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geng.c
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/* TODO: insert new timings
* add chordal graphs
* add perfect graphs
* add complements for ordinary graphs */
/* geng.c version 2.9; B D McKay, Jan 2016. */
#define USAGE \
"geng [-cCmtfbd#D#] [-uygsnh] [-lvq] \n\
[-x#X#] n [mine[:maxe]] [res/mod] [file]"
#define HELPTEXT \
" Generate all graphs of a specified class.\n\
\n\
n : the number of vertices\n\
mine:maxe : a range for the number of edges\n\
#:0 means '# or more' except in the case 0:0\n\
res/mod : only generate subset res out of subsets 0..mod-1\n\
\n\
-c : only write connected graphs\n\
-C : only write biconnected graphs\n\
-t : only generate triangle-free graphs\n\
-f : only generate 4-cycle-free graphs\n\
-b : only generate bipartite graphs\n\
(-t, -f and -b can be used in any combination)\n\
-m : save memory at the expense of time (only makes a\n\
difference in the absence of -b, -t, -f and n <= 28).\n\
-d# : a lower bound for the minimum degree\n\
-D# : a upper bound for the maximum degree\n\
-v : display counts by number of edges\n\
-l : canonically label output graphs\n\
\n\
-u : do not output any graphs, just generate and count them\n\
-g : use graph6 output (default)\n\
-s : use sparse6 output\n\
-y : use the obsolete y-format instead of graph6 format\n\
-h : for graph6 or sparse6 format, write a header too\n\
\n\
-q : suppress auxiliary output (except from -v)\n\
\n\
See program text for much more information.\n"
/* Parameters:
n = the number of vertices (1..min(32,WORDSIZE))
mine = the minimum number of edges (no bounds if missing)
maxe = the maximum number of edges (same as mine if missing)
0 means "infinity" except in the case "0-0"
mod, res = a way to restrict the output to a subset.
All the graphs in G(n,mine..maxe) are divided into
disjoint classes C(0,mod),C(1,mod),...,C(mod-1,mod),
of very approximately equal size.
Only the class C(res,mod) is written.
If the -x or -X switch is used, they must have the
same value for different values of res; otherwise
the partitioning may not be valid. In this case
(-x,-X with constant value), the usual relationships
between modulo classes are obeyed; for example
C(3,4) = C(3,8) union C(7,8). This is not true
if 3/8 and 7/8 are done with -x or -X values
different from those used for 3/4.
file = a name for the output file (stdout if missing or "-")
All switches can be concatenated or separate. However, the
value of -d must be attached to the "d", and similarly for "x".
-c : only write connected graphs
-C : only write biconnected graphs
-t : only generate triangle-free graphs
-f : only generate 4-cycle-free graphs
-b : only generate bipartite graphs
(-t, -f and -b can be used in any combination)
-m : save memory at expense of time (only makes a
difference in the absence of -b, -t, -f and n <= 30).
-d<int> : specify an upper bound for the maximum degree.
The value of the upper bound must be adjacent to
the "d". Example: -d6
-v : display counts by number of edges
-l : canonically label output graphs
-u : do not output any graphs, just generate and count them
-g : use graph6 output (default)
-s : use sparse6 output
-n : use nauty format instead of graph6 format for output
-y : use the obsolete y-format instead of graph6 format
-h : for graph6 or sparse6 format, write a header too
-q : suppress auxiliary output (except from -v)
-x<int> : specify a parameter that determines how evenly
the res/mod facility splits the graphs into subsets.
High values mean more even splitting at slight cost
to the total time. The default is 20*mod, and the
the legal minimum is 3*mod. More information is given
under "res/mod" above.
-X<lev> : move the initial splitting level higher by <lev>,
in order to force more even splitting at the cost
of speed. Default is -X0. More information is given
under "res/mod" above.
Output formats.
The output format is determined by the mutually exclusive switches
-u, -n, -y, -g and -s. The default is -g.
-u suppresses output of graphs completely.
-s and -g specify sparse6 and graph6 format, defined elsewhere.
In this case a header is also written if -h is present.
If -y is present, graphs will be written in y-format.
y-format is obsolete and only provided for backwards compatibility.
Each graph occupies one line with a terminating newline.
Except for the newline, each byte has the format 01xxxxxx, where
each "x" represents one bit of data.
First byte: xxxxxx is the number of vertices n
Other ceiling(n(n-1)/12) bytes: These contain the upper triangle of
the adjacency matrix in column major order. That is, the entries
appear in the order (0,1),(0,2),(1,2),(0,3),(1,3),(2,3),(0,4),... .
The bits are used in left to right order within each byte.
Any unused bits on the end are set to zero.
If -n is present, any output graphs are written in nauty format.
For a graph of n vertices, the output consists of one int giving
the number of vertices, and n setwords containing the adjacency
matrix. Note that this is system dependent (i.e. don't use it).
It will not work properly if the output is to stdout and your
system distinguishes binary and text files.
OUTPROC feature.
By defining the C preprocessor variable OUTPROC at compile time
(for Unix the syntax is -DOUTPROC=procname on the cc command),
geng can be made to call a procedure of your manufacture with
each output graph instead of writing anything. Your procedure
needs to have type void and the argument list (FILE *f, graph
*g, int n). f is a stream open for writing, g is the graph in
nauty format, and n is the number of vertices. Your procedure
can be in a separate file so long as it is linked with geng. The
global variables sparse6, graph6, quiet, nooutput, nautyformat,
yformat and canonise (all type boolean) can be used to test
for the presence of the flags -s, -g, -q, -u, -n, -y and -l,
respectively. If -l is present, the group size and similar
details can be found in the global variable nauty_stats.
PRUNE feature.
By defining the C preprocessor variable PRUNE at compile time, geng
can be made to call
int PRUNE(graph *g,int n,int maxn)
for each intermediate (and final) graph, and reject it if
the value returned is nonzero. The arguments are:
g = the graph in nauty format (m=1)
n = the number of vertices in g
maxn = the number of vertices for output
(the value you gave on the command line to geng)
geng constructs the graph starting with vertex 0, then adding
vertices 1,2,3,... in that order. Each graph in the sequence is
an induced subgraph of all later graphs in the sequence.
A call is made for all orders from 1 to maxn. In testing for
a uniform property (such as a forbidden subgraph or forbidden
induced subgraph) it might save time to notice that a call to
PRUNE for n implies that the call for n-1 already passed.
For very fast tests, it might be worthwhile using PREPRUNE as
well. It has the same meaning but is applied earlier and more
often.
SUMMARY
If the C preprocessor variable SUMMARY is defined at compile time, the
procedure SUMMARY(nauty_counter nout, double cpu) is called just before
the program exits. The purpose is to allow reporting of statistics
collected by PRUNE or OUTPROC. The values nout and cpu are the output
count and cpu time reported on the >Z line.
Output should be written to stderr.
INSTRUMENT feature.
If the C preprocessor variable INSTRUMENT is defined at compile time,
extra code is inserted to collect statistics during execution, and
more information is written to stderr at termination.
CALLING FROM A PROGRAM
It is possible to call geng from another program instead of using it
as a stand-alone program. The main requirement is to change the name
of the main program to be other than "main". This is done by defining
the preprocessor variable GENG_MAIN. You might also like to define
OUTPROC to be the name of a procedure to receive the graphs. To call
the program you need to define an argument list argv[] consistent with
the usual one; don't forget that argv[0] is the command name and not
the first argument. The value of argc is the number of strings in
argv[]; that is, one more than the number of arguments. See the
sample program callgeng.c.
**************************************************************************
Sample performance statistics.
Here we give some graph counts and execution times on a Linux
Pentium III running at 550 MHz. Times are with the -u option
(generate but don't write); add 3-5 microseconds per graph for
output to a file. Add another 0.2-0.3 microseconds per graph
if you specify connectivity (-c), or 0.6-0.7 microseconds per
graph if you specific biconnectivity (-C).
General Graphs C3-free Graphs (-t)
1 1 1 1
2 2 2 2
3 4 3 3
4 11 4 7
5 34 5 14
6 156 6 38
7 1044 7 107
8 12346 0.11 sec 8 410
9 274668 1.77 sec 9 1897
10 12005168 1.22 min 10 12172 0.21 sec
11 1018997864 1.72 hr 11 105071 1.49 sec
12 165091172592 285 hr 12 1262180 15.9 sec
13 50502031367952 ~10 years 13 20797002 4.08 min
These can be done in about half 14 467871369 1.50 hr
the time by setting the edge limit 15 14232552452 45.6 hr
half way then adding complements. 16 581460254001 79 days
17 31720840164950
C4-free Graphs (-f) (C3,C4)-free Graphs (-tf)
1 1 1 1
2 2 2 2
3 4 3 3
4 8 4 6
5 18 5 11
6 44 6 23
7 117 7 48
8 351 8 114
9 1230 9 293
10 5069 0.11 sec 10 869
11 25181 0.48 sec 11 2963 0.10 sec
12 152045 2.67 sec 12 12066 0.36 sec
13 1116403 18.0 sec 13 58933 1.50 sec
14 9899865 2.50 min 14 347498 7.76 sec
15 104980369 25.7 min 15 2455693 50.9 sec
16 1318017549 5.33 hr 16 20592932 6.79 min
17 19427531763 82.6 hr 17 202724920 1.11 hr
18 333964672216 62 days 18 2322206466 12.7 hr
19 6660282066936 19 30743624324 168 hr
20 468026657815 110 days
Old value was wrong: 18 2142368552 (The program was
ok, but somehow we tabulated the answer incorrectly.)
Bipartite Graphs (-b) C4-free Bipartite Graphs (-bf)
1 1 1 1
2 2 2 2
3 3 3 3
4 7 4 6
5 13 5 10
6 35 6 21
7 88 7 39
8 303 8 86
9 1119 9 182
10 5479 0.11 sec 10 440
11 32303 0.59 sec 11 1074
12 251135 3.99 sec 12 2941 0.15 sec
13 2527712 35.1 sec 13 8424 0.43 sec
14 33985853 7.22 min 14 26720 1.37 sec
15 611846940 2.05 hr 15 90883 4.30 sec
16 14864650924 48.9 hr 16 340253 14.9 sec
17 488222721992 70 days 17 1384567 57.1 sec
18 21712049275198 18 6186907 4.01 min
19 30219769 18.4 min
20 161763233 1.57 hr
21 946742190 8.85 hr
22 6054606722 56.2 hr
23 42229136988 16.6 days
24 320741332093 121 days
If you know any more of these counts, please tell me.
**************************************************************************
Hints:
To make all the graphs of order n, without restriction on type,
it is fastest to make them up to binomial(n,2)/2 edges and append
the complement of those with strictly less than binomial(n,2)/2 edges.
If it is necessary to split the computation into pieces, it is more
efficient to use the res/mod feature than to split by numbers of edges.
The memory requirements are exponential in n if no maxdeg is given.
For maxdeg=D, the requirements are still exponential (but smaller)
for general graphs, but O(n^D) for other graphs. Use -m to reduce
the memory requirements to O(n^D) for general graphs too, at the
cost of a small increase in cpu time.
**************************************************************************
Author: B. D. McKay, Sep 1991 and many later dates.
Copyright B. McKay (1991-2013). All rights reserved.
This software is subject to the conditions and waivers
detailed in the file nauty.h.
Changes: Nov 18, 1991 : added -d switch
fixed operation for n=16
Nov 26, 1991 : added OUTPROC feature
Nov 29, 1991 : -c implies mine >= n-1
Jan 8, 1992 : make writeny() not static
Jan 10, 1992 : added -n switch
Feb 9, 1992 : fixed case of n=1
Feb 16, 1992 : changed mine,maxe,maxdeg testing
Feb 19, 1992 : added -b, -t and -u options
documented OUTPROC and added external
declaration for it.
Feb 20, 1992 : added -v option
Feb 22, 1992 : added INSTRUMENT compile-time option
Feb 23, 1992 : added xbnds() for more effective pruning
Feb 24, 1992 : added -l option
Feb 25, 1992 : changed writenauty() to use fwrite()
Mar 11, 1992 : completely revised many parts, incl
new refinement procedure for fast rejection,
distance invariant for regular graphs
May 19, 1992 : modified userautomproc slightly. xorb[]
is no longer idempotent but it doesn't matter.
Speed-up of 2-5% achieved.
June 5, 1993 : removed ";" after "CPUDEFS" to avoid illegal
empty declaration.
Nov 24, 1994 : tested for 0 <= res < mod
Apr 13, 1996 : Major overhaul. Renamed "geng".
Changed argument syntax.
Removed 16-vertex limit.
Added -s, -m, -x. Allowed combinations.
Replaced code for non-general graphs.
Very many small changes.
Jul 12, 1996 : Changed semantics of -x and res/mod.
Changed >A line and added fflush()/
All switches can be concatenated or not.
Aug 16, 1996 : Added -X switch and PRUNE() feature.
Fixed case of argument 0-0.
Sep 22, 1996 : Improved 1-2% by tweaking refinex().
Jan 21, 1997 : Renamed to geng.
Changed -s to -f, and added -sghq.
Sep 7, 1997 : Fixed WORDSIZE=16 problems.
Sep 22, 1997 : Use "wb" open for nautyformat.
Jan 26, 1998 : Added SUMMARY feature.
Mar 4, 1998 : Added -C.
Mar 12, 1998 : Moved stats to nauty_stats.
Jan 1, 2000 : Changed -d to -D and added -d.
Feb 24, 2000 : Raised limit to 32 vertices.
Mar 3, 2000 : Made some counts into unsigned long.
(Includes first arg to SUMMARY.)
Mar 12, 2000 : Used bigint for counts that may exceed 2^32.
Now all counts from very long runs are ok.
Oct 12, 2000 : Changed maxef[32] to 92 after confirmation
from Yang Yuansheng. The old value of 93 was
valid but 92 is slightly more efficient.
Nov 16, 2000 : Used fuction prototypes.
Jul 31, 2001 : Added PREPRUNE
May 7, 2004 : Complete all function prototypes
Nov 24, 2004 : Force -m for very large sizes
Add -bf automatically if generating trees
Apr 1, 2007 : Write >A in one fputs() to try to reduce
mixing of outputs in multi-process pipes.
Sep 19, 2007 : Force -m for n > 28 regardless of word size.
Nov 29, 2008 : Slightly improved connectivity testing.
Mar 3, 2015 : Improve maxdeg tweaking.
Jan 18, 2016 : Replace bigint by nauty_counter.
**************************************************************************/
#define NAUTY_PGM 1 /* 1 = geng, 2 = genbg, 3 = gentourng */
#ifndef MAXN
#define MAXN 32 /* not more than max(32,WORDSIZE) */
#endif
#if MAXN > 32
#error "Can't have MAXN greater than 32"
#endif
#define ONE_WORD_SETS
#include "gtools.h" /* which includes nauty.h and stdio.h */
#if MAXN < 32
typedef int xword; /* Must be as large as MAXN bits, and
must be unsigned if equal to MAXN bits */
#else
typedef unsigned int xword;
#endif
static void (*outproc)(FILE*,graph*,int);
static FILE *outfile; /* file for output graphs */
static int connec; /* 1 for -c, 2 for -C, 0 for neither */
static boolean bipartite; /* presence of -b */
static boolean trianglefree; /* presence of -t */
static boolean squarefree; /* presence of -f */
static boolean savemem; /* presence of -m */
static boolean verbose; /* presence of -v */
boolean nautyformat; /* presence of -n */
boolean yformat; /* presence of -y */
boolean graph6; /* presence of -g */
boolean sparse6; /* presence of -s */
boolean nooutput; /* presence of -u */
boolean canonise; /* presence of -l */
boolean quiet; /* presence of -q */
boolean header; /* presence of -h */
statsblk nauty_stats;
static int mindeg,maxdeg,maxn,mine,maxe,mod,res;
#define PRUNEMULT 20 /* bigger -> more even split at greater cost */
static int min_splitlevel,odometer,splitlevel,multiplicity;
static graph gcan[MAXN];
#if MAXN <= 16
static xword xbit[] = {0x0001,0x0002,0x0004,0x0008,
0x0010,0x0020,0x0040,0x0080,
0x0100,0x0200,0x0400,0x0800,
0x1000,0x2000,0x4000,0x8000};
#define XNEXTBIT(x) \
((x)&0xFF ? 7-leftbit[(x)&0xFF] : 15-leftbit[((x)>>8)&0xFF])
#define XPOPCOUNT(x) (bytecount[((x)>>8)&0xFF] + bytecount[(x)&0xFF])
#elif MAXN <= 24
static xword xbit[] = {0x000001,0x000002,0x000004,0x000008,
0x000010,0x000020,0x000040,0x000080,
0x000100,0x000200,0x000400,0x000800,
0x001000,0x002000,0x004000,0x008000,
0x010000,0x020000,0x040000,0x080000,
0x100000,0x200000,0x400000,0x800000};
#define XNEXTBIT(x) \
((x)&0xFF ? 7-leftbit[(x)&0xFF] : \
(x)&0xFF00 ? 15-leftbit[((x)>>8)&0xFF] : 23-leftbit[((x)>>16)&0xFF])
#define XPOPCOUNT(x) (bytecount[((x)>>8)&0xFF] \
+ bytecount[((x)>>16)&0xFF] + bytecount[(x)&0xFF])
#else
static xword xbit[] = {0x00000001,0x00000002,0x00000004,0x00000008,
0x00000010,0x00000020,0x00000040,0x00000080,
0x00000100,0x00000200,0x00000400,0x00000800,
0x00001000,0x00002000,0x00004000,0x00008000,
0x00010000,0x00020000,0x00040000,0x00080000,
0x00100000,0x00200000,0x00400000,0x00800000,
0x01000000,0x02000000,0x04000000,0x08000000,
0x10000000,0x20000000,0x40000000,0x80000000};
#define XNEXTBIT(x) \
((x)&0xFF ? 7-leftbit[(x)&0xFF] : \
(x)&0xFF00 ? 15-leftbit[((x)>>8)&0xFF] : \
(x)&0xFF0000 ? 23-leftbit[((x)>>16)&0xFF] : \
31-leftbit[((x)>>24)&0xFF])
#define XPOPCOUNT(x) (bytecount[((x)>>8)&0xFF] \
+ bytecount[((x)>>16)&0xFF] + \
+ bytecount[((x)>>24)&0xFF] + bytecount[(x)&0xFF])
#endif
typedef struct
{
int ne,dmax; /* values used for xlb,xub calculation */
int xlb,xub; /* saved bounds on extension degree */
xword lo,hi; /* work purposes for orbit calculation */
xword xstart[MAXN+1]; /* index into xset[] for each cardinality */
xword *xset; /* array of all x-sets in card order */
xword *xcard; /* cardinalities of all x-sets */
xword *xinv; /* map from x-set to index in xset */
xword *xorb; /* min orbit representative */
xword *xx; /* (-b, -t, -s, -m) candidate x-sets */
/* note: can be the same as xcard */
xword xlim; /* number of x-sets in xx[] */
} leveldata;
static leveldata data[MAXN]; /* data[n] is data for n -> n+1 */
static nauty_counter ecount[1+MAXN*(MAXN-1)/2]; /* counts by number of edges */
static nauty_counter nodes[MAXN]; /* nodes at each level */
#ifdef INSTRUMENT
static unsigned long rigidnodes[MAXN],fertilenodes[MAXN];
static unsigned long a1calls,a1nauty,a1succs;
static unsigned long a2calls,a2nauty,a2uniq,a2succs;
#endif
/* The numbers below are actual maximum edge counts. The apparently
anomolous value of 92 for maxef[32] has been confirmed independently
by Yang Yuansheng (as well as all the smaller maxef[] values).
geng works correctly with any upper bounds.
To extend an upper bound upwards: (n-1, E) -> (n, E + floor(2*E/(n-2))).
*/
static int maxeb[] = /* max edges for -b */
{0,0,1,2,4, 6,9,12,16,20, 25,30,36,42,49, 56,64,72,81,90,
100,110,121,132,144, 156,169,182,196,210, 225,240,256};
static int maxet[] = /* max edges for -t */
{0,0,1,2,4, 6,9,12,16,20, 25,30,36,42,49, 56,64,72,81,90,
100,110,121,132,144, 156,169,182,196,210, 225,240,256};
static int maxef[] = /* max edges for -f */
{0,0,1,3,4, 6,7,9,11,13, 16,18,21,24,27, 30,33,36,39,42,
46,50,52,56,59, 63,67,71,76,80, 85,90,92};
static int maxeft[] = /* max edges for -ft */
{0,0,1,2,3, 5,6,8,10,12, 15,16,18,21,23, 26,28,31,34,38,
41,44,47,50,54, 57,61,65,68,72, 76,80,85};
static int maxebf[] = /* max edges for -bf */
{0,0,1,2,3, 4,6,7,9,10, 12,14,16,18,21, 22,24,26,29,31,
34,36,39,42,45, 48,52,53,56,58, 61,64,67};
#ifdef PLUGIN
#include PLUGIN
#endif
#ifdef OUTPROC
extern void OUTPROC(FILE*,graph*,int);
#endif
#ifdef PRUNE
extern int PRUNE(graph*,int,int);
#endif
#ifdef PREPRUNE
extern int PREPRUNE(graph*,int,int);
#endif
#ifdef SUMMARY
extern void SUMMARY(nauty_counter,double);
#endif
/************************************************************************/
void
writeny(FILE *f, graph *g, int n)
/* write graph g (n vertices) to file f in y format */
{
static char ybit[] = {32,16,8,4,2,1};
char s[(MAXN*(MAXN-1)/2 + 5)/6 + 4];
int i,j,k;
char y,*sp;
sp = s;
*(sp++) = 0x40 | n;
y = 0x40;
k = -1;
for (j = 1; j < n; ++j)
for (i = 0; i < j; ++i)
{
if (++k == 6)
{
*(sp++) = y;
y = 0x40;
k = 0;
}
if (g[i] & bit[j]) y |= ybit[k];
}
if (n >= 2) *(sp++) = y;
*(sp++) = '\n';
*sp = '\0';
if (fputs(s,f) == EOF || ferror(f))
{
fprintf(stderr,">E writeny : error on writing file\n");
exit(2);
}
}
/************************************************************************/
void
writeg6x(FILE *f, graph *g, int n)
/* write graph g (n vertices) to file f in graph6 format */
{
writeg6(f,g,1,n);
}
/************************************************************************/
void
writes6x(FILE *f, graph *g, int n)
/* write graph g (n vertices) to file f in sparse6 format */
{
writes6(f,g,1,n);
}
/***********************************************************************/
static void
nullwrite(FILE *f, graph *g, int n)
/* don't write graph g (n vertices) to file f */
{
}
/***********************************************************************/
void
writenauty(FILE *f, graph *g, int n)
/* write graph g (n vertices) to file f in nauty format */
{
int nn;
nn = n;
if (fwrite((char *)&nn,sizeof(int),(size_t)1,f) != 1 ||
fwrite((char*)g,sizeof(setword),(size_t)n,f) != n)
{
fprintf(stderr,">E writenauty : error on writing file\n");
exit(2);
}
}
/*********************************************************************/
static boolean
isconnected(graph *g, int n)
/* test if g is connected */
{
setword seen,expanded,toexpand,allbits;
int i;
allbits = ALLMASK(n);
expanded = bit[n-1];
seen = expanded | g[n-1];
while (seen != allbits && (toexpand = (seen & ~expanded))) /* not == */
{
i = FIRSTBITNZ(toexpand);
expanded |= bit[i];
seen |= g[i];
}
return seen == allbits;
}
/**********************************************************************/
static boolean
isbiconnected(graph *g, int n)
/* test if g is biconnected */
{
int sp,v,w;
setword sw;
setword visited;
int numvis,num[MAXN],lp[MAXN],stack[MAXN];
if (n <= 2) return FALSE;
visited = bit[0];
stack[0] = 0;
num[0] = 0;
lp[0] = 0;
numvis = 1;
sp = 0;
v = 0;
for (;;)
{
if ((sw = g[v] & ~visited)) /* not "==" */
{
w = v;
v = FIRSTBITNZ(sw); /* visit next child */
stack[++sp] = v;
visited |= bit[v];
lp[v] = num[v] = numvis++;
sw = g[v] & visited & ~bit[w];
while (sw)
{
w = FIRSTBITNZ(sw);
sw &= ~bit[w];
if (num[w] < lp[v]) lp[v] = num[w];
}
}
else
{
w = v; /* back up to parent */
if (sp <= 1) return numvis == n;
v = stack[--sp];
if (lp[w] >= num[v]) return FALSE;
if (lp[w] < lp[v]) lp[v] = lp[w];
}
}
}
/**********************************************************************/
static void
gcomplement(graph *g, graph *gc, int n)
/* Take the complement of g and put it in gc */
{
int i;
setword all;
all = ~(setword)BITMASK(n-1);
for (i = 0; i < n; ++i)
gc[i] = g[i] ^ all ^ bit[i];
}
/**********************************************************************/
static boolean
distinvar(graph *g, int *invar, int n)
/* make distance invariant
return FALSE if n-1 not maximal else return TRUE */
{
int w;
setword workset,frontier;
setword sofar;
int inv,d,v;
for (v = n-1; v >= 0; --v)
{
inv = 0;
sofar = frontier = bit[v];
for (d = 1; frontier != 0; ++d)
{
workset = 0;
inv += POPCOUNT(frontier) ^ (0x57 + d);
while (frontier)
{
w = FIRSTBITNZ(frontier);
frontier ^= bit[w];
workset |= g[w];
}
frontier = workset & ~sofar;
sofar |= frontier;
}
invar[v] = inv;
if (v < n-1 && inv > invar[n-1]) return FALSE;
}
return TRUE;
}
/**************************************************************************/
static void
makexgraph(graph *g, xword *h, int n)
/* make x-format graph from nauty format graph */
{
setword gi;
int i,j;
xword hi;
for (i = 0; i < n; ++i)
{
hi = 0;
gi = g[i];
while (gi)
{
j = FIRSTBITNZ(gi);
gi ^= bit[j];
hi |= xbit[j];
}
h[i] = hi;
}
}
/**************************************************************************/
static void
make0graph(graph *g, xword *h, int n)
/* make x-format graph without edges */
{
int i;
for (i = 0; i < n; ++i) h[i] = 0;
}
/**************************************************************************/
static void
makebgraph(graph *g, xword *h, int n)
/* make x-format graph of different colour graph */
{
setword seen1,seen2,expanded,w;
setword restv;
xword xseen1,xseen2;
int i;
restv = 0;
for (i = 0; i < n; ++i) restv |= bit[i];
seen1 = seen2 = 0;
expanded = 0;
while (TRUE)
{
if ((w = ((seen1 | seen2) & ~expanded)) == 0)
{
xseen1 = 0;
w = seen1;
while (w)
{
i = FIRSTBITNZ(w);
w ^= bit[i];
xseen1 |= xbit[i];
}
xseen2 = 0;
w = seen2;
while (w)
{
i = FIRSTBITNZ(w);
w ^= bit[i];
xseen2 |= xbit[i];
}
w = seen1;
while (w)
{
i = FIRSTBITNZ(w);
w ^= bit[i];
h[i] = xseen2;
}
w = seen2;
while (w)
{
i = FIRSTBITNZ(w);
w ^= bit[i];
h[i] = xseen1;
}
restv &= ~(seen1 | seen2);
if (restv == 0) return;
i = FIRSTBITNZ(restv);
seen1 = bit[i];
seen2 = 0;
}
else
i = FIRSTBITNZ(w);
expanded |= bit[i];
if (bit[i] & seen1) seen2 |= g[i];
else seen1 |= g[i];
}
}
/**************************************************************************/
static void
makeb6graph(graph *g, xword *h, int n)
/* make x-format bipartite girth 6 graph */
{
setword w,x;
xword hi;
int i,j;
makebgraph(g,h,n);
for (i = 0; i < n; ++i)
{
w = g[i];
x = 0;
while (w)
{
j = FIRSTBITNZ(w);
w ^= bit[j];
x |= g[j];
}
x &= ~bit[i];
hi = h[i];
while (x)
{
j = FIRSTBITNZ(x);
x ^= bit[j];
hi |= xbit[j];
}
h[i] = hi;
}
}
/**************************************************************************/
static void
makesgraph(graph *g, xword *h, int n)
/* make x-format square graph */
{
setword w,x;
xword hi;
int i,j;
for (i = 0; i < n; ++i)
{
w = g[i];
x = 0;
while (w)
{
j = FIRSTBITNZ(w);
w ^= bit[j];
x |= g[j];
}
x &= ~bit[i];
hi = 0;
while (x)
{
j = FIRSTBITNZ(x);
x ^= bit[j];
hi |= xbit[j];
}
h[i] = hi;
}
}
/**************************************************************************/
static void
makeg5graph(graph *g, xword *h, int n)
/* make x-format girth-5 graph */
{
setword w,x;
xword hi;
int i,j;
for (i = 0; i < n; ++i)
{
w = g[i];
x = g[i];
while (w)
{
j = FIRSTBITNZ(w);
w ^= bit[j];
x |= g[j];
}
x &= ~bit[i];
hi = 0;
while (x)
{
j = FIRSTBITNZ(x);
x ^= bit[j];
hi |= xbit[j];
}
h[i] = hi;
}
}
/**************************************************************************/
static void
makeleveldata(boolean restricted)
/* make the level data for each level */
{
long h;
int n,nn;
long ncj;
leveldata *d;
xword *xcard,*xinv;
xword *xset,xw,tttn,nxsets;
xword cw;
xword i,j;
for (n = 1; n < maxn; ++n)
{
nn = maxdeg <= n ? maxdeg : n;
ncj = nxsets = 1;
for (j = 1; j <= nn; ++j)
{
ncj = (ncj * (n - j + 1)) / j;
nxsets += ncj;
}
tttn = 1L << n;
d = &data[n];
d->ne = d->dmax = d->xlb = d->xub = -1;
if (restricted)
{
d->xorb = (xword*) calloc(nxsets,sizeof(xword));
d->xx = (xword*) calloc(nxsets,sizeof(xword));
if (d->xorb == NULL || d->xx == NULL)
{
fprintf(stderr,
">E geng: calloc failed in makeleveldata()\n");
exit(2);
}
continue; /* <--- NOTE THIS! */
}
d->xset = xset = (xword*) calloc(nxsets,sizeof(xword));
d->xcard = xcard = (xword*) calloc(nxsets,sizeof(xword));
d->xinv = xinv = (xword*) calloc(tttn,sizeof(xword));
d->xorb = (xword*) calloc(nxsets,sizeof(xword));
d->xx = d->xcard;
if (xset==NULL || xcard==NULL || xinv==NULL || d->xorb==NULL)
{
fprintf(stderr,">E geng: calloc failed in makeleveldata()\n");
exit(2);
}
j = 0;
for (i = 0;; ++i)
{
if ((h = XPOPCOUNT(i)) <= maxdeg)
{
xset[j] = i;
xcard[j] = h;
++j;
}
if (i == (xword)((1L<<n)-1)) break;
}
if (j != nxsets)
{
fprintf(stderr,">E geng: j=%u mxsets=%u\n",
j,(unsigned)nxsets);
exit(2);
}
h = 1;
do
h = 3 * h + 1;
while (h < nxsets);
do
{
for (i = h; i < nxsets; ++i)
{
xw = xset[i];
cw = xcard[i];
for (j = i; xcard[j-h] > cw ||
(xcard[j-h] == cw && xset[j-h] > xw); )
{
xset[j] = xset[j-h];
xcard[j] = xcard[j-h];
if ((j -= h) < h) break;
}
xset[j] = xw;
xcard[j] = cw;
}
h /= 3;
}
while (h > 0);
for (i = 0; i < nxsets; ++i) xinv[xset[i]] = i;
d->xstart[0] = 0;
for (i = 1; i < nxsets; ++i)
if (xcard[i] > xcard[i-1]) d->xstart[xcard[i]] = i;
d->xstart[xcard[nxsets-1]+1] = nxsets;
}
}
/**************************************************************************/
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 void
userautomprocb(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 j1,j2,moved,pi,pxi,lo,hi,x;
xword i,*xorb,*xx,w,xlim,xlb;
xorb = data[n].xorb;
xx = data[n].xx;
xlim = data[n].xlim;
if (count == 1) /* first automorphism */
{
j1 = 0;
xlb = data[n].xlb;
for (i = 0; i < xlim; ++i)
{
x = xx[i];
if (XPOPCOUNT(x) >= xlb)
{
xx[j1] = x;
xorb[j1] = j1;
++j1;
}
}
data[n].xlim = xlim = j1;
}
moved = 0;
for (i = 0; i < n; ++i)
if (p[i] != i) moved |= xbit[i];
for (i = 0; i < xlim; ++i)
{
if ((w = xx[i] & moved) == 0) continue;
pxi = xx[i] & ~moved;
while (w)
{
j1 = XNEXTBIT(w);
w ^= xbit[j1];
pxi |= xbit[p[j1]];
}
/* pi = position of pxi */
lo = 0;
hi = xlim - 1;
for (;;)
{
pi = (lo + hi) >> 1;
if (xx[pi] == pxi) break;
else if (xx[pi] < pxi) lo = pi + 1;
else hi = pi - 1;
}
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;
}
}
/*****************************************************************************
* *
* refinex(g,lab,ptn,level,numcells,count,active,goodret,code,m,n) is a *
* custom version of refine() which can exit quickly if required. *
* *
* Only use at level==0. *
* goodret : whether to do an early return for code 1 *
* code := -1 for n-1 not max, 0 for maybe, 1 for definite *
* *
*****************************************************************************/
static void
refinex(graph *g, int *lab, int *ptn, int level, int *numcells,
int *count, set *active, boolean goodret, int *code, int m, int n)
{
int i,c1,c2,labc1;
setword x,lact;
int split1,split2,cell1,cell2;
int cnt,bmin,bmax;
set *gptr;
setword workset;
int workperm[MAXN];
int bucket[MAXN+2];
if (n == 1)
{
*code = 1;
return;
}
*code = 0;
lact = *active;
while (*numcells < n && lact)
{
TAKEBIT(split1,lact);
for (split2 = split1; ptn[split2] > 0; ++split2) {}
if (split1 == split2) /* trivial splitting cell */
{
gptr = GRAPHROW(g,lab[split1],1);
for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{
for (cell2 = cell1; ptn[cell2] > 0; ++cell2) {}
if (cell1 == cell2) continue;
c1 = cell1;
c2 = cell2;
while (c1 <= c2)
{
labc1 = lab[c1];
if (ISELEMENT1(gptr,labc1))
++c1;
else
{
lab[c1] = lab[c2];
lab[c2] = labc1;
--c2;
}
}
if (c2 >= cell1 && c1 <= cell2)
{
ptn[c2] = 0;
++*numcells;
lact |= bit[c1];
}
}
}
else /* nontrivial splitting cell */
{
workset = 0;
for (i = split1; i <= split2; ++i) workset |= bit[lab[i]];
for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{
for (cell2 = cell1; ptn[cell2] > 0; ++cell2) {}
if (cell1 == cell2) continue;
i = cell1;
if ((x = workset & g[lab[i]]) != 0) cnt = POPCOUNT(x);
else cnt = 0;
count[i] = bmin = bmax = cnt;
bucket[cnt] = 1;
while (++i <= cell2)
{
if ((x = workset & g[lab[i]]) != 0)
cnt = POPCOUNT(x);
else
cnt = 0;
while (bmin > cnt) bucket[--bmin] = 0;
while (bmax < cnt) bucket[++bmax] = 0;
++bucket[cnt];
count[i] = cnt;
}
if (bmin == bmax) continue;
c1 = cell1;
for (i = bmin; i <= bmax; ++i)
if (bucket[i])
{
c2 = c1 + bucket[i];
bucket[i] = c1;
if (c1 != cell1)
{
lact |= bit[c1];
++*numcells;
}
if (c2 <= cell2) ptn[c2-1] = 0;
c1 = c2;
}
for (i = cell1; i <= cell2; ++i)
workperm[bucket[count[i]]++] = lab[i];
for (i = cell1; i <= cell2; ++i) lab[i] = workperm[i];
}
}
if (ptn[n-2] == 0)
{
if (lab[n-1] == n-1)
{
*code = 1;
if (goodret) return;
}
else
{
*code = -1;
return;
}
}
else
{
i = n - 1;
while (TRUE)
{
if (lab[i] == n-1) break;
--i;
if (ptn[i] == 0)
{
*code = -1;
return;
}
}
}
}
}
/**************************************************************************/
static void
makecanon(graph *g, graph *gcan, int n)
/* gcan := canonise(g) */
{
int lab[MAXN],ptn[MAXN],orbits[MAXN];
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[50];
options.getcanon = TRUE;
nauty(g,lab,ptn,NULL,orbits,&options,&nauty_stats,
workspace,50,1,n,gcan);
}
/**************************************************************************/
static boolean
accept1(graph *g, int n, xword x, graph *gx, int *deg, boolean *rigid)
/* decide if n in theta(g+x) - version for n+1 < maxn */
{
int i;
int lab[MAXN],ptn[MAXN],orbits[MAXN];
int count[MAXN];
graph h[MAXN];
xword 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
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 PREPRUNE
if (PREPRUNE(gx,n+1,maxn)) return FALSE;
#endif
i0 = 0;
i1 = n;
for (i = 0; i < nx; ++i)
{
if (deg[i] == degn) lab[i1--] = i;
else lab[i0++] = i;
ptn[i] = 1;
}
ptn[n] = 0;
if (i0 == 0)
{
numcells = 1;
active[0] = bit[0];
}
else
{
numcells = 2;
active[0] = bit[0] | 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
return TRUE;
}
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
return TRUE;
}
else
return FALSE;
}
/**************************************************************************/
static boolean
accept1b(graph *g, int n, xword x, graph *gx, int *deg, boolean *rigid,
void (*makeh)(graph*,xword*,int))
/* decide if n in theta(g+x) -- version for n+1 < maxn */
{
int i,v;
xword z,hv,bitv,ixx;
int lab[MAXN],ptn[MAXN],orbits[MAXN];
int count[MAXN];
graph gc[MAXN];
xword h[MAXN],xw,jxx,kxx,*xx;
int nx,numcells,code;
int i0,i1,degn,xubx;
set active[MAXM];
statsblk stats;
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[50];
#ifdef INSTRUMENT
++a1calls;
#endif
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 PREPRUNE
if (PREPRUNE(gx,n+1,maxn)) return FALSE;
#endif
i0 = 0;
i1 = n;
for (i = 0; i < nx; ++i)
{
if (deg[i] == degn) lab[i1--] = i;
else lab[i0++] = i;
ptn[i] = 1;
}
ptn[n] = 0;
if (i0 == 0)
{
numcells = 1;
active[0] = bit[0];
}
else
{
numcells = 2;
active[0] = bit[0] | bit[i1+1];
ptn[i1] = 0;
}
refinex(gx,lab,ptn,0,&numcells,count,active,FALSE,&code,1,nx);
if (code < 0) return FALSE;
(*makeh)(gx,h,nx);
xx = data[nx].xx;
xubx = data[nx].xub;
xx[0] = 0;
kxx = 1;
for (v = 0; v < nx; ++v)
{
bitv = xbit[v];
hv = h[v];
jxx = kxx;
for (ixx = 0; ixx < jxx; ++ixx)
if ((hv & xx[ixx]) == 0)
{
z = xx[ixx] | bitv;
if (XPOPCOUNT(z) <= xubx) xx[kxx++] = z;
}
}
data[nx].xlim = kxx;
if (numcells == nx)
{
*rigid = TRUE;
#ifdef INSTRUMENT
++a1succs;
#endif
return TRUE;
}
options.getcanon = TRUE;
options.defaultptn = FALSE;
options.userautomproc = userautomprocb;
active[0] = 0;
#ifdef INSTRUMENT
++a1nauty;
#endif
nauty(gx,lab,ptn,active,orbits,&options,&stats,workspace,50,1,nx,gc);
if (orbits[lab[n]] == orbits[n])
{
*rigid = stats.numorbits == nx;
#ifdef INSTRUMENT
++a1succs;
#endif
return TRUE;
}
else
return FALSE;
}
/**************************************************************************/
static boolean
accept2(graph *g, int n, xword x, graph *gx, int *deg, boolean nuniq)
/* decide if n in theta(g+x) -- version for n+1 == maxn */
{
int i;
int lab[MAXN],ptn[MAXN],orbits[MAXN];
int degx[MAXN],invar[MAXN];
setword vmax,gv;
int qn,qv;
int count[MAXN];
xword xw;
int nx,numcells,code;
int degn,i0,i1,j,j0,j1;
set active[MAXM];
statsblk stats;
static DEFAULTOPTIONS_GRAPH(options);
setword workspace[50];
boolean cheapacc;
#ifdef INSTRUMENT
++a2calls;
if (nuniq) ++a2uniq;
#endif
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 PREPRUNE
if (PREPRUNE(gx,n+1,maxn)) return FALSE;
#endif
if (nuniq)
{
#ifdef INSTRUMENT
++a2succs;
#endif
if (canonise) makecanon(gx,gcan,nx);
return TRUE;
}
i0 = 0;
i1 = n;
for (i = 0; i < nx; ++i)
{
if (degx[i] == degn) lab[i1--] = i;
else lab[i0++] = i;
ptn[i] = 1;
}
ptn[n] = 0;
if (i0 == 0)
{
numcells = 1;
active[0] = bit[0];
if (!distinvar(gx,invar,nx)) return FALSE;
qn = invar[n];
j0 = 0;
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 > 0)
{
if (j0 == n)
{
#ifdef INSTRUMENT
++a2succs;
#endif
if (canonise) makecanon(gx,gcan,nx);
return TRUE;
}
ptn[j1] = 0;
++numcells;
active[0] |= bit[j0];
}
}
else
{
numcells = 2;
ptn[i1] = 0;
active[0] = bit[0] | bit[i1+1];
vmax = 0;
for (i = i1+1; i < nx; ++i) vmax |= bit[lab[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
if (canonise) makecanon(gx,gcan,nx);
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;
cheapacc = FALSE;
if (code > 0 || numcells >= nx-4)
cheapacc = TRUE;
else if (numcells == nx-5)
{
for (j1 = nx-2; j1 >= 0 && ptn[j1] > 0; --j1) {}
if (nx - j1 != 5) cheapacc = TRUE;
}
else
{
j1 = nx;
j0 = 0;
for (i1 = 0; i1 < nx; ++i1)
{
--j1;
if (ptn[i1] > 0)
{
++j0;
while (ptn[++i1] > 0) {}
}
}
if (j1 <= j0 + 1) cheapacc = TRUE;
}
if (cheapacc)
{
#ifdef INSTRUMENT
++a2succs;
#endif
if (canonise) makecanon(gx,gcan,nx);
return TRUE;
}
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
if (canonise) makecanon(gx,gcan,nx);
return TRUE;
}
else
return FALSE;
}
/**************************************************************************/
static void
xbnds(int n, int ne, int dmax)
/* find bounds on extension degree; store answer in data[*].* */
{
int xlb,xub,d,nn,m,xc;
xlb = n == 1 ? 0 : (dmax > (2*ne + n - 2)/(n - 1) ?
dmax : (2*ne + n - 2)/(n - 1));
xub = n < maxdeg ? n : maxdeg;
for (xc = xub; xc >= xlb; --xc)
{
d = xc;
m = ne + d;
for (nn = n+1; nn < maxn; ++nn)
{
if (d < (2*m + nn - 2)/(nn - 1)) d = (2*m + nn - 2)/(nn - 1);
m += d;
}
if (d > maxdeg || m > maxe) xub = xc - 1;
else break;
}
if (ne + xlb < mine)
for (xc = xlb; xc <= xub; ++xc)
{
m = ne + xc;
for (nn = n + 1; nn < maxn; ++nn)
m += maxdeg < nn ? maxdeg : nn;
if (m < mine) xlb = xc + 1;
else break;
}
data[n].ne = ne;
data[n].dmax = dmax;
data[n].xlb = xlb;
data[n].xub = xub;
}
/**************************************************************************/
static void
spaextend(graph *g, int n, int *deg, int ne, boolean rigid,
int xlb, int xub, void (*makeh)(graph*,xword*,int))
/* extend from n to n+1 -- version for restricted graphs */
{
xword x,d,dlow;
xword xlim,*xorb;
int xc,nx,i,j,dmax,dcrit,xlbx,xubx;
graph gx[MAXN];
xword *xx,ixx;
int degx[MAXN];
boolean rigidx;
#ifdef INSTRUMENT
boolean haschild;
haschild = FALSE;
if (rigid) ++rigidnodes[n];
#endif
++nodes[n];
nx = n + 1;
dmax = deg[n-1];
dcrit = mindeg - maxn + n;
d = dlow = 0;
for (i = 0; i < n; ++i)
{
if (deg[i] == dmax) d |= xbit[i];
if (deg[i] == dcrit) dlow |= xbit[i];
}
if (xlb == dmax && XPOPCOUNT(d) + dmax > n) ++xlb;
if (nx == maxn && xlb < mindeg) xlb = mindeg;
if (xlb > xub) return;
#ifdef PRUNE
if (PRUNE(g,n,maxn)) return;
#endif
xorb = data[n].xorb;
xx = data[n].xx;
xlim = data[n].xlim;
if (nx == maxn)
{
for (ixx = 0; ixx < xlim; ++ixx)
{
x = xx[ixx];
xc = XPOPCOUNT(x);
if (xc < xlb || xc > xub) continue;
if ((rigid || xorb[ixx] == ixx)
&& (xc > dmax || (xc == dmax && (x & d) == 0))
&& (dlow & ~x) == 0)
{
if (accept2(g,n,x,gx,deg,
xc > dmax+1 || (xc == dmax+1 && (x & d) == 0))
&& (!connec ||
(connec==1 && isconnected(gx,nx)) ||
(connec>1 && isbiconnected(gx,nx))))
{
#ifdef PRUNE
if (!PRUNE(gx,nx,maxn))
#endif
{
#ifdef INSTRUMENT
haschild = TRUE;
#endif
++ecount[ne+xc];
(*outproc)(outfile,canonise ? gcan : gx,nx);
}
}
}
}
}
else
{
for (ixx = 0; ixx < xlim; ++ixx)
{
if (nx == splitlevel)
{
if (odometer-- != 0) continue;
odometer = mod - 1;
}
x = xx[ixx];
xc = XPOPCOUNT(x);
if (xc < xlb || xc > xub) continue;
if ((rigid || xorb[ixx] == ixx)
&& (xc > dmax || (xc == dmax && (x & d) == 0))
&& (dlow & ~x) == 0)
{
for (j = 0; j < n; ++j) degx[j] = deg[j];
if (data[nx].ne != ne+xc || data[nx].dmax != xc)
xbnds(nx,ne+xc,xc);
xlbx = data[nx].xlb;
xubx = data[nx].xub;
if (xlbx <= xubx
&& accept1b(g,n,x,gx,degx,&rigidx,makeh))
{
#ifdef INSTRUMENT
haschild = TRUE;
#endif
spaextend(gx,nx,degx,ne+xc,rigidx,xlbx,xubx,makeh);
}
}
}
if (n == splitlevel - 1 && n >= min_splitlevel
&& nodes[n] >= multiplicity)
--splitlevel;
}
#ifdef INSTRUMENT
if (haschild) ++fertilenodes[n];
#endif
}
/**************************************************************************/
static void
genextend(graph *g, int n, int *deg, int ne, boolean rigid, int xlb, int xub)
/* extend from n to n+1 -- version for general graphs */
{
xword x,d,dlow;
xword *xset,*xcard,*xorb;
xword i,imin,imax;
int nx,xc,j,dmax,dcrit;
int xlbx,xubx;
graph gx[MAXN];
int degx[MAXN];
boolean rigidx;
#ifdef INSTRUMENT
boolean haschild;
haschild = FALSE;
if (rigid) ++rigidnodes[n];
#endif
++nodes[n];
nx = n + 1;
dmax = deg[n-1];
dcrit = mindeg - maxn + n;
d = dlow = 0;
for (i = 0; i < n; ++i)
{
if (deg[i] == dmax) d |= xbit[i];
if (deg[i] == dcrit) dlow |= xbit[i];
}
if (xlb == dmax && XPOPCOUNT(d) + dmax > n) ++xlb;
if (nx == maxn && xlb < mindeg) xlb = mindeg;
if (xlb > xub) return;
#ifdef PRUNE
if (PRUNE(g,n,maxn)) return;
#endif
imin = data[n].xstart[xlb];
imax = data[n].xstart[xub+1];
xset = data[n].xset;
xcard = data[n].xcard;
xorb = data[n].xorb;
if (nx == maxn)
for (i = imin; i < imax; ++i)
{
if (!rigid && xorb[i] != i) continue;
x = xset[i];
xc = xcard[i];
if (xc == dmax && (x & d) != 0) continue;
if ((dlow & ~x) != 0) continue;
if (accept2(g,n,x,gx,deg,
xc > dmax+1 || (xc == dmax+1 && (x & d) == 0)))
if (!connec || (connec==1 && isconnected(gx,nx))
|| (connec>1 && isbiconnected(gx,nx)))
{
#ifdef PRUNE
if (!PRUNE(gx,nx,maxn))
#endif
{
#ifdef INSTRUMENT
haschild = TRUE;
#endif
++ecount[ne+xc];
(*outproc)(outfile,canonise ? gcan : gx,nx);
}
}
}
else
for (i = imin; i < imax; ++i)
{
if (!rigid && xorb[i] != i) continue;
x = xset[i];
xc = xcard[i];
if (xc == dmax && (x & d) != 0) continue;
if ((dlow & ~x) != 0) continue;
if (nx == splitlevel)
{
if (odometer-- != 0) continue;
odometer = mod - 1;
}
for (j = 0; j < n; ++j) degx[j] = deg[j];
if (data[nx].ne != ne+xc || data[nx].dmax != xc)
xbnds(nx,ne+xc,xc);
xlbx = data[nx].xlb;
xubx = data[nx].xub;
if (xlbx > xubx) continue;
data[nx].lo = data[nx].xstart[xlbx];
data[nx].hi = data[nx].xstart[xubx+1];
if (accept1(g,n,x,gx,degx,&rigidx))
{
#ifdef INSTRUMENT
haschild = TRUE;
#endif
genextend(gx,nx,degx,ne+xc,rigidx,xlbx,xubx);
}
}
if (n == splitlevel-1 && n >= min_splitlevel
&& nodes[n] >= multiplicity)
--splitlevel;
#ifdef INSTRUMENT
if (haschild) ++fertilenodes[n];
#endif
}
/**************************************************************************/
/**************************************************************************/
#ifdef GENG_MAIN
int
GENG_MAIN(int argc, char *argv[])
#else
int
main(int argc, char *argv[])
#endif
{
char *arg;
boolean badargs,gote,gotmr,gotf,gotd,gotD,gotx,gotX;
boolean secret,connec1,connec2,safe,sparse;
char *outfilename,sw;
int i,j,argnum;
graph g[1];
int tmaxe,deg[1];
nauty_counter nout;
int splitlevinc;
xword testxword;
double t1,t2;
char msg[201];
HELP; PUTVERSION;
nauty_check(WORDSIZE,1,MAXN,NAUTYVERSIONID);
testxword = (xword)(-1);
if (MAXN > 32 || MAXN > WORDSIZE || MAXN > 8*sizeof(xword)
|| (MAXN == 8*sizeof(xword) && testxword < 1))
{
fprintf(stderr,"geng: incompatible MAXN, WORDSIZE, or xword\n");
fprintf(stderr,"--See notes in program source\n");
exit(1);
}
badargs = FALSE;
trianglefree = FALSE;
bipartite = FALSE;
squarefree = FALSE;
verbose = FALSE;
nautyformat = FALSE;
yformat = FALSE;
graph6 = FALSE;
sparse6 = FALSE;
savemem = FALSE;
nooutput = FALSE;
canonise = FALSE;
header = FALSE;
outfilename = NULL;
secret = FALSE;
safe = FALSE;
connec1 = connec2 = FALSE;
maxdeg = MAXN;
mindeg = 0;
gotX = gotx = gotd = gotD = gote = gotmr = gotf = FALSE;
argnum = 0;
for (j = 1; !badargs && j < argc; ++j)
{
arg = argv[j];
if (arg[0] == '-' && arg[1] != '\0')
{
++arg;
while (*arg != '\0')
{
sw = *arg++;
SWBOOLEAN('n',nautyformat)
else SWBOOLEAN('u',nooutput)
else SWBOOLEAN('g',graph6)
else SWBOOLEAN('s',sparse6)
else SWBOOLEAN('t',trianglefree)
else SWBOOLEAN('f',squarefree)
else SWBOOLEAN('b',bipartite)
else SWBOOLEAN('v',verbose)
else SWBOOLEAN('l',canonise)
else SWBOOLEAN('y',yformat)
else SWBOOLEAN('h',header)
else SWBOOLEAN('m',savemem)
else SWBOOLEAN('c',connec1)
else SWBOOLEAN('C',connec2)
else SWBOOLEAN('q',quiet)
else SWBOOLEAN('$',secret)
else SWBOOLEAN('S',safe)
else SWINT('d',gotd,mindeg,"geng -d")
else SWINT('D',gotD,maxdeg,"geng -D")
else SWINT('x',gotx,multiplicity,"geng -x")
else SWINT('X',gotX,splitlevinc,"geng -X")
#ifdef PLUGIN_SWITCHES
PLUGIN_SWITCHES
#endif
else badargs = TRUE;
}
}
else if (arg[0] == '-' && arg[1] == '\0')
gotf = TRUE;
else
{
if (argnum == 0)
{
if (sscanf(arg,"%d",&maxn) != 1) badargs = TRUE;
++argnum;
}
else if (gotf)
badargs = TRUE;
else
{
if (!gotmr)
{
if (sscanf(arg,"%d/%d",&res,&mod) == 2)
{
gotmr = TRUE;
continue;
}
}
if (!gote)
{
if (sscanf(arg,"%d:%d",&mine,&maxe) == 2
|| sscanf(arg,"%d-%d",&mine,&maxe) == 2)
{
gote = TRUE;
if (maxe == 0 && mine > 0) maxe = MAXN*(MAXN-1)/2;
continue;
}
else if (sscanf(arg,"%d",&mine) == 1)
{
gote = TRUE;
maxe = mine;
continue;
}
}
if (!gotf)
{
outfilename = arg;
gotf = TRUE;
continue;
}
}
}
}
if (argnum == 0)
badargs = TRUE;
else if (maxn < 1 || maxn > MAXN)
{
fprintf(stderr,">E geng: n must be in the range 1..%d\n",MAXN);
badargs = TRUE;
}
if (!gotmr)
{
mod = 1;
res = 0;
}
if (!gote)
{
mine = 0;
maxe = (maxn*maxn - maxn) / 2;
}
if (connec1 && mindeg < 1 && maxn > 1) mindeg = 1;
if (connec2 && mindeg < 2 && maxn > 2) mindeg = 2;
if (maxdeg >= maxn) maxdeg = maxn - 1;
if (maxe > maxn*maxdeg / 2) maxe = maxn*maxdeg / 2;
if (maxdeg > maxe) maxdeg = maxe;
if (mindeg < 0) mindeg = 0;
if (mine < (maxn*mindeg+1) / 2) mine = (maxn*mindeg+1) / 2;
if (maxdeg > 2*maxe - mindeg*(maxn-1)) maxdeg = 2*maxe - mindeg*(maxn-1);
if (!badargs && (mine > maxe || maxe < 0 || maxdeg < 0))
{
fprintf(stderr,
">E geng: impossible mine,maxe,mindeg,maxdeg values\n");
badargs = TRUE;
}
if (!badargs && (res < 0 || res >= mod))
{
fprintf(stderr,">E geng: must have 0 <= res < mod\n");
badargs = TRUE;
}
if (connec2) connec = 2;
else if (connec1) connec = 1;
else connec = 0;
if (connec && mine < maxn-1) mine = maxn - 2 + connec;
if (badargs)
{
fprintf(stderr,">E Usage: %s\n",USAGE);
GETHELP;
exit(1);
}
if ((nautyformat!=0) + (yformat!=0) + (graph6!=0)
+ (sparse6!=0) + (nooutput!=0) > 1)
gt_abort(">E geng: -uyngs are incompatible\n");
#ifdef OUTPROC
outproc = OUTPROC;
#else
if (nautyformat) outproc = writenauty;
else if (yformat) outproc = writeny;
else if (nooutput) outproc = nullwrite;
else if (sparse6) outproc = writes6x;
else outproc = writeg6x;
#endif
#ifdef PLUGIN_INIT
PLUGIN_INIT
#endif
for (i = 0; i <= maxe; ++i) ecount[i] = 0;
for (i = 0; i < maxn; ++i) nodes[i] = 0;
if (nooutput)
outfile = stdout;
else if (!gotf || outfilename == NULL)
{
outfilename = "stdout";
outfile = stdout;
}
else if ((outfile = fopen(outfilename,
nautyformat ? "wb" : "w")) == NULL)
{
fprintf(stderr,
">E geng: can't open %s for writing\n",outfilename);
gt_abort(NULL);
}
if (bipartite)
if (squarefree) tmaxe = maxebf[maxn];
else tmaxe = maxeb[maxn];
else if (trianglefree)
if (squarefree) tmaxe = maxeft[maxn];
else tmaxe = maxet[maxn];
else if (squarefree) tmaxe = maxef[maxn];
else tmaxe = (maxn*maxn - maxn) / 2;
if (safe) ++tmaxe;
if (maxe > tmaxe) maxe = tmaxe;
if (gotx)
{
if (multiplicity < 3 * mod || multiplicity > 999999999)
gt_abort(">E geng: -x value must be in [3*mod,10^9-1]\n");
}
else
{
multiplicity = PRUNEMULT * mod;
if (multiplicity / PRUNEMULT != mod)
gt_abort(">E geng: mod value is too large\n");
}
if (!gotX) splitlevinc = 0;
if (!quiet)
{
msg[0] = '\0';
if (strlen(argv[0]) > 75)
fprintf(stderr,">A %s",argv[0]);
else
CATMSG1(">A %s",argv[0]);
CATMSG6(" -%s%s%s%s%s%s",
connec2 ? "C" : connec1 ? "c" : "",
trianglefree ? "t" : "",
squarefree ? "f" : "",
bipartite ? "b" : "",
canonise ? "l" : "",
savemem ? "m" : "");
if (mod > 1)
CATMSG2("X%dx%d",splitlevinc,multiplicity);
CATMSG4("d%dD%d n=%d e=%d",mindeg,maxdeg,maxn,mine);
if (maxe > mine) CATMSG1("-%d",maxe);
if (mod > 1) CATMSG2(" class=%d/%d",res,mod);
CATMSG0("\n");
fputs(msg,stderr);
fflush(stderr);
}
g[0] = 0;
deg[0] = 0;
sparse = bipartite || squarefree || trianglefree || savemem;
t1 = CPUTIME;
if (header)
{
if (sparse6)
{
writeline(outfile,SPARSE6_HEADER);
fflush(outfile);
}
else if (!yformat && !nautyformat && !nooutput)
{
writeline(outfile,GRAPH6_HEADER);
fflush(outfile);
}
}
if (maxn == 1)
{
if (res == 0)
{
++ecount[0];
(*outproc)(outfile,g,1);
}
}
else
{
if (maxn > 28 || maxn+4 > 8*sizeof(xword))
savemem = sparse = TRUE;
if (maxn == maxe+1 && connec)
bipartite = squarefree = sparse = TRUE; /* trees */
makeleveldata(sparse);
if (maxn >= 14 && mod > 1) splitlevel = maxn - 4;
else if (maxn >= 6 && mod > 1) splitlevel = maxn - 3;
else splitlevel = -1;
if (splitlevel > 0) splitlevel += splitlevinc;
if (splitlevel > maxn - 1) splitlevel = maxn - 1;
if (splitlevel < 3) splitlevel = -1;
min_splitlevel = 6;
odometer = secret ? -1 : res;
if (maxe >= mine &&
(mod <= 1 || (mod > 1 && (splitlevel > 2 || res == 0))))
{
xbnds(1,0,0);
if (sparse)
{
data[1].xx[0] = 0;
if (maxdeg > 0) data[1].xx[1] = xbit[0];
data[1].xlim = data[1].xub + 1;
}
if (bipartite)
if (squarefree)
spaextend(g,1,deg,0,TRUE,
data[1].xlb,data[1].xub,makeb6graph);
else
spaextend(g,1,deg,0,TRUE,
data[1].xlb,data[1].xub,makebgraph);
else if (trianglefree)
if (squarefree)
spaextend(g,1,deg,0,TRUE,
data[1].xlb,data[1].xub,makeg5graph);
else
spaextend(g,1,deg,0,TRUE,
data[1].xlb,data[1].xub,makexgraph);
else if (squarefree)
spaextend(g,1,deg,0,TRUE,
data[1].xlb,data[1].xub,makesgraph);
else if (savemem)
spaextend(g,1,deg,0,TRUE,
data[1].xlb,data[1].xub,make0graph);
else
genextend(g,1,deg,0,TRUE,data[1].xlb,data[1].xub);
}
}
t2 = CPUTIME;
nout = 0;
for (i = 0; i <= maxe; ++i) nout += ecount[i];
if (verbose)
{
for (i = 0; i <= maxe; ++i)
if (ecount[i] != 0)
{
fprintf(stderr,">C " COUNTER_FMT " graphs with %d edges\n",
ecount[i],i);
}
}
#ifdef INSTRUMENT
fprintf(stderr,"\n>N node counts\n");
for (i = 1; i < maxn; ++i)
{
fprintf(stderr," level %2d: \n",i);
fprintf(stderr,COUNTER_FMT " (%lu rigid, %lu fertile)\n",
nodes[i],rigidnodes[i],fertilenodes[i]);
}
fprintf(stderr,">A1 %lu calls to accept1, %lu nauty, %lu succeeded\n",
a1calls,a1nauty,a1succs);
fprintf(stderr,
">A2 %lu calls to accept2, %lu nuniq, %lu nauty, %lu succeeded\n",
a2calls,a2uniq,a2nauty,a2succs);
fprintf(stderr,"\n");
#endif
#ifdef SUMMARY
SUMMARY(nout,t2-t1);
#endif
if (!quiet)
{
fprintf(stderr,">Z " COUNTER_FMT " graphs generated in %3.2f sec\n",
nout,t2-t1);
}
#ifdef GENG_MAIN
for (i = 1; i < maxn; ++i)
if (sparse)
{
free(data[i].xorb);
free(data[i].xx);
}
else
{
free(data[i].xorb);
free(data[i].xset);
free(data[i].xinv);
free(data[i].xcard);
}
return 0;
#else
exit(0);
#endif
}

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