,026416};
static const int fuzz2[] = {006532,070236,035523,062437};
#define FUZZ1(x) ((x) ^ fuzz1[(x)&3])
#define FUZZ2(x) ((x) ^ fuzz2[(x)&3])
/* aproto: header new_nauty_protos.h */
dispatchvec dispatch_sparse =
{isautom_sg,testcanlab_sg,updatecan_sg,refine_sg,refine_sg,cheapautom_sg,
targetcell_sg,nausparse_freedyn,nausparse_check,init_sg,NULL};
#if !MAXN
DYNALLSTAT(short,vmark1,vmark1_sz);
DYNALLSTAT(short,vmark2,vmark2_sz);
DYNALLSTAT(int,work1,work1_sz);
DYNALLSTAT(int,work2,work2_sz);
DYNALLSTAT(int,work3,work3_sz);
DYNALLSTAT(int,work4,work4_sz);
DYNALLSTAT(set,snwork,snwork_sz);
#else
static TLS_ATTR short vmark1[MAXN];
static TLS_ATTR short vmark2[MAXN];
static TLS_ATTR int work1[MAXN];
static TLS_ATTR int work2[MAXN];
static TLS_ATTR int work3[MAXN];
static TLS_ATTR int work4[MAXN];
static TLS_ATTR set snwork[2*500*MAXM];
#endif
static TLS_ATTR short vmark1_val = 32000;
#define MARK1(i) vmark1[i] = vmark1_val
#define UNMARK1(i) vmark1[i] = 0
#define ISMARKED1(i) (vmark1[i] == vmark1_val)
#define ISNOTMARKED1(i) (vmark1[i] != vmark1_val)
static TLS_ATTR short vmark2_val = 32000;
#define MARK2(i) vmark2[i] = vmark2_val
#define UNMARK2(i) vmark2[i] = 0
#define ISMARKED2(i) (vmark2[i] == vmark2_val)
#define ISNOTMARKED2(i) (vmark2[i] != vmark2_val)
#if !MAXN
#define RESETMARKS1 {if (vmark1_val++ >= 32000) \
{size_t ij; for (ij=0;ij<vmark1_sz;++ij) vmark1[ij]=0; vmark1_val=1;}}
#define PREPAREMARKS1(nn) preparemarks1(nn)
#define RESETMARKS2 {if (vmark2_val++ >= 32000) \
{size_t ij; for (ij=0;ij<vmark2_sz;++ij) vmark2[ij]=0; vmark2_val=1;}}
#define PREPAREMARKS2(nn) preparemarks2(nn)
#else
#define RESETMARKS1 {if (vmark1_val++ >= 32000) \
{size_t ij; for (ij=0;ij<MAXN;++ij) vmark1[ij]=0; vmark1_val=1;}}
#define PREPAREMARKS1(nn)
#define RESETMARKS2 {if (vmark2_val++ >= 32000) \
{size_t ij; for (ij=0;ij<MAXN;++ij) vmark2[ij]=0; vmark2_val=1;}}
#define PREPAREMARKS2(nn)
#endif
/*****************************************************************************
* *
* preparemarks1(N) and preparemarks2(N) *
* make vmarks array large enough to mark 0..N-1 and such that *
* the next RESETMARKS command will work correctly *
* *
*****************************************************************************/
#if !MAXN
static void
preparemarks1(size_t nn)
{
size_t oldsize;
short *oldpos;
oldsize = vmark1_sz;
oldpos = vmark1;
DYNALLOC1(short,vmark1,vmark1_sz,nn,"preparemarks");
if (vmark1_sz != oldsize || vmark1 != oldpos) vmark1_val = 32000;
}
#endif
#if !MAXN
static void
preparemarks2(size_t nn)
{
size_t oldsize;
short *oldpos;
oldsize = vmark2_sz;
oldpos = vmark2;
DYNALLOC1(short,vmark2,vmark2_sz,nn,"preparemarks");
if (vmark2_sz != oldsize || vmark2 != oldpos) vmark2_val = 32000;
}
#endif
/*****************************************************************************
* *
* isautom_sg(g,perm,digraph,m,n) = TRUE iff perm is an automorphism of g *
* (i.e., g^perm = g). Symmetry is assumed unless digraph = TRUE. *
* *
*****************************************************************************/
boolean
isautom_sg(graph *g, int *p, boolean digraph, int m, int n)
{
int *d,*e;
size_t *v;
int i,pi,di;
size_t vi,vpi,j;
SG_VDE(g,v,d,e);
PREPAREMARKS1(n);
for (i = 0; i < n; ++i)
if (p[i] != i || digraph)
{
pi = p[i];
di = d[i];
if (d[pi] != di) return FALSE;
vi = v[i];
vpi = v[pi];
RESETMARKS1;
for (j = 0; j < di; ++j) MARK1(p[e[vi+j]]);
for (j = 0; j < di; ++j) if (ISNOTMARKED1(e[vpi+j])) return FALSE;
}
return TRUE;
}
/*****************************************************************************
* *
* aresame_sg(g1,g2) = TRUE iff g1 and g2 are identical as labelled digraphs *
* *
*****************************************************************************/
boolean
aresame_sg(sparsegraph *g1, sparsegraph *g2)
{
int *d1,*e1;
int *d2,*e2;
int n,i,di;
size_t vi,*v1,*v2,j;
n = g1->nv;
if (g2->nv != n || g2->nde != g1->nde) return FALSE;
SG_VDE(g1,v1,d1,e1);
SG_VDE(g2,v2,d2,e2);
PREPAREMARKS1(n);
for (i = 0; i < n; ++i)
{
di = d1[i];
if (d2[i] != di) return FALSE;
vi = v1[i];
RESETMARKS1;
for (j = 0; j < di; ++j) MARK1(e1[vi+j]);
vi = v2[i];
for (j = 0; j < di; ++j) if (ISNOTMARKED1(e2[vi+j])) return FALSE;
}
return TRUE;
}
/*****************************************************************************
* *
* testcanlab_sg(g,canong,lab,samerows,m,n) compares g^lab to canong, *
* using an ordering which is immaterial since it's only used here. The *
* value returned is -1,0,1 if g^lab <,=,> canong. *samerows is set to *
* the number of rows (0..n) of canong which are the same as those of g^lab. *
* *
*****************************************************************************/
int
testcanlab_sg(graph *g, graph *canong, int *lab, int *samerows, int m, int n)
{
int *d,*e;
int *cd,*ce;
int i,k,di,dli;
size_t j,vi,vli,*v,*cv;
int mina;
SG_VDE(g,v,d,e);
SG_VDE(canong,cv,cd,ce);
#if !MAXN
DYNALLOC1(int,work1,work1_sz,n,"testcanlab_sg");
#endif
#define INVLAB work1
PREPAREMARKS1(n);
for (i = 0; i < n; ++i) INVLAB[lab[i]] = i;
for (i = 0; i < n; ++i)
{
/* compare g[lab[i]]^INVLAB to canong[i] */
vi = cv[i];
di = cd[i];
vli = v[lab[i]];
dli = d[lab[i]];
if (di != dli)
{
*samerows = i;
if (di < dli) return -1;
return 1;
}
RESETMARKS1;
mina = n;
for (j = 0; j < di; ++j) MARK1(ce[vi+j]);
for (j = 0; j < di; ++j)
{
k = INVLAB[e[vli+j]];
if (ISMARKED1(k)) UNMARK1(k);
else if (k < mina) mina = k;
}
if (mina != n)
{
*samerows = i;
for (j = 0; j < di; ++j)
{
k = ce[vi+j];
if (ISMARKED1(k) && k < mina) return -1;
}
return 1;
}
}
*samerows = n;
return 0;
}
/*****************************************************************************
* *
* updatecan_sg(g,canong,lab,samerows,m,n) sets canong = g^lab, assuming *
* the first samerows vertices of canong are ok already. Also assumes *
* contiguity and ample space in canong. *
* *
*****************************************************************************/
void
updatecan_sg(graph *g, graph *canong, int *lab, int samerows, int m, int n)
{
int *d,*e;
int *cd,*ce;
int i,dli;
size_t *v,*cv,vli,j,k;
sg_weight *wt,*cwt;
SWG_VDE(g,v,d,e,wt);
SWG_VDE(canong,cv,cd,ce,cwt);
#if !MAXN
DYNALLOC1(int,work1,work1_sz,n,"testcanlab_sg");
#endif
#define INVLAB work1
((sparsegraph*)canong)->nv = n;
((sparsegraph*)canong)->nde = ((sparsegraph*)g)->nde;
for (i = 0; i < n; ++i) INVLAB[lab[i]] = i;
if (samerows == 0) k = 0;
else k = cv[samerows-1]+cd[samerows-1];
for (i = samerows; i < n; ++i)
{
cv[i] = k;
cd[i] = dli = d[lab[i]];
vli = v[lab[i]];
if (wt)
{
for (j = 0; j < dli; ++j)
{
ce[k] = INVLAB[e[vli+j]];
cwt[k] = wt[vli+j];
++k;
}
}
else
for (j = 0; j < dli; ++j) ce[k++] = INVLAB[e[vli+j]];
}
}
/*****************************************************************************
* *
* comparelab_tr(g,lab1,invlab1,lab2,invlab2,cls,col) compares *
* g^lab1 to g^lab2 and returns -1,0,1 according to the comparison. *
* invlab1[] and invlab2[] are assumed to hold inverses of lab1,lab2. *
* *
*****************************************************************************/
int
comparelab_tr(sparsegraph *g,
int *lab1, int *invlab1, int *lab2, int *invlab2, int *cls, int *col)
{
int d1,*e1,d2,*e2;
int i,j,k,n,c,end;
int mina;
n = g->nv;
#if !MAXN
DYNALLOC1(int,work1,work1_sz,n,"comparelab_tr");
#endif
#define NGHCOUNTS work1
memset(NGHCOUNTS,0,n*sizeof(int));
for (c=0; c<n; c+=cls[c])
{
if (cls[c] == 1)
{
end = c+cls[c];
for (i = c; i < end; ++i)
{
e1 = g->e + g->v[lab1[i]];
d1 = g->d[lab1[i]];
e2 = g->e + g->v[lab2[i]];
d2 = g->d[lab2[i]];
if (d1 < d2) return -1;
else if (d1 > d2) return 1;
mina = n;
for (j = 0; j < d1; ++j) {
(NGHCOUNTS[col[invlab1[e1[j]]]])++;
}
for (j = 0; j < d1; ++j)
{
k = col[invlab2[e2[j]]];
if (NGHCOUNTS[k]) {
(NGHCOUNTS[k])--;
}
else {
if (k < mina) mina = k;
}
}
if (mina != n)
{
for (j = 0; j < d1; ++j)
{
k = col[invlab1[e1[j]]];
if (NGHCOUNTS[k] && k < mina) return -1;
}
return 1;
}
}
}
}
return 0;
}
/*****************************************************************************
* *
* testcanlab_tr(g,canong,lab,invlab,samerows) compares g^lab to canong, *
* using an ordering which is immaterial since it's only used here. The *
* value returned is -1,0,1 if g^lab <,=,> canong. *samerows is set to *
* the number of rows (0..n) of canong which are the same as those of g^lab. *
* invlab[] is assumed to hold the inverse of lab[] *
* *
*****************************************************************************/
int
testcanlab_tr(sparsegraph *g, sparsegraph *canong,
int *lab, int *invlab, int *samerows)
{
int *d,*e;
int *cd,*ce;
int i,di,dli;
int k,n;
size_t *v,*cv,vi,vli,j;
int mina;
SG_VDE(g,v,d,e);
SG_VDE(canong,cv,cd,ce);
n = g->nv;
PREPAREMARKS1(n);
for (i = 0; i < n; ++i)
{
/* compare g[lab[i]]^invlab to canong[i] */
vi = cv[i];
di = cd[i];
vli = v[lab[i]];
dli = d[lab[i]];
if (di != dli)
{
*samerows = i;
if (di < dli) return -1;
return 1;
}
RESETMARKS1;
mina = n;
for (j = 0; j < di; ++j) MARK1(ce[vi+j]);
for (j = 0; j < di; ++j)
{
k = invlab[e[vli+j]];
if (ISMARKED1(k)) UNMARK1(k);
else if (k < mina) mina = k;
}
if (mina != n)
{
*samerows = i;
for (j = 0; j < di; ++j)
{
k = ce[vi+j];
if (ISMARKED1(k) && k < mina) return -1;
}
return 1;
}
}
*samerows = n;
return 0;
}
/*****************************************************************************
* *
* updatecan_tr(g,canong,lab,invlab,samerows) sets canong = g^lab, *
* assuming the first samerows vertices of canong are ok already. *
* Also assumes contiguity and ample space in canong. *
* Assumes invlab[] holds the inverse of lab[] *
* *
*****************************************************************************/
void
updatecan_tr(sparsegraph *g, sparsegraph *canong,
int *lab, int *invlab, int samerows)
{
int *d,*e;
int *cd,*ce;
int i,dli,n;
size_t *v,*cv,vli,j,k;
SG_VDE(g,v,d,e);
SG_VDE(canong,cv,cd,ce);
n = g->nv;
PREPAREMARKS1(n);
canong->nv = n;
canong->nde = g->nde;
if (samerows == 0) k = 0;
else k = cv[samerows-1]+cd[samerows-1];
for (i = samerows; i < n; ++i)
{
cv[i] = k;
cd[i] = dli = d[lab[i]];
vli = v[lab[i]];
for (j = 0; j < dli; ++j) ce[k++] = invlab[e[vli+j]];
}
}
#define SORT_OF_SORT 3
#define SORT_NAME sortindirect
#define SORT_TYPE1 int
#define SORT_TYPE2 int
#include "sorttemplates.c"
#define SORT_OF_SORT 1
#define SORT_NAME sortints
#define SORT_TYPE1 int
#include "sorttemplates.c"
#define SORT_OF_SORT 2
#define SORT_NAME sortweights
#define SORT_TYPE1 int
#define SORT_TYPE2 sg_weight
#include "sorttemplates.c"
/*****************************************************************************
* *
* init_sg(graph *gin, graph **gout, graph *hin, graph **hout, *
* int *lab, int *ptn, set *active, optionblk *options, *
* int *status, int m, int n) *
* Initialise routine for dispatch vector. This one just makes sure *
* that *hin has enough space and sets fields for n=0. *
* *
*****************************************************************************/
void
init_sg(graph *gin, graph **gout, graph *hin, graph **hout, int *lab,
int *ptn, set *active, struct optionstruct *options, int *status,
int m, int n)
{
sparsegraph *sg,*sh;
if (options->getcanon)
{
sg = (sparsegraph*)gin;
sh = (sparsegraph*)hin;
SG_ALLOC(*sh,sg->nv,sg->nde,"init_sg");
sh->nv = sg->nv;
sh->nde = sg->nde;
}
*status = 0;
}
/*****************************************************************************
* *
* cleanup_sg(graph *gin, graph **gout, graph *hin, graph **hout, *
* int *lab, int *ptn, optionblk *options, *
* statsblk *stats, int m, int n) *
* Cleanup routine for dispatch vector. This one sorts the adjacency *
* lists for the canonical labelling. *
* *
*****************************************************************************/
void
cleanup_sg(graph *gin, graph **gout, graph *hin, graph **hout, int *lab,
int *ptn, optionblk *options, statsblk *stats, int m, int n)
{
sparsegraph *sh;
if (options->getcanon
&& (stats->errstatus == 0 || stats->errstatus == NAUABORTED))
{
sh = (sparsegraph*)hin;
sortlists_sg(sh);
}
}
/*****************************************************************************
* *
* distvals(sparsegraph *sg, int v0, int *dist, int n) sets dist[i] *
* to the distance from v0 to i, for each i, or to n if there is no such *
* distance. work4[] is used as a queue. *
* *
*****************************************************************************/
void
distvals(sparsegraph *g, int v0, int *dist, int n)
{
int *d,*e;
int i,head,tail;
int di,k;
size_t *v,vi,j;
SG_VDE(g,v,d,e);
#if !MAXN
DYNALLOC1(int,work4,work4_sz,n,"distvals");
#endif
#define QUEUE work4
for (i = 0; i < n; ++i) dist[i] = n;
QUEUE[0] = v0;
dist[v0] = 0;
head = 0;
tail = 1;
while (tail < n && head < tail)
{
i = QUEUE[head++];
vi = v[i];
di = d[i];
for (j = 0; j < di; ++j)
{
k = e[vi+j];
if (dist[k] == n)
{
dist[k] = dist[i] + 1;
QUEUE[tail++] = k;
}
}
}
}
/*****************************************************************************
* *
* refine_sg(g,lab,ptn,level,numcells,count,active,code,m,n) performs a *
* refinement operation on the partition at the specified level of the *
* partition nest (lab,ptn). *numcells is assumed to contain the number of *
* cells on input, and is updated. The initial set of active cells (alpha *
* in the paper) is specified in the set active. Precisely, x is in active *
* iff the cell starting at index x in lab is active. *
* The resulting partition is equitable if active is correct (see the paper *
* and the Guide). *
* *code is set to a value which depends on the fine detail of the *
* algorithm, but which is independent of the labelling of the graph. *
* count is used for work space. *
* *
*****************************************************************************/
void
refine_sg(graph *g, int *lab, int *ptn, int level, int *numcells,
int *count, set *active, int *code, int m, int n)
{
int i,j,k,l,v1,v2,v3,isplit;
int w1,w2,w3;
long longcode;
int *d,*e;
int size,bigsize,bigpos;
int nactive,hitcells;
int lj,di,splitv;
boolean trivsplit;
size_t *v,vi,ii;
SG_VDE(g,v,d,e);
#if !MAXN
DYNALLOC1(int,work1,work1_sz,n,"refine_sg");
DYNALLOC1(int,work2,work2_sz,n,"refine_sg");
DYNALLOC1(int,work3,work3_sz,n,"refine_sg");
DYNALLOC1(int,work4,work4_sz,n,"refine_sg");
#endif
#define CELLSTART work1
#define ACTIVE work2
#define HITS work3
#define HITCELL work4
PREPAREMARKS1(n);
PREPAREMARKS2(n);
longcode = *numcells;
/* Set ACTIVE[0..nactive-1] = queue of active cell starts */
nactive = 0;
for (i = -1; (i = nextelement(active,m,i)) >= 0;)
ACTIVE[nactive++] = i;
if (nactive == 0)
{
*code = CLEANUP(longcode);
return;
}
/* Set CELLSTART[i] = starting point in lab[] of nontrivial cell
containing i, or n if i is a singleton */
for (i = 0; i < n; )
{
/* Just here, i is a cell starting position */
if (ptn[i] <= level)
{
CELLSTART[lab[i]] = n;
++i;
}
else
{
j = i;
do
{
CELLSTART[lab[i]] = j;
} while (ptn[i++] > level);
}
}
if (level <= 2 && nactive == 1 && ptn[ACTIVE[0]] <= level
&& *numcells <= n/8)
{
isplit = ACTIVE[--nactive];
DELELEMENT(active,isplit);
distvals((sparsegraph*)g,lab[isplit],HITS,n);
for (v1 = 0; v1 < n; )
{
if (ptn[v1] <= level)
{
++v1;
continue;
}
longcode = MASH(longcode,v1);
w1 = HITS[lab[v1]];
v2 = v1+1;
while (ptn[v2-1] > level && HITS[lab[v2]] == w1) ++v2;
if (ptn[v2-1] <= level)
{
v1 = v2;
continue;
}
w2 = NAUTY_INFINITY;
v3 = j = v2;
do
{
lj = lab[j];
w3 = HITS[lj];
if (w3 == w1)
{
lab[j] = lab[v3];
lab[v3] = lab[v2];
lab[v2] = lj;
++v2;
++v3;
}
else if (w3 == w2)
{
lab[j] = lab[v3];
lab[v3] = lj;
++v3;
}
else if (w3 < w1)
{
lab[j] = lab[v2];
lab[v2] = lab[v1];
lab[v1] = lj;
v3 = v2 + 1;
v2 = v1 + 1;
w2 = w1;
w1 = w3;
}
else if (w3 < w2)
{
lab[j] = lab[v2];
lab[v2] = lj;
v3 = v2 + 1;
w2 = w3;
}
} while (ptn[j++] > level);
longcode = MASH(longcode,w2);
longcode = MASH(longcode,v2);
if (j != v2) /* At least two fragments
* v1..v2-1 = w1; v2..v3-1 = w2 */
{
if (v2 == v1+1)
CELLSTART[lab[v1]] = n;
if (v3 == v2+1)
CELLSTART[lab[v2]] = n;
else
for (k = v2; k < v3; ++k)
CELLSTART[lab[k]] = v2;
++*numcells;
ptn[v2-1] = level;
if (j == v3)
{
/* Two fragments only */
if (v2-v1 <= v3-v2 && !ISELEMENT(active,v1))
{
ADDELEMENT(active,v1);
ACTIVE[nactive++] = v1;
}
else
{
ADDELEMENT(active,v2);
ACTIVE[nactive++] = v2;
}
}
else
{
/* Extra fragments: v3..j-1 > w2 */
sortindirect(lab+v3,HITS,j-v3);
ACTIVE[nactive++] = v2;
ADDELEMENT(active,v2);
if (v2-v1 >= v3-v2)
{
bigpos = -1;
bigsize = v2-v1;
}
else
{
bigpos = nactive-1;
bigsize = v3-v2;
}
for (k = v3-1; k < j-1;)
{
ptn[k] = level;
longcode = MASH(longcode,k);
++*numcells;
l = k+1;
ADDELEMENT(active,l);
ACTIVE[nactive++] = l;
w3 = HITS[lab[l]];
for (k = l; k < j-1
&& HITS[lab[k+1]] == w3; ++k)
CELLSTART[lab[k+1]] = l;
size = k-l+1;
if (size == 1)
CELLSTART[lab[l]] = n;
else
{
CELLSTART[lab[l]] = l;
if (size > bigsize)
{
bigsize = size;
bigpos = nactive-1;
}
}
}
if (bigpos >= 0 && !ISELEMENT(active,v1))
{
longcode = MASH(longcode,bigpos);
DELELEMENT(active,ACTIVE[bigpos]);
ADDELEMENT(active,v1);
ACTIVE[bigpos] = v1;
}
}
}
v1 = j;
}
}
/* Iterate until complete */
while (nactive > 0 && *numcells < n)
{
for (i = 0; i < nactive && i < 10; ++i)
if (ptn[ACTIVE[i]] <= level) break;
if (i < nactive && i < 10)
{
trivsplit = TRUE;
isplit = ACTIVE[i];
ACTIVE[i] = ACTIVE[--nactive];
}
else
{
isplit = ACTIVE[--nactive];
trivsplit = ptn[isplit] <= level;
}
DELELEMENT(active,isplit);
longcode = MASH(longcode,isplit);
if (trivsplit)
{
RESETMARKS1;
RESETMARKS2;
hitcells = 0;
splitv = lab[isplit];
vi = v[splitv];
di = d[splitv];
for (ii = 0; ii < di; ++ii)
{
j = e[vi+ii];
MARK2(j);
k = CELLSTART[j];
if (k != n && ISNOTMARKED1(k))
{
MARK1(k);
HITCELL[hitcells++] = k;
}
}
if (hitcells > 1) sortints(HITCELL,hitcells);
longcode = MASH(longcode,hitcells);
/* divide cells according to which vertices are hit */
for (i = 0; i < hitcells; ++i)
{
j = v1 = v2 = HITCELL[i];
longcode = MASH(longcode,v2);
k = 0;
do
{
lj = lab[j];
if (ISMARKED2(lj))
HITS[k++] = lj;
else
lab[v2++] = lj;
} while (ptn[j++] > level);
longcode = MASH(longcode,k);
v3 = v2;
while (--k >= 0)
{
j = HITS[k];
CELLSTART[j] = v2;
lab[v3++] = j;
}
if (v2 != v3 && v2 != v1)
{
++*numcells;
if (v2 == v1+1) CELLSTART[lab[v1]] = n;
if (v3 == v2+1) CELLSTART[lab[v2]] = n;
ptn[v2-1] = level;
longcode = MASH(longcode,v2);
if (v2-v1 <= v3-v2 && !ISELEMENT(active,v1))
{
ADDELEMENT(active,v1);
ACTIVE[nactive++] = v1;
}
else
{
ADDELEMENT(active,v2);
ACTIVE[nactive++] = v2;
}
}
}
}
else /* non-trivial splitting */
{
/* isplit is the start of the splitting cell.
Set HITS[i] = hits of i for i in non-trivial cells,
HITCELL[0..hitcells-1] = starts of hit non-trivial cells */
RESETMARKS1;
hitcells = 0;
do
{
vi = v[lab[isplit]];
di = d[lab[isplit]];
for (ii = 0; ii < di; ++ii)
{
j = e[vi+ii];
k = CELLSTART[j];
if (k != n)
{
if (ISNOTMARKED1(k))
{
MARK1(k);
HITCELL[hitcells++] = k;
do
{
HITS[lab[k]] = 0;
} while (ptn[k++] > level);
}
++HITS[j];
}
}
} while (ptn[isplit++] > level);
if (hitcells > 1) sortints(HITCELL,hitcells);
/* divide cells according to hit counts */
longcode = MASH(longcode,hitcells);
for (i = 0; i < hitcells; ++i)
{
v1 = HITCELL[i];
w1 = HITS[lab[v1]];
longcode = MASH(longcode,v1);
v2 = v1+1;
while (ptn[v2-1] > level && HITS[lab[v2]] == w1) ++v2;
if (ptn[v2-1] <= level) continue;
w2 = NAUTY_INFINITY;
v3 = j = v2;
do
{
lj = lab[j];
w3 = HITS[lj];
if (w3 == w1)
{
lab[j] = lab[v3];
lab[v3] = lab[v2];
lab[v2] = lj;
++v2;
++v3;
}
else if (w3 == w2)
{
lab[j] = lab[v3];
lab[v3] = lj;
++v3;
}
else if (w3 < w1)
{
lab[j] = lab[v2];
lab[v2] = lab[v1];
lab[v1] = lj;
v3 = v2 + 1;
v2 = v1 + 1;
w2 = w1;
w1 = w3;
}
else if (w3 < w2)
{
lab[j] = lab[v2];
lab[v2] = lj;
v3 = v2 + 1;
w2 = w3;
}
} while (ptn[j++] > level);
longcode = MASH(longcode,w1);
longcode = MASH(longcode,v2);
if (j != v2) /* At least two fragments
* v1..v2-1 = w1; v2..v3-1 = w2 */
{
if (v2 == v1+1)
CELLSTART[lab[v1]] = n;
if (v3 == v2+1)
CELLSTART[lab[v2]] = n;
else
for (k = v2; k < v3; ++k)
CELLSTART[lab[k]] = v2;
++*numcells;
ptn[v2-1] = level;
if (j == v3)
{
/* Two fragments only */
if (v2-v1 <= v3-v2 && !ISELEMENT(active,v1))
{
ADDELEMENT(active,v1);
ACTIVE[nactive++] = v1;
}
else
{
ADDELEMENT(active,v2);
ACTIVE[nactive++] = v2;
}
}
else
{
/* Extra fragments: v3..j-1 > w2 */
longcode = MASH(longcode,v3);
sortindirect(lab+v3,HITS,j-v3);
ACTIVE[nactive++] = v2;
ADDELEMENT(active,v2);
if (v2-v1 >= v3-v2)
{
bigpos = -1;
bigsize = v2-v1;
}
else
{
bigpos = nactive-1;
bigsize = v3-v2;
longcode = MASH(longcode,bigsize);
}
for (k = v3-1; k < j-1;)
{
ptn[k] = level;
++*numcells;
l = k+1;
ADDELEMENT(active,l);
ACTIVE[nactive++] = l;
w3 = HITS[lab[l]];
longcode = MASH(longcode,w3);
for (k = l; k < j-1
&& HITS[lab[k+1]] == w3; ++k)
CELLSTART[lab[k+1]] = l;
size = k-l+1;
if (size == 1)
CELLSTART[lab[l]] = n;
else
{
CELLSTART[lab[l]] = l;
if (size > bigsize)
{
bigsize = size;
bigpos = nactive-1;
}
}
}
if (bigpos >= 0 && !ISELEMENT(active,v1))
{
DELELEMENT(active,ACTIVE[bigpos]);
ADDELEMENT(active,v1);
ACTIVE[bigpos] = v1;
}
}
}
}
}
}
longcode = MASH(longcode,*numcells);
*code = CLEANUP(longcode);
}
/*****************************************************************************
* *
* cheapautom_sg(ptn,level,digraph,n) returns TRUE if the partition at the *
* specified level in the partition nest (lab,ptn) {lab is not needed here} *
* satisfies a simple sufficient condition for its cells to be the orbits of *
* some subgroup of the automorphism group. Otherwise it returns FALSE. *
* It always returns FALSE if digraph!=FALSE. *
* *
* nauty assumes that this function will always return TRUE for any *
* partition finer than one for which it returns TRUE. *
* *
*****************************************************************************/
boolean
cheapautom_sg(int *ptn, int level, boolean digraph, int n)
{
int i,k,nnt;
if (digraph) return FALSE;
k = n;
nnt = 0;
for (i = 0; i < n; ++i)
{
--k;
if (ptn[i] > level)
{
++nnt;
while (ptn[++i] > level) {}
}
}
return (k <= nnt + 1 || k <= 4);
}
/*****************************************************************************
* *
* bestcell_sg(g,lab,ptn,level,tc_level,m,n) returns the index in lab of *
* the start of the "best non-singleton cell" for fixing. If there is no *
* non-singleton cell it returns n. *
* This implementation finds the first cell which is non-trivially joined *
* to the greatest number of other cells, assuming equitability. *
* This is not good for digraphs! *
* *
*****************************************************************************/
static int
bestcell_sg(graph *g, int *lab, int *ptn, int level,
int tc_level, int m, int n)
{
int nnt;
int *d,*e;
int i,k,di;
int *work1b;
int maxcnt;
size_t *v,vi,j;
SG_VDE(g,v,d,e);
#if !MAXN
DYNALLOC1(int,work1,work1_sz,n,"bestcell_sg");
DYNALLOC1(int,work2,work2_sz,n,"bestcell_sg");
DYNALLOC1(int,work3,work3_sz,n,"bestcell_sg");
DYNALLOC1(int,work4,work4_sz,n,"bestcell_sg");
#endif
work1b = work1 + (n/2);
#define START work1
#define SIZE work1b
#define NNTCELL work2
#define HITS work3
#define COUNT work4
/* find non-singleton cells: put starts in START[0..nnt-1],
sizes in SIZE[0..nnt-1].
Also NNTCELL[i] = n if {i} is a singelton, else index of
nontriv cell containing i. */
i = nnt = 0;
while (i < n)
{
if (ptn[i] > level)
{
START[nnt] = i;
j = i;
do
NNTCELL[lab[j]] = nnt;
while (ptn[j++] > level);
SIZE[nnt] = j-i;
++nnt;
i = j;
}
else
{
NNTCELL[lab[i]] = n;
++i;
}
}
if (nnt == 0) return n;
/* set COUNT[i] to # non-trivial neighbours of n.s. cell i */
for (i = 0; i < nnt; ++i) HITS[i] = COUNT[i] = 0;
for (i = 0; i < nnt; ++i)
{
vi = v[lab[START[i]]];
di = d[lab[START[i]]];
for (j = 0; j < di; ++j)
{
k = NNTCELL[e[vi+j]];
if (k != n) ++HITS[k];
}
for (j = 0; j < di; ++j)
{
k = NNTCELL[e[vi+j]];
if (k != n)
{
if (HITS[k] > 0 && HITS[k] < SIZE[k]) ++COUNT[i];
HITS[k] = 0;
}
}
}
/* find first greatest bucket value */
j = 0;
maxcnt = COUNT[0];
for (i = 1; i < nnt; ++i)
if (COUNT[i] > maxcnt)
{
j = i;
maxcnt = COUNT[i];
}
return (int)START[j];
}
/*****************************************************************************
* *
* targetcell_sg(g,lab,ptn,level,tc_level,digraph,hint,m,n) returns the *
* index in lab of the next cell to split. *
* hint is a suggestion for the answer, which is obeyed if it is valid. *
* Otherwise we use bestcell() up to tc_level and the first non-trivial *
* cell after that. *
* *
*****************************************************************************/
int
targetcell_sg(graph *g, int *lab, int *ptn, int level, int tc_level,
boolean digraph, int hint, int m, int n)
{
int i;
if (hint >= 0 && ptn[hint] > level &&
(hint == 0 || ptn[hint-1] <= level))
return hint;
else if (level <= tc_level)
return bestcell_sg(g,lab,ptn,level,tc_level,m,n);
else
{
for (i = 0; i < n && ptn[i] <= level; ++i) {}
return (i == n ? 0 : i);
}
}
/*****************************************************************************
* *
* sortlists_sg(g) sorts the adjacency lists into numerical order *
* *
*****************************************************************************/
void
sortlists_sg(sparsegraph *g)
{
int *d,*e;
int n,i;
size_t *v;
sg_weight *wt;
SWG_VDE(g,v,d,e,wt);
n = g->nv;
if (wt)
{
for (i = 0; i < n; ++i)
if (d[i] > 1) sortweights(e+v[i],wt+v[i],d[i]);
}
else
{
for (i = 0; i < n; ++i)
if (d[i] > 1) sortints(e+v[i],d[i]);
}
}
/*****************************************************************************
* *
* put_sg(f,sg,digraph,linelength) writes the sparse graph to file f using *
* at most linelength characters per line. If digraph then all directed *
* edges are written; else one v-w for w>=v is written. *
* *
*****************************************************************************/
void
put_sg(FILE *f, sparsegraph *sg, boolean digraph, int linelength)
{
int *d,*e;
int n,di;
int i,curlen,slen;
size_t *v,vi,j;
char s[12];
SG_VDE(sg,v,d,e);
n = sg->nv;
for (i = 0; i < n; ++i)
{
vi = v[i];
di = d[i];
if (di == 0) continue;
slen = itos(i+labelorg,s);
putstring(f,s);
putstring(f," :");
curlen = slen + 2;
for (j = 0; j < di; ++j)
{
if (!digraph && e[vi+j] < i) continue;
slen = itos(e[vi+j]+labelorg,s);
if (linelength && curlen + slen + 1 >= linelength)
{
putstring(f,"\n ");
curlen = 2;
}
PUTC(' ',f);
putstring(f,s);
curlen += slen + 1;
}
PUTC('\n',f);
}
}
/*****************************************************************************
* *
* sg_to_nauty(sg,g,reqm,&m) creates a nauty-format graph from a sparse *
* graph. reqm is the required m value (computed from n if reqm=0), and *
* m is the actual value used. g is dynamically generated if NULL is given. *
* A pointer to g is returned. *
* *
*****************************************************************************/
graph*
sg_to_nauty(sparsegraph *sg, graph *g, int reqm, int *pm)
{
int *d,*e;
int m,n,i,di;
size_t *v,vi,j;
set *gi;
SG_VDE(sg,v,d,e);
n = sg->nv;
if (reqm != 0 && reqm*WORDSIZE < n)
{
fprintf(ERRFILE,"sg_to_nauty: reqm is impossible\n");
exit(1);
}
if (reqm != 0) m = reqm;
else m = (n+WORDSIZE-1)/WORDSIZE;
*pm = m;
if (g == NULL)
{
if ((g = (graph*)ALLOCS(n,m*sizeof(graph))) == NULL)
{
fprintf(ERRFILE,"sg_to_nauty: malloc failed\n");
exit(1);
}
}
for (i = 0, gi = g; i < n; ++i, gi += m)
{
vi = v[i];
di = d[i];
EMPTYSET(gi,m);
for (j = 0; j < di; ++j) ADDELEMENT(gi,e[vi+j]);
}
return g;
}
/*****************************************************************************
* *
* copy_sg(sg1,sg2) makes a copy of sg1 into sg2. *
* If sg2 is not NULL, it is assumed that the vlen,dlen,elen fields are *
* correct and v,d,e are dynamically allocated (or NULL); they are *
* reallocated if necessary. If sg2==NULL, a new structure is allocated. *
* A pointer to the copy is returned. *
* The new graph e component is the same, no compression is done. *
* *
*****************************************************************************/
sparsegraph*
copy_sg(sparsegraph *sg1, sparsegraph *sg2)
{
int *d1,*e1,*d2,*e2;
int i,n;
size_t *v1,*v2,k;
sg_weight *wt1,*wt2;
if (!sg2)
{
if ((sg2 = (sparsegraph*)ALLOCS(1,sizeof(sparsegraph))) == NULL)
{
fprintf(ERRFILE,"copy_sg: malloc failed\n");
exit(1);
}
SG_INIT(*sg2);
}
SWG_VDE(sg1,v1,d1,e1,wt1);
n = sg1->nv;
k = 0;
for (i = 0; i < n; ++i)
if (v1[i]+d1[i]>k) k = v1[i] + d1[i];
if (wt1)
SWG_ALLOC(*sg2,n,k,"copy_sg malloc");
else
{
SG_ALLOC(*sg2,n,k,"copy_sg malloc");
DYNFREE(sg2->w,sg2->wlen);
}
SWG_VDE(sg2,v2,d2,e2,wt2);
sg2->nv = n;
sg2->nde = sg1->nde;
memcpy(v2,v1,n*sizeof(size_t));
memcpy(d2,d1,n*sizeof(int));
memcpy(e2,e1,k*sizeof(int));
if (wt1) memcpy(wt2,wt1,k*sizeof(sg_weight));
return sg2;
}
/*****************************************************************************
* *
* nauty_to_sg(g,sg,m,n) creates a sparse graph from a nauty format graph *
* If sg is not NULL, it is assumed that the vlen,dlen,elen fields are *
* correct and v,d,e are dynamically allocated (or NULL); they are *
* reallocated if necessary. If sg==NULL, a new structure is allocated. *
* A pointer to the sparse graph is returned. *
* *
*****************************************************************************/
sparsegraph*
nauty_to_sg(graph *g, sparsegraph *sg, int m, int n)
{
int *d,*e;
int i,k;
set *gi;
size_t j,*v,nde;
if (!sg)
{
if ((sg = (sparsegraph*)ALLOCS(1,sizeof(sparsegraph))) == NULL)
{
fprintf(ERRFILE,"nauty_to_sg: malloc failed\n");
exit(1);
}
SG_INIT(*sg);
}
nde = 0;
for (gi = g + (size_t)m*(size_t)n; --gi >= g; )
if (*gi != 0) nde += POPCOUNT(*gi);
sg->nv = n;
sg->nde = nde;
SG_ALLOC(*sg,n,nde,"nauty_to_sg");
SG_VDE(sg,v,d,e);
j = 0;
for (i = 0, gi = g; i < n; ++i, gi += m)
{
v[i] = j;
for (k = -1; (k = nextelement(gi,m,k)) >= 0; )
e[j++] = k;
d[i] = j - v[i];
}
return sg;
}
/*****************************************************************************
* *
* distances_sg() assigns to each vertex v a value depending on the number *
* of vertices at each distance from v, and what cells they lie in. *
* If we find any cell which is split in this manner, we don't try any *
* further cells. *
* *
*****************************************************************************/
void
distances_sg(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos,
int *invar, int invararg, boolean digraph, int m, int n)
{
int *d,*e;
int i,k,dlim,wt;
int di;
int cell1,cell2,iv,liv,kcode;
int head,tail;
long longcode;
size_t *v,vi,j;
boolean success;
SG_VDE(g,v,d,e);
#if !MAXN
DYNALLOC1(int,work1,work1_sz,n,"distances_sg");
DYNALLOC1(int,work4,work4_sz,n,"distances_sg");
DYNALLOC1(int,work3,work3_sz,n,"distances_sg");
#endif
#define CELLCODE work1
#define QUEUE work4
#define DIST work3
for (i = n; --i >= 0;) invar[i] = 0;
wt = 1;
for (i = 0; i < n; ++i)
{
CELLCODE[lab[i]] = FUZZ1(wt);
if (ptn[i] <= level) ++wt;
}
if (invararg > n || invararg == 0) dlim = n;
else dlim = invararg+1;
success = FALSE;
for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{
for (cell2 = cell1; ptn[cell2] > level; ++cell2) {}
if (cell2 == cell1) continue;
for (iv = cell1; iv <= cell2; ++iv)
{
liv = lab[iv];
QUEUE[0] = liv;
DIST[liv] = 0;
RESETMARKS1;
MARK1(liv);
longcode = 0;
head = 0;
tail = 1;
while (tail < n && head < tail)
{
i = QUEUE[head++];
if (DIST[i] >= dlim) break;
vi = v[i];
di = d[i];
for (j = 0; j < di; ++j)
{
k = e[vi+j];
if (ISNOTMARKED1(k))
{
MARK1(k);
DIST[k] = DIST[i] + 1;
kcode = DIST[k]+CELLCODE[k];
ACCUM(longcode,FUZZ1(kcode));
QUEUE[tail++] = k;
}
}
}
invar[liv] = CLEANUP(longcode);
if (invar[liv] != invar[lab[cell1]]) success = TRUE;
}
if (success) break;
}
}
/*****************************************************************************
* *
* adjacencies_sg() assigns to each vertex v a code depending on which cells *
* it is joined to and from, and how many times. It is intended to provide *
* better partitioning that the normal refinement routine for digraphs. *
* It will not help with undirected graphs in nauty at all. *
* *
*****************************************************************************/
void
adjacencies_sg(graph *g, int *lab, int *ptn, int level, int numcells,
int tvpos, int *invar, int invararg, boolean digraph,
int m, int n)
{
int *d,*e;
int vwt,wwt;
int *ei,di,i;
size_t *v,j;
SG_VDE(g,v,d,e);
#if !MAXN
DYNALLOC1(int,work2,work2_sz,n,"adjacencies_sg");
#endif
vwt = 1;
for (i = 0; i < n; ++i)
{
work2[lab[i]] = vwt;
if (ptn[i] <= level) ++vwt;
invar[i] = 0;
}
for (i = 0; i < n; ++i)
{
vwt = FUZZ1(work2[i]);
wwt = 0;
di = d[i];
ei = e + v[i];
for (j = 0; j < di; ++j)
{
ACCUM(wwt,FUZZ2(work2[ei[j]]));
ACCUM(invar[ei[j]],vwt);
}
ACCUM(invar[i],wwt);
}
}
/*****************************************************************************
* *
* sparsenauty(g,lab,ptn,orbits,&options,&stats,h) *
* is a slightly simplified interface to nauty(). It allocates enough *
* workspace for 500 automorphisms and checks that the sparsegraph dispatch *
* vector is in use. *
* *
*****************************************************************************/
void
sparsenauty(sparsegraph *g, int *lab, int *ptn, int *orbits,
optionblk *options, statsblk *stats, sparsegraph *h)
{
int m,n;
if (options->dispatch != &dispatch_sparse)
{
fprintf(ERRFILE,"Error: sparsenauty() needs standard options block\n");
exit(1);
}
n = g->nv;
m = SETWORDSNEEDED(n);
#if !MAXN
/* Don't increase 2*500*m in the following without also increasing
the static decalaration of snwork[] above. */
DYNALLOC1(set,snwork,snwork_sz,2*500*m,"densenauty malloc");
#endif
nauty((graph*)g,lab,ptn,NULL,orbits,options,stats,
snwork,2*500*m,m,n,(graph*)h);
}
/*****************************************************************************
* *
* nausparse_check() checks that this file is compiled compatibly with the *
* given parameters. If not, call exit(1). *
* *
*****************************************************************************/
void
nausparse_check(int wordsize, int m, int n, int version)
{
if (wordsize != WORDSIZE)
{
fprintf(ERRFILE,"Error: WORDSIZE mismatch in nausparse.c\n");
exit(1);
}
#if MAXN
if (m > MAXM)
{
fprintf(ERRFILE,"Error: MAXM inadequate in nausparse.c\n");
exit(1);
}
if (n > MAXN)
{
fprintf(ERRFILE,"Error: MAXN inadequate in nausparse.c\n");
exit(1);
}
#endif
if (version < NAUTYREQUIRED)
{
fprintf(ERRFILE,"Error: nausparse.c version mismatch\n");
exit(1);
}
}
/*****************************************************************************
* *
* nausparse_freedyn() - free the dynamic memory in this module *
* *
*****************************************************************************/
void
nausparse_freedyn(void)
{
#if !MAXN
DYNFREE(vmark1,vmark1_sz);
DYNFREE(vmark2,vmark2_sz);
DYNFREE(work1,work1_sz);
DYNFREE(work2,work2_sz);
DYNFREE(work3,work3_sz);
DYNFREE(work4,work4_sz);
DYNFREE(snwork,snwork_sz);
#endif
}
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