static void
fragments(int *x, int nx, int *frag, int *nfrag)
/* For each v in union(x[0..nx-1]), find the components of the
hypergraph x - v and add them to frag if there are more than one. */
/* This implementation is shocking. Improve it! */
{
int allx,i,j,v;
int vbit,nw,w[MAXN];
boolean done;
allx = 0;
for (i = 0; i < nx; ++i) allx |= x[i];
*nfrag = 0;
while (allx)
{
v = XNEXTBIT(allx);
vbit = xbit[v];
allx &= ~vbit;
for (i = 0; i < nx; ++i) w[i] = x[i] & ~vbit;
nw = nx;
done = FALSE;
while (!done && nw > 1)
{
done = TRUE;
for (i = 0; i < nw-1; ++i)
for (j = i+1; j < nw; )
if ((w[i] & w[j]) != 0)
{
w[i] |= w[j];
w[j] = w[nw-1];
--nw;
done = FALSE;
}
else
++j;
}
if (nw > 1)
for (i = 0; i < nw; ++i)
frag[(*nfrag)++] = w[i];
}
}
static UPROC
userautomproc(int count, int *p, int *orbits, int numorbits,
int stabvertex, int n)
/* Automorphism procedure called by nauty
Form orbits on powerset of VG
Operates on data[n-n1] */
{
int i,j1,j2;
int moved,pxi,pi;
int w,lo,hi;
int *xorb;
xorb = data[n-n1].xorb;
lo = data[n-n1].lo;
hi = data[n-n1].hi;
if (count == 1) /* first automorphism */
for (i = lo; i < hi; ++i) xorb[i] = i;
moved = 0;
for (i = 0; i < n; ++i)
if (p[i] != i) moved |= xbit[i];
for (i = lo; i < hi; ++i)
{
if ((w = xset[i] & moved) == 0) continue;
pxi = xset[i] & ~moved;
while (w)
{
j1 = XNEXTBIT(w);
w &= ~xbit[j1];
pxi |= xbit[p[j1]];
}
pi = xinv[pxi];
j1 = xorb[i];
while (xorb[j1] != j1) j1 = xorb[j1];
j2 = xorb[pi];
while (xorb[j2] != j2) j2 = xorb[j2];
if (j1 < j2) xorb[j2] = xorb[i] = xorb[pi] = j1;
else if (j1 > j2) xorb[j1] = xorb[i] = xorb[pi] = j2;
}
}
static void
userautomproc(int count, int *p, int *orbits,
int numorbits, int stabvertex, int n)
/* form orbits on powerset of VG
called by nauty; operates on data[n] */
{
xword i,j1,j2,moved,pi,pxi;
xword lo,hi;
xword *xorb,*xinv,*xset,w;
xorb = data[n].xorb;
xset = data[n].xset;
xinv = data[n].xinv;
lo = data[n].lo;
hi = data[n].hi;
if (count == 1) /* first automorphism */
for (i = lo; i < hi; ++i) xorb[i] = i;
moved = 0;
for (i = 0; i < n; ++i)
if (p[i] != i) moved |= xbit[i];
for (i = lo; i < hi; ++i)
{
if ((w = xset[i] & moved) == 0) continue;
pxi = xset[i] & ~moved;
while (w)
{
j1 = XNEXTBIT(w);
w ^= xbit[j1];
pxi |= xbit[p[j1]];
}
pi = xinv[pxi];
j1 = xorb[i];
while (xorb[j1] != j1) j1 = xorb[j1];
j2 = xorb[pi];
while (xorb[j2] != j2) j2 = xorb[j2];
if (j1 < j2) xorb[j2] = xorb[i] = xorb[pi] = j1;
else if (j1 > j2) xorb[j1] = xorb[i] = xorb[pi] = j2;
}
}
static boolean
accept2(graph *g, int n2, int x, graph *gx, int *deg, boolean nuniq)
/* decide if n in theta(g+x) -- version for n+1 == maxn */
{
int i,n;
int lab[MAXN],ptn[MAXN],orbits[MAXN];
int degx[MAXN],invar[MAXN];
setword vmax,gv;
int qn,qv;
int count[MAXN];
int xw;
int nx,numcells,code;
int degn,i0,i1,j,j0,j1;
set active[MAXM];
statsblk stats;
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[50];
#ifdef INSTRUMENT
++a2calls;
if (nuniq) ++a2uniq;
#endif
n = n1 + n2;
nx = n + 1;
for (i = 0; i < n; ++i)
{
gx[i] = g[i];
degx[i] = deg[i];
}
gx[n] = 0;
degx[n] = degn = XPOPCOUNT(x);
xw = x;
while (xw)
{
i = XNEXTBIT(xw);
xw &= ~xbit[i];
gx[i] |= bit[n];
gx[n] |= bit[i];
++degx[i];
}
#ifdef PRUNE1
if (PRUNE1(gx,degx,n1,n2+1,maxn2)) return FALSE;
#endif
if (nuniq)
{
#ifdef INSTRUMENT
++a2succs;
#endif
#ifdef PRUNE2
if (PRUNE2(gx,degx,n1,n2+1,maxn2)) return FALSE;
#endif
if (canonise) makecanon(gx,gcan,n1,n2+1);
return TRUE;
}
for (i = 0; i < n1; ++i)
{
lab[i] = i;
ptn[i] = 1;
}
ptn[n1-1] = 0;
i0 = n1;
i1 = n;
for (i = n1; i < nx; ++i)
{
if (degx[i] == degn) lab[i1--] = i;
else lab[i0++] = i;
ptn[i] = 1;
}
ptn[n] = 0;
if (i0 == n1)
{
numcells = 2;
active[0] = bit[0] | bit[n1];
if (!distinvar(gx,invar,n1,n2+1)) return FALSE;
qn = invar[n];
j0 = n1;
j1 = n;
while (j0 <= j1)
{
j = lab[j0];
qv = invar[j];
if (qv < qn)
++j0;
else
{
lab[j0] = lab[j1];
lab[j1] = j;
--j1;
}
}
if (j0 > n1)
{
if (j0 == n)
{
#ifdef INSTRUMENT
++a2succs;
#endif
#ifdef PRUNE2
if (PRUNE2(gx,degx,n1,n2+1,maxn2)) return FALSE;
#endif
if (canonise) makecanon(gx,gcan,n1,n2+1);
return TRUE;
}
ptn[j1] = 0;
++numcells;
active[0] |= bit[j0];
}
}
else
{
numcells = 3;
ptn[i1] = 0;
active[0] = bit[0] | bit[n1] | bit[i1+1];
vmax = 0;
j = MAXN;
for (i = 0; i < n1; ++i)
if (degx[i] < j && degx[i] > 0)
{
j = degx[i];
vmax = bit[i];
}
else if (degx[i] == j)
vmax |= bit[i];
gv = gx[n] & vmax;
qn = POPCOUNT(gv);
j0 = i1+1;
j1 = n;
while (j0 <= j1)
{
j = lab[j0];
gv = gx[j] & vmax;
qv = POPCOUNT(gv);
if (qv > qn)
return FALSE;
else if (qv < qn)
++j0;
else
{
lab[j0] = lab[j1];
lab[j1] = j;
--j1;
}
}
if (j0 > i1+1)
{
if (j0 == n)
{
#ifdef INSTRUMENT
++a2succs;
#endif
#ifdef PRUNE2
if (PRUNE2(gx,degx,n1,n2+1,maxn2)) return FALSE;
#endif
if (canonise) makecanon(gx,gcan,n1,n2+1);
return TRUE;
}
ptn[j1] = 0;
++numcells;
active[0] |= bit[j0];
}
}
refinex(gx,lab,ptn,0,&numcells,count,active,TRUE,&code,1,nx);
if (code < 0)
return FALSE;
else if (code > 0 || numcells >= nx-4)
{
#ifdef INSTRUMENT
++a2succs;
#endif
#ifdef PRUNE2
if (PRUNE2(gx,degx,n1,n2+1,maxn2)) return FALSE;
#endif
if (canonise) makecanon(gx,gcan,n1,n2+1);
return TRUE;
}
options.writemarkers = FALSE;
options.writeautoms = FALSE;
options.getcanon = TRUE;
options.defaultptn = FALSE;
active[0] = 0;
#ifdef INSTRUMENT
++a2nauty;
#endif
nauty(gx,lab,ptn,active,orbits,&options,&stats,workspace,50,1,nx,gcan);
if (orbits[lab[n]] == orbits[n])
{
#ifdef INSTRUMENT
++a2succs;
#endif
#ifdef PRUNE2
if (PRUNE2(gx,degx,n1,n2+1,maxn2)) return FALSE;
#endif
if (canonise) makecanon(gx,gcan,n1,n2+1);
return TRUE;
}
else
return FALSE;
}
static boolean
accept1(graph *g, int n2, int x, graph *gx, int *deg, boolean *rigid)
/* decide if n2 in theta(g+x) -- version for n2+1 < maxn2 */
{
int i,n;
int lab[MAXN],ptn[MAXN],orbits[MAXN];
int count[MAXN];
graph h[MAXN];
int xw;
int nx,numcells,code;
int i0,i1,degn;
set active[MAXM];
statsblk stats;
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[50];
#ifdef INSTRUMENT
++a1calls;
#endif
n = n1 + n2;
nx = n + 1;
for (i = 0; i < n; ++i) gx[i] = g[i];
gx[n] = 0;
deg[n] = degn = XPOPCOUNT(x);
xw = x;
while (xw)
{
i = XNEXTBIT(xw);
xw &= ~xbit[i];
gx[i] |= bit[n];
gx[n] |= bit[i];
++deg[i];
}
#ifdef PRUNE1
if (PRUNE1(gx,deg,n1,n2+1,maxn2)) return FALSE;
#endif
for (i = 0; i < n1; ++i)
{
lab[i] = i;
ptn[i] = 1;
}
ptn[n1-1] = 0;
i0 = n1;
i1 = n;
for (i = n1; i < nx; ++i)
{
if (deg[i] == degn) lab[i1--] = i;
else lab[i0++] = i;
ptn[i] = 1;
}
ptn[n] = 0;
if (i0 == n1)
{
numcells = 2;
active[0] = bit[0] | bit[n1];
}
else
{
numcells = 3;
active[0] = bit[0] | bit[n1] | bit[i1+1];
ptn[i1] = 0;
}
refinex(gx,lab,ptn,0,&numcells,count,active,FALSE,&code,1,nx);
if (code < 0) return FALSE;
if (numcells == nx)
{
*rigid = TRUE;
#ifdef INSTRUMENT
++a1succs;
#endif
#ifdef PRUNE2
if (PRUNE2(gx,deg,n1,n2+1,maxn2)) return FALSE;
#endif
return TRUE;
}
options.writemarkers = FALSE;
options.writeautoms = FALSE;
options.getcanon = TRUE;
options.defaultptn = FALSE;
options.userautomproc = userautomproc;
active[0] = 0;
#ifdef INSTRUMENT
++a1nauty;
#endif
nauty(gx,lab,ptn,active,orbits,&options,&stats,workspace,50,1,nx,h);
if (orbits[lab[n]] == orbits[n])
{
*rigid = stats.numorbits == nx;
#ifdef INSTRUMENT
++a1succs;
#endif
#ifdef PRUNE2
if (PRUNE2(gx,deg,n1,n2+1,maxn2)) return FALSE;
#endif
return TRUE;
}
else
return FALSE;
}
