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multig.c
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/* multig.c version 1.7; B D McKay, May 17, 2014 */
#define USAGE \
"multig [-q] [-u|-T|-G|-A|-B] [-e#|-e#:#] \n" \
" [-m#] [-f#] [-D#|-r#|-l#] [infile [outfile]]"
#define HELPTEXT \
" Read undirected loop-free graphs and replace their edges with multiple\n\
edges in all possible ways (multiplicity at least 1).\n\
Isomorphic multigraphs derived from the same input are suppressed.\n\
If the input graphs are non-isomorphic then the output graphs are also.\n\
\n\
-e# | -e#:# specify a value or range of the total number of edges\n\
counting multiplicities\n\
-m# maximum edge multiplicity (minimum is 1)\n\
-D# upper bound on maximum degree\n\
-r# make regular of specified degree (incompatible with -l, -D, -e)\n\
-l# make regular multigraphs with multiloops, degree #\n\
(incompatible with -r, -D, -e)\n\
Either -l, -r, -D, -e or -m with a finite maximum must be given\n\
-f# Use the group that fixes the first # vertices setwise\n\
-T use a simple text output format (nv ne {v1 v2 mult})\n\
-G like -T but includes group size as third item (if less than 10^10)\n\
The group size does not include exchange of isolated vertices.\n\
-A write as the upper triangle of an adjacency matrix, row by row,\n\
including the diagonal, and preceded by the number of vertices\n\
-B write as an integer matrix preceded by the number of rows and\n\
number of columns, where -f determines the number of rows\n\
-u no output, just count them\n\
-q suppress auxiliary information\n"
/*************************************************************************/
#include "gtools.h"
#include "naugroup.h"
nauty_counter mg_nin,mg_nout,mg_skipped;
FILE *outfile;
#define MAXNV 128
#define MAXNE 1024
static int v0[MAXNE+MAXNV],v1[MAXNE+MAXNV];
static int edgeno[MAXNV][MAXNV];
static int lastlev[MAXNE];
static int ix[MAXNE+MAXNV],nix;
static boolean first;
static int lastreject[MAXNV];
static boolean lastrejok;
static unsigned long groupsize;
static unsigned long newgroupsize;
static boolean Gswitch,Tswitch,Aswitch,Bswitch;
static int Brows;
#define GROUPTEST_NOT
#ifdef GROUPTEST
static long long totallab;
#endif
#define PATHCOUNTS_NOT
#ifdef PATHCOUNTS
static long long count0,count1,count2,count3,count4,count5;
static nauty_counter oldlo;
#endif
/* INPUTGRAPH feature
*
* If INPUTGRAPH is defined, it must expand as the name of a procedure
* with prototype like int INPUTGRAPH(graph *g, int m, int n).
* This procedure will be called for each input graph before it is
* processed. The graph will be skipped if the value 0 is returned.
*/
/* If OUTPROC is defined at compile time, and -u is not used, the
* procedure OUTPROC is called for each graph. This must be linked
* by the compiler. The arguments are
* f = open output file
* n = number of vertices
* ne = number of edges
* gp = group size ignoring isolated vertices (note: may have overflowed)
* v0[*], v1[*], ix[*] = integer arrays. The edges are
* v0[i]-v1[i] with multiplicity ix[i] for i=0..ne-1. ix[i]>0 always.
*/
/* SUMMARY feature
*
* If SUMMARY is defined, it must expand as the name of a procedure
* with prototype void SUMMARY(void). It is called at the end before
* the normal summary (which can be suppressed with -q). The numbers of
* graphs read and multigraphs produced are available in the global variables
* mg_nin and mg_nout (type nauty_counter).
*/
#ifdef INPUTGRAPH
extern int INPUTGRAPH(graph*,int,int);
#endif
#ifdef OUTPROC
extern void OUTPROC(FILE*,int,int,unsigned long,int*,int*,int*);
#endif
#ifdef SUMMARY
extern void SUMMARY(void);
#endif
/**************************************************************************/
static void
writeautom(int *p, int n)
/* Called by allgroup. */
{
int i;
for (i = 0; i < n; ++i) printf(" %2d",p[i]);
printf("\n");
}
/**************************************************************************/
static boolean
ismax(int *p, int n)
/* test if x^p <= x */
{
int i,k;
for (i = 0; i < nix; ++i)
{
k = edgeno[p[v1[i]]][p[v0[i]]];
if (ix[k] > ix[i]) return FALSE;
else if (ix[k] < ix[i]) return TRUE;
}
++newgroupsize;
return TRUE;
}
/**************************************************************************/
static void
testmax(int *p, int n, int *abort)
/* Called by allgroup2. */
{
int i;
if (first)
{ /* only the identity */
first = FALSE;
return;
}
if (!ismax(p,n))
{
*abort = 1;
for (i = 0; i < n; ++i) lastreject[i] = p[i];
lastrejok = TRUE;
}
}
/**************************************************************************/
static void
printam(FILE *f, int n, int ne, int *ix)
/* Write adjacency matrix formats */
{
int i,j;
if (Aswitch)
{
fprintf(f,"%d ",n);
for (i = 0; i < n; ++i)
for (j = i; j < n; ++j)
fprintf(f," %d",(edgeno[i][j]>=0 ? ix[edgeno[i][j]]: 0));
fprintf(f,"\n");
}
else
{
if (Brows <= 0 || Brows > n)
{
fprintf(stderr,">E multig: impossible matrix size for output\n");
exit(1);
}
fprintf(f,"%d %d",Brows,n-Brows);
for (i = 0; i < Brows; ++i)
{
fprintf(f," ");
for (j = Brows; j < n; ++j)
fprintf(f," %d",(edgeno[i][j]>=0 ? ix[edgeno[i][j]]: 0));
}
fprintf(f,"\n");
}
}
/**************************************************************************/
static void
trythisone(grouprec *group,
boolean lswitch, int *deg, int maxdeg, int ne, int n)
/* Try one solution, accept if minimal. */
{
int i,ne2;
boolean accept;
nix = ne;
newgroupsize = 1;
if (!group || groupsize == 1)
accept = TRUE;
else if (lastrejok && !ismax(lastreject,n))
accept = FALSE;
else if (lastrejok && groupsize == 2)
accept = TRUE;
else
{
newgroupsize = 1;
first = TRUE;
if (allgroup2(group,testmax) == 0)
accept = TRUE;
else
accept = FALSE;
}
if (accept)
{
#ifdef GROUPTEST
if (groupsize % newgroupsize != 0)
gt_abort("group size error\n");
totallab += groupsize/newgroupsize;
#endif
++mg_nout;
if (outfile)
{
ne2 = ne;
if (lswitch)
for (i = 0; i < n; ++i)
if (deg[i] < maxdeg)
{
v0[ne2] = v1[ne2] = i;
ix[ne2] = (maxdeg-deg[i])/2;
++ne2;
}
#ifdef OUTPROC
OUTPROC(outfile,n,ne2,newgroupsize,v0,v1,ix);
#else
if (Aswitch || Bswitch)
printam(outfile,n,ne2,ix);
else
{
fprintf(outfile,"%d %d",n,ne2);
if (Gswitch) fprintf(outfile," %lu",newgroupsize);
for (i = 0; i < ne2; ++i)
fprintf(outfile," %d %d %d",v0[i],v1[i],ix[i]);
fprintf(outfile,"\n");
}
#endif
}
return;
}
else
return;
}
/**************************************************************************/
static void
scan(int level, int ne, long minedges, long maxedges, long sofar,
long maxmult, grouprec *group, int n)
/* Recursive scan for default case */
{
int left;
long min,max,k;
if (level == ne)
{
trythisone(group,FALSE,NULL,0,ne,n);
return;
}
left = ne - level - 1;
min = minedges - sofar - maxmult*left;
if (min < 1) min = 1;
max = maxedges - sofar - left;
if (max > maxmult) max = maxmult;
for (k = min; k <= max; ++k)
{
ix[level] = k;
scan(level+1,ne,minedges,maxedges,sofar+k,maxmult,group,n);
}
return;
}
/**************************************************************************/
static void
scan_md(int level, int ne, long minedges, long maxedges, long sofar,
long maxmult, grouprec *group, int n, int *deg, int maxdeg)
/* Recursive scan, maxdeg version */
{
int left;
int min,max,k;
int x1,x2;
if (level == ne)
{
trythisone(group,FALSE,deg,maxdeg,ne,n);
return;
}
x1 = v0[level];
x2 = v1[level];
left = ne - level - 1;
min = minedges - sofar - maxmult*left;
if (min < 1) min = 1;
max = maxedges - sofar - left;
if (max > maxmult) max = maxmult;
if (deg[x1] + max - 1 > maxdeg) max = maxdeg - deg[x1] + 1;
if (deg[x2] + max - 1 > maxdeg) max = maxdeg - deg[x2] + 1;
for (k = min; k <= max; ++k)
{
ix[level] = k;
deg[x1] += k-1; deg[x2] += k-1;
scan_md(level+1,ne,minedges,maxedges,sofar+k,maxmult,group,
n,deg,maxdeg);
deg[x1] -= k-1; deg[x2] -= k-1;
}
return;
}
/**************************************************************************/
static void
scan_lp(int level, int ne, long minedges, long maxedges, long sofar,
long maxmult, grouprec *group, int n, int *deg, int maxdeg)
/* Recursive scan, regular-with-loops version. */
{
int left;
long min,max,k;
int x1,x2;
boolean odd,even;
if (level == ne)
{
trythisone(group,TRUE,deg,maxdeg,ne,n);
return;
}
x1 = v0[level];
x2 = v1[level];
left = ne - level - 1;
min = minedges - sofar - maxmult*left;
if (min < 1) min = 1;
max = maxedges - sofar - left;
if (max > maxmult) max = maxmult;
if (deg[x1] + max - 1 > maxdeg) max = maxdeg - deg[x1] + 1;
if (deg[x2] + max - 1 > maxdeg) max = maxdeg - deg[x2] + 1;
odd = even = FALSE;
if (lastlev[x1] == level)
{
if (((maxdeg-deg[x1])&1) == 1) even = TRUE; else odd = TRUE;
}
if (lastlev[x2] == level)
{
if (((maxdeg-deg[x2])&1) == 1) even = TRUE; else odd = TRUE;
}
if (even && odd) return;
for (k = min; k <= max; ++k)
{
if (even && (k&1) == 1) continue;
if (odd && (k&1) == 0) continue;
ix[level] = k;
deg[x1] += k-1; deg[x2] += k-1;
scan_lp(level+1,ne,minedges,maxedges,sofar+k,maxmult,group,
n,deg,maxdeg);
deg[x1] -= k-1; deg[x2] -= k-1;
}
return;
}
/**************************************************************************/
static void
scan_reg(int level, int ne, long minedges, long maxedges, long sofar,
long maxmult, grouprec *group, int n, int *delta, int *def, int maxdeg)
/* Recursive scan, regular version. */
{
int left;
long min,max,k;
int x1,x2;
if (level == ne)
{
trythisone(group,FALSE,NULL,maxdeg,ne,n);
return;
}
x1 = v0[level];
x2 = v1[level];
left = ne - level - 1;
min = minedges - sofar - maxmult*left;
if (min < 1) min = 1;
max = maxedges - sofar - left;
if (max > maxmult) max = maxmult;
if (max > def[x1] + 1) max = def[x1] + 1;
if (max > def[x2] + 1) max = def[x2] + 1;
if (min < def[x2] + 1 - delta[x1]) min = def[x2] + 1 - delta[x1];
if (min < def[x1] + 1 - delta[x2]) min = def[x1] + 1 - delta[x2];
if (lastlev[x1] == level && min < def[x1] + 1) min = def[x1] + 1;
if (lastlev[x2] == level && min < def[x2] + 1) min = def[x2] + 1;
for (k = min; k <= max; ++k)
{
ix[level] = k;
delta[x1] += k-1 - def[x2];
delta[x2] += k-1 - def[x1];
def[x1] -= k-1;
def[x2] -= k-1;
scan_reg(level+1,ne,minedges,maxedges,sofar+k,maxmult,group,
n,delta,def,maxdeg);
def[x1] += k-1;
def[x2] += k-1;
delta[x1] -= k-1 - def[x2];
delta[x2] -= k-1 - def[x1];
}
return;
}
/**************************************************************************/
static void
multi(graph *g, int nfixed, long minedges, long maxedges, long maxmult,
int maxdeg, boolean lswitch, int m, int n)
{
static DEFAULTOPTIONS_GRAPH(options);
statsblk stats;
setword workspace[100];
grouprec *group;
int ne;
int i,j,k,j0,j1,thisdeg,maxd,x0,x1;
set *gi;
int lab[MAXNV],ptn[MAXNV],orbits[MAXNV],deg[MAXNV];
int delta[MAXNV],def[MAXNV];
set active[(MAXNV+WORDSIZE-1)/WORDSIZE];
boolean isreg;
#ifdef PATHCOUNTS
++count0;
#endif
j0 = -1; /* last vertex with degree 0 */
j1 = n; /* first vertex with degree > 0 */
ne = 0;
maxd = 0;
for (i = 0, gi = g; i < n; ++i, gi += m)
{
thisdeg = 0;
for (j = 0; j < m; ++j) thisdeg += POPCOUNT(gi[j]);
deg[i] = thisdeg;
if (thisdeg > maxd) maxd = thisdeg;
if (thisdeg == 0) lab[++j0] = i;
else lab[--j1] = i;
ne += thisdeg;
}
ne /= 2;
if (maxdeg >= 0 && maxd > maxdeg) return;
#ifdef PATHCOUNTS
++count1;
#endif
if (Aswitch || Bswitch)
for (i = 0; i < n; ++i)
for (j = 0; j < n; ++j)
edgeno[i][j] = -1;
if (ne == 0 && minedges <= 0
&& (!lswitch || (lswitch && (maxdeg&1) == 0)))
{
trythisone(NULL,lswitch,deg,maxdeg,0,n);
return;
}
#ifdef PATHCOUNTS
++count2;
#endif
k = 0;
for (i = 0, gi = g; i < n; ++i, gi += m)
{
for (j = i; (j = nextelement(gi,m,j)) >= 0; )
{
v0[k] = i;
v1[k] = j;
edgeno[i][j] = edgeno[j][i] = k;
lastlev[i] = lastlev[j] = k;
++k;
}
}
isreg = !lswitch && (maxdeg >= 0 && 2*minedges == n*(long)maxdeg);
/* Case of regular multigraphs */
if (isreg) /* regular case */
/* Condition: def(v) <= total def of neighbours */
{
for (i = 0; i < n; ++i)
{
def[i] = maxdeg - deg[i];
delta[i] = -def[i];
}
for (i = 0; i < k; ++i)
{
x0 = v0[i]; x1 = v1[i];
delta[x0] += def[x1];
delta[x1] += def[x0];
}
for (i = 0; i < n; ++i) if (delta[i] < 0) return;
}
if ((isreg || lswitch) && (maxdeg & n & 1) == 1) return;
if (isreg && j0 >= 0 && maxdeg > 0) return;
if (lswitch && j0 >= 0 && (maxdeg&1) == 1) return;
#ifdef PATHCOUNTS
++count3;
#endif
if (maxedges == NOLIMIT)
{
if (maxmult == NOLIMIT) maxedges = maxdeg*n/2;
else maxedges = ne*maxmult;
}
if (maxmult == NOLIMIT) maxmult = maxedges - ne + 1;
if (maxdeg >= 0 && maxmult > maxdeg) maxmult = maxdeg;
if (maxedges < ne || ne*maxmult < minedges) return;
#ifdef PATHCOUNTS
++count4;
#endif
if (n > MAXNV || ne > MAXNE)
{
fprintf(stderr,">E multig: MAXNV or MAXNE exceeded\n");
exit(1);
}
nauty_check(WORDSIZE,m,n,NAUTYVERSIONID);
for (i = 0; i < n; ++i) ptn[i] = 1;
ptn[n-1] = 0;
EMPTYSET(active,m);
if (j0 != n-1) ADDELEMENT(active,j0+1);
for (i = 0; i <= j0; ++i) ptn[i] = 0;
for (i = j0+1; i < n; ++i)
if (lab[i] < nfixed) break;
if (i != j0+1 && i != n)
{
ptn[i-1] = 0;
ADDELEMENT(active,i);
}
options.defaultptn = FALSE;
options.userautomproc = groupautomproc;
options.userlevelproc = grouplevelproc;
nauty(g,lab,ptn,active,orbits,&options,&stats,workspace,100,m,n,NULL);
if (stats.grpsize2 == 0)
groupsize = stats.grpsize1 + 0.1;
else
groupsize = 0;
group = groupptr(FALSE);
makecosetreps(group);
lastrejok = FALSE;
if (isreg)
scan_reg(0,ne,minedges,maxedges,0,maxmult,group,n,delta,def,maxdeg);
else if (lswitch)
scan_lp(0,ne,minedges,maxedges,0,maxmult,group,n,deg,maxdeg);
else if (maxdeg >= 0)
scan_md(0,ne,minedges,maxedges,0,maxmult,group,n,deg,maxdeg);
else
scan(0,ne,minedges,maxedges,0,maxmult,group,n);
}
/**************************************************************************/
int
main(int argc, char *argv[])
{
graph *g;
int m,n,codetype;
int argnum,j,nfixed,maxdeg,regdeg,ldeg;
char *arg,sw;
boolean badargs;
boolean fswitch,uswitch,eswitch,qswitch,mswitch,Dswitch;
boolean lswitch,rswitch;
long minedges,maxedges,maxmult;
double t;
char *infilename,*outfilename;
FILE *infile;
char msg[201];
int msglen;
HELP; PUTVERSION;
nauty_check(WORDSIZE,1,1,NAUTYVERSIONID);
rswitch = fswitch = Tswitch = Gswitch = FALSE;
uswitch = eswitch = mswitch = qswitch = FALSE;
lswitch = Aswitch = Bswitch = Dswitch = FALSE;
infilename = outfilename = NULL;
argnum = 0;
badargs = FALSE;
for (j = 1; !badargs && j < argc; ++j)
{
arg = argv[j];
if (arg[0] == '-' && arg[1] != '\0')
{
++arg;
while (*arg != '\0')
{
sw = *arg++;
SWLONG('m',mswitch,maxmult,"multig -m")
else SWBOOLEAN('q',qswitch)
else SWBOOLEAN('u',uswitch)
else SWBOOLEAN('T',Tswitch)
else SWBOOLEAN('G',Gswitch)
else SWBOOLEAN('A',Aswitch)
else SWBOOLEAN('B',Bswitch)
else SWINT('f',fswitch,nfixed,"multig -f")
else SWINT('D',Dswitch,maxdeg,"multig -D")
else SWINT('r',rswitch,regdeg,"multig -r")
else SWINT('l',lswitch,ldeg,"multig -l")
else SWRANGE('e',":-",eswitch,minedges,maxedges,"multig -e")
else badargs = TRUE;
}
}
else
{
++argnum;
if (argnum == 1) infilename = arg;
else if (argnum == 2) outfilename = arg;
else badargs = TRUE;
}
}
if (badargs || argnum > 2)
{
fprintf(stderr,">E Usage: %s\n",USAGE);
GETHELP;
exit(1);
}
if ((Gswitch!=0) + (Tswitch!=0) + (uswitch!=0)
+ (Aswitch!=0) + (Bswitch!=0) >= 2)
gt_abort(">E multig: -G, -T, -A, -B and -u are incompatible\n");
#ifndef OUTPROC
if (!Tswitch && !Gswitch && !Aswitch && !Bswitch && !uswitch)
gt_abort(">E multig: must use -A, -B, -T, -G or -u\n");
#endif
if (rswitch && (Dswitch || eswitch))
gt_abort(">E multig: -r is incompatible with -D and -e\n");
if (lswitch && (rswitch || Dswitch || eswitch))
gt_abort(">E multig: -l is incompatible with -r, -D and -e\n");
if (!eswitch)
{
minedges = 0;
maxedges = NOLIMIT;
}
if (!mswitch) maxmult = NOLIMIT;
if (!fswitch) nfixed = 0;
if (Bswitch && nfixed == 0)
gt_abort(">E multig: -B requires -f# with #>0\n");
if (fswitch) Brows = nfixed;
if (maxedges >= NOLIMIT && maxmult >= NOLIMIT
&& !Dswitch && !rswitch && !lswitch)
gt_abort(
">E multig: either -D or -e or -m or -r must impose a real limit\n");
if (!qswitch)
{
msg[0] = '\0';
CATMSG0(">A multig");
if (eswitch || mswitch || uswitch || (fswitch && nfixed > 0)
|| lswitch || rswitch || Dswitch || Tswitch
|| Gswitch || Aswitch || Bswitch)
CATMSG0(" -");
if (mswitch) CATMSG1("m%ld",maxmult);
if (uswitch) CATMSG0("u");
if (Tswitch) CATMSG0("T");
if (Gswitch) CATMSG0("G");
if (Aswitch) CATMSG0("A");
if (Bswitch) CATMSG0("B");
if (fswitch) CATMSG1("f%d",nfixed);
if (eswitch) CATMSG2("e%ld:%ld",minedges,maxedges);
if (Dswitch) CATMSG1("D%d",maxdeg);
if (rswitch) CATMSG1("r%d",regdeg);
if (lswitch) CATMSG1("l%d",ldeg);
msglen = strlen(msg);
if (argnum > 0) msglen += strlen(infilename);
if (argnum > 1) msglen += strlen(outfilename);
if (msglen >= 196)
{
fputs(msg,stderr);
if (argnum > 0) fprintf(stderr," %s",infilename);
if (argnum > 1) fprintf(stderr," %s",outfilename);
fprintf(stderr,"\n");
}
else
{
if (argnum > 0) CATMSG1(" %s",infilename);
if (argnum > 1) CATMSG1(" %s",outfilename);
CATMSG0("\n");
fputs(msg,stderr);
}
fflush(stderr);
}
if (rswitch)
{
eswitch = Dswitch = TRUE;
maxdeg = regdeg;
}
if (lswitch)
{
eswitch = Dswitch = TRUE;
maxdeg = ldeg;
}
if (infilename && infilename[0] == '-') infilename = NULL;
infile = opengraphfile(infilename,&codetype,FALSE,1);
if (!infile) exit(1);
if (!infilename) infilename = "stdin";
NODIGRAPHSYET(codetype);
if (uswitch)
outfile = NULL;
else
{
if (!outfilename || outfilename[0] == '-')
{
outfilename = "stdout";
outfile = stdout;
}
else if ((outfile = fopen(outfilename,"w")) == NULL)
{
fprintf(stderr,"Can't open output file %s\n",outfilename);
gt_abort(NULL);
}
}
mg_nin = mg_nout = mg_skipped = 0;
t = CPUTIME;
while (TRUE)
{
if ((g = readg(infile,NULL,0,&m,&n)) == NULL) break;
++mg_nin;
#ifdef PATHCOUNTS
oldlo = mg_nout;
#endif
#ifdef INPUTGRAPH
if (!INPUTGRAPH(g,m,n))
{
++mg_skipped;
FREES(g);
continue;
}
#endif
if (rswitch)
{
minedges = ((long)n * (long)regdeg + 1) / 2;
maxedges = ((long)n * (long)regdeg) / 2;
}
if (lswitch)
{
maxedges = ((long)n * (long)ldeg) / 2;
if ((ldeg & 1) == 1) minedges = (n + 1) / 2;
else minedges = 0;
}
multi(g,nfixed,minedges,maxedges,maxmult,
(Dswitch?maxdeg:-1),lswitch,m,n);
#ifdef PATHCOUNTS
if (mg_nout != oldlo) ++count5;
#endif
if (!uswitch && ferror(outfile))
gt_abort(">E multig output error\n");
FREES(g);
}
t = CPUTIME - t;
#ifdef SUMMARY
SUMMARY();
#endif
if (!qswitch)
{
fprintf(stderr,">Z " COUNTER_FMT " graphs read from %s; ",
mg_nin,infilename);
#ifdef INPUTGRAPH
fprintf(stderr,COUNTER_FMT " skipped; ",mg_skipped);
#endif
PRINT_COUNTER(stderr,mg_nout);
if (!uswitch)
fprintf(stderr," multigraphs written to %s",outfilename);
else
fprintf(stderr," multigraphs generated");
fprintf(stderr,"; %.2f sec\n",t);
}
#ifdef GROUPTEST
fprintf(stderr,"Group test = %lld\n",totallab);
#endif
#ifdef PATHCOUNTS
fprintf(stderr,"Counts: %lld %lld %lld %lld %lld %lld\n",
count0,count1,count2,count3,count4,count5);
#endif
exit(0);
}

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