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gutil2.c
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gutil2.c
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/* gutil2.c: Some more graph utilities. */
#include "gtools.h"
#include "gutils.h"
/**************************************************************************/
int
loopcount(graph *g, int m, int n)
/* Number of loops */
{
set *gi;
int i,nl;
nl = 0;
for (i = 0, gi = g; i < n; ++i, gi += m)
if (ISELEMENT(gi,i)) ++nl;
return nl;
}
/**************************************************************************/
long
pathcount1(graph *g, int start, setword body, setword last)
/* Number of paths in g starting at start, lying within body and
ending in last. {start} and last should be disjoint subsets of body. */
{
long count;
setword gs,w;
int i;
gs = g[start];
w = gs & last;
count = POPCOUNT(w);
body &= ~bit[start];
w = gs & body;
while (w)
{
TAKEBIT(i,w);
count += pathcount1(g,i,body,last&~bit[i]);
}
return count;
}
/**************************************************************************/
long
cyclecount1(graph *g, int n)
/* The total number of cycles in g (assumed no loops), m=1 only */
{
setword body,nbhd;
long total;
int i,j;
body = ALLMASK(n);
total = 0;
for (i = 0; i < n-2; ++i)
{
body ^= bit[i];
nbhd = g[i] & body;
while (nbhd)
{
TAKEBIT(j,nbhd);
total += pathcount1(g,j,body,nbhd);
}
}
return total;
}
/**************************************************************************/
long
cyclecount(graph *g, int m, int n)
/* The total number of cycles in g (assumed no loops) */
{
if (m == 1) return cyclecount1(g,n);
gt_abort(">E cycle counting is only implemented for n <= WORDSIZE\n");
return 0;
}
/**************************************************************************/
long
indpathcount1(graph *g, int start, setword body, setword last)
/* Number of induced paths in g starting at start, extravertices within
* body and ending in last.
* {start}, body and last should be disjoint. */
{
long count;
setword gs,w;
int i;
gs = g[start];
w = gs & last;
count = POPCOUNT(w);
w = gs & body;
while (w)
{
TAKEBIT(i,w);
count += indpathcount1(g,i,body&~gs,last&~bit[i]&~gs);
}
return count;
}
/**************************************************************************/
long
indcyclecount1(graph *g, int n)
/* The total number of induced cycles in g (assumed no loops), m=1 only */
{
setword body,last,cni;
long total;
int i,j;
body = ALLMASK(n);
total = 0;
for (i = 0; i < n-2; ++i)
{
body ^= bit[i];
last = g[i] & body;
cni = g[i] | bit[i];
while (last)
{
TAKEBIT(j,last);
total += indpathcount1(g,j,body&~cni,last);
}
}
return total;
}
/**************************************************************************/
long
indcyclecount(graph *g, int m, int n)
/* The total number of induced cycles in g (assumed no loops) */
{
if (m == 1) return indcyclecount1(g,n);
gt_abort(
">E induced cycle counting is only implemented for n <= WORDSIZE\n");
return 0;
}
/**************************************************************************/
long
numtriangles1(graph *g, int n)
/* The number of triangles in g */
{
int i,j;
setword gi,w;
long total;
total = 0;
for (i = 0; i < n-2; ++i)
{
gi = g[i] & BITMASK(i);
while (gi)
{
TAKEBIT(j,gi);
w = g[j] & gi;
if (w) total += POPCOUNT(w);
}
}
return total;
}
/**************************************************************************/
long
numtriangles(graph *g, int m, int n)
/* The number of triangles in g */
{
int i,j,k,kw;
setword *gi,*gj,w;
long total;
if (m == 1) return numtriangles1(g,n);
total = 0;
for (i = 0, gi = g; i < n-2; ++i, gi += m)
for (j = i; (j = nextelement(gi,m,j)) > 0; )
{
gj = GRAPHROW(g,j,m);
kw = SETWD(j);
w = gi[kw] & gj[kw] & BITMASK(SETBT(j));
if (w) total += POPCOUNT(w);
for (k = kw+1; k < m; ++k)
{
w = gi[k] & gj[k];
if (w) total += POPCOUNT(w);
}
}
return total;
}
/**************************************************************************/
long
numdirtriangles(graph *g, int m, int n)
/* The number of directed triangles in g */
{
long total;
int i,j,k;
set *gi,*gj;
total = 0;
for (i = 0, gi = g; i < n-2; ++i, gi += m)
for (j = i; (j = nextelement(gi,m,j)) >= 0;)
{
gj = GRAPHROW(g,j,m);
for (k = i; (k = nextelement(gj,m,k)) >= 0; )
if (k != j && ISELEMENT(GRAPHROW(g,k,m),i)) ++total;
}
return total;
}
/**************************************************************************/
void
commonnbrs(graph *g, int *minadj, int *maxadj, int *minnon, int *maxnon,
int m, int n)
/* Count the common neighbours of pairs of vertices, and give the minimum
and maximum for adjacent and non-adjacent vertices. Undirected only.
Null minimums are n+1 and null maximums are -1.
*/
{
int j,k;
int mina,maxa,minn,maxn;
int cn;
set *gi,*gj;
setword w;
mina = minn = n+1;
maxa = maxn = -1;
for (j = 0, gj = g; j < n; ++j, gj += m)
for (gi = g; gi != gj; gi += m)
{
cn = 0;
for (k = 0; k < m; ++k)
{
w = gi[k] & gj[k];
if (w) cn += POPCOUNT(w);
}
if (ISELEMENT(gi,j))
{
if (cn < mina) mina = cn;
if (cn > maxa) maxa = cn;
}
else
{
if (cn < minn) minn = cn;
if (cn > maxn) maxn = cn;
}
}
*minadj = mina;
*maxadj = maxa;
*minnon = minn;
*maxnon = maxn;
}
/**************************************************************************/
void
delete1(graph *g, graph *h, int v, int n)
/* Delete vertex v from g, result in h */
{
setword mask1,mask2,gi;
int i;
mask1 = ALLMASK(v);
mask2 = BITMASK(v);
for (i = 0; i < v; ++i)
{
gi = g[i];
h[i] = (gi & mask1) | ((gi & mask2) << 1);
}
for (i = v; i < n-1; ++i)
{
gi = g[i+1];
h[i] = (gi & mask1) | ((gi & mask2) << 1);
}
}
/**************************************************************************/
void
contract1(graph *g, graph *h, int v, int w, int n)
/* Contract distinct vertices v and w (not necessarily adjacent)
with result in h. No loops are created. */
{
int x,y;
setword bitx,bity,mask1,mask2;
int i;
if (w < v)
{
x = w;
y = v;
}
else
{
x = v;
y = w;
}
bitx = bit[x];
bity = bit[y];
mask1 = ALLMASK(y);
mask2 = BITMASK(y);
for (i = 0; i < n; ++i)
if (g[i] & bity)
h[i] = (g[i] & mask1) | bitx | ((g[i] & mask2) << 1);
else
h[i] = (g[i] & mask1) | ((g[i] & mask2) << 1);
h[x] |= h[y];
for (i = y+1; i < n; ++i) h[i-1] = h[i];
h[x] &= ~bitx;
}
/**************************************************************************/
static TLS_ATTR int knm[18][16]; /* knm[n,m] = conncontent(K_n - m*K_2) */
static TLS_ATTR boolean knm_computed = FALSE;
int
conncontent(graph *g, int m, int n)
/* number of connected spanning subgraphs with an even number
of edges minus the number with an odd number of edges */
{
graph h[WORDSIZE];
setword gj;
int i,j,v1,v2,x,y;
int minv,mindeg,deg,goodv;
long ne;
if (m > 1) ABORT("conncontent only implemented for m=1");
/* First handle tiny graphs */
if (n <= 3)
{
if (n == 1) return 1;
if (n == 2) return (g[0] ? -1 : 0);
if (!g[0] || !g[1] || !g[2]) return 0; /* disconnected */
if (g[0]^g[1]^g[2]) return 1; /* path */
return 2; /* triangle */
}
/* Now compute
ne = number of edges
mindeg = minimum degree
minv = a vertex of minimum degree
goodv = a vertex with a clique neighbourhood (-1 if none)
*/
mindeg = n;
ne = 0;
goodv = -1;
for (j = 0; j < n; ++j)
{
gj = g[j];
deg = POPCOUNT(gj);
ne += deg;
if (deg < mindeg)
{
mindeg = deg;
minv = j;
if (deg == 1) goodv = j;
}
if (deg >= 3 && deg <= 4 && goodv < 0)
{
while (gj)
{
TAKEBIT(i,gj);
if (gj & ~g[i]) break;
}
if (!gj) goodv = j;
}
}
ne /= 2;
/* Cases of isolated vertex or tree */
if (mindeg == 0) return 0;
#if 0
if (mindeg == 1 && ne == n-1)
{
if (isconnected1(g,n)) return ((n&1) ? 1 : -1);
else return 0;
}
#endif
/* Cases of clique and near-clique */
if (mindeg == n-1)
{
j = -1;
for (i = 2; i < n; ++i) j *= -i;
return j;
}
if (mindeg == n-2 && n < 16)
{
if (!knm_computed)
{
knm_computed = TRUE;
knm[1][0] = 1;
for (i = 2; i < 16; ++i)
{
knm[i][0] = -knm[i-1][0] * (i-1);
for (j = 1; j+j <= i; ++j)
knm[i][j] = knm[i][j-1] + knm[i-1][j-1];
}
}
return knm[n][(n*n-n)/2-ne];
}
/* Case of vertex with clique neighbourhood */
if (goodv >= 0)
{
delete1(g,h,goodv,n);
return -POPCOUNT(g[goodv]) * conncontent(h,m,n-1);
}
/* Case of minimum degree 2 */
if (mindeg == 2)
{
x = FIRSTBITNZ(g[minv]);
y = FIRSTBITNZ(g[minv]^bit[x]);
if (x > minv) --x;
if (y > minv) --y;
delete1(g,h,minv,n);
v1 = conncontent(h,m,n-1);
if (h[x] & bit[y]) return -2*v1; /* adjacent neighbours */
h[x] |= bit[y];
h[y] |= bit[x];
v2 = conncontent(h,m,n-1);
return -v1 - v2;
}
/* Case of more than 2/3 dense but not complete */
if (3*ne > n*n-n)
{
j = FIRSTBITNZ(g[minv] ^ bit[minv] ^ ALLMASK(n)); /* non-neighbour */
g[minv] ^= bit[j];
g[j] ^= bit[minv];
v1 = conncontent(g,m,n);
g[minv] ^= bit[j];
g[j] ^= bit[minv];
contract1(g,h,minv,j,n);
v2 = conncontent(h,m,n-1);
return v1 + v2;
}
/* All remaining cases */
j = FIRSTBITNZ(g[minv]); /* neighbour */
g[minv] ^= bit[j];
g[j] ^= bit[minv];
v1 = conncontent(g,m,n);
g[minv] ^= bit[j];
g[j] ^= bit[minv];
contract1(g,h,minv,j,n);
v2 = conncontent(h,m,n-1);
return v1 - v2;
}
boolean
stronglyconnected(graph *g, int m, int n)
/* test if digraph g is strongly connected */
{
int sp,v,vc;
int numvis;
set *gv;
#if MAXN
int num[MAXN],lowlink[MAXN],stack[MAXN];
#else
DYNALLSTAT(int,num,num_sz);
DYNALLSTAT(int,lowlink,lowlink_sz);
DYNALLSTAT(int,stack,stack_sz);
#endif
#if !MAXN
DYNALLOC1(int,num,num_sz,n,"stronglyconnected");
DYNALLOC1(int,lowlink,lowlink_sz,n,"stronglyconnected");
DYNALLOC1(int,stack,stack_sz,n,"stronglyconnected");
#endif
num[0] = 0;
for (v = 1; v < n; ++v) num[v] = -1;
lowlink[0] = 0;
numvis = 1;
sp = 0;
v = 0;
vc = -1;
gv = (set*)g;
for (;;)
{
vc = nextelement(gv,m,vc);
if (vc < 0)
{
if (sp == 0) break;
if (lowlink[v] == num[v]) return FALSE;
vc = v;
v = stack[--sp];
gv = GRAPHROW(g,v,m);
if (lowlink[vc] < lowlink[v]) lowlink[v] = lowlink[vc];
}
else if (num[vc] < 0)
{
stack[++sp] = vc;
v = vc;
gv = GRAPHROW(g,v,m);
vc = -1;
lowlink[v] = num[v] = numvis++;
}
else if (vc != v)
{
if (num[vc] < lowlink[v]) lowlink[v] = num[vc];
}
}
return numvis == n;
}
/**************************************************************************/

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