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Quelle geng.c Sprache: C |
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/* TODO: * add complements for ordinary graphs * add 5-cycle rejection */ /* geng.c version 3.6; B D McKay, October 2022. */ #define USAGE \ "geng [-cCmtfkbd#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\ -k : only generate K4-free graphs\n\ -T : only generate chordal graphs\n\ -S : only generate split graphs\n\ -P : only generate perfect graphs\n\ -F : only generate claw-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# : an 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\ -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..MAXN) Note that MAXN is limited to min(WORDSIZE,64) 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 -d<int> : specify a lower bound for the minimum 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 for output -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, and canonise (all type boolean) can be used to test for the presence of the flags -s, -g, -q, -u, -n, 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 or instead. It has the same meaning but is applied earlier and more often. If -c or -C is given, the connectivity test is done before PRUNE but not necessarily before PREPRUNE. Some parameters are available in global variables: geng_mindeg, geng_maxdeg, geng_mine, geng_maxe, geng_connec; 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. You can also call geng from multiple threads at once, see the sample program callgeng2.c. ************************************************************************** Counts and sample performance statistics. Here we give some graph counts and approximate execution times on a Linux computer with Intel Core i7-4790 nominally 3.6GHz, compiled with gcc 6.2.0. Times are with the -u option (generate but don't write); add 0.2-0.3 microseconds per graph for output to a file. 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 8 410 9 274668 0.08 sec 9 1897 10 12005168 2.7 sec 10 12172 11 1018997864 207 sec 11 105071 0.09 sec 12 165091172592 9 hr 12 1262180 0.8 sec 13 50502031367952 108 days 13 20797002 11 sec These can be done in about half 14 467871369 220 sec the time by setting the edge limit 15 14232552452 1.7 hr half way then adding complements. 16 581460254001 65 hr 17 31720840164950 145 days 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 10 869 11 25181 0.04 sec 11 2963 12 152045 0.17 sec 12 12066 0.03 sec 13 1116403 1.0 sec 13 58933 0.10 sec 14 9899865 7.5 sec 14 347498 0.5 sec 15 104980369 71 sec 15 2455693 2.7 sec 16 1318017549 14 min 16 20592932 19 sec 17 19427531763 3.4 hr 17 202724920 170 sec 18 333964672216 56 hr 18 2322206466 32 min 19 6660282066936 45 days 19 30743624324 7 hr 20 468026657815 4 days 21 8161170076257 106 days 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 10 440 11 32303 0.03 sec 11 1074 12 251135 2.3 sec 12 2941 13 2527712 1.7 sec 13 8424 0.04 sec 14 33985853 19 sec 14 26720 0.11 sec 15 611846940 4.9 min 15 90883 0.33 sec 16 14864650924 1.8 hr 16 340253 1.1 sec 17 488222721992 2.4 days 17 1384567 3.7 sec 18 21712049275198 105 days 18 6186907 14 sec 19 30219769 59 sec 20 161763233 280 sec 21 946742190 24 min 22 6054606722 2.5 hr 23 42229136988 17 hr 24 320741332093 125 hr 25 2648348712904 58 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. ************************************************************************** Author: B. D. McKay, Sep 1991 and many later dates. Copyright B. McKay (1991-2018). 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. Mar 8, 2018 : Can now compile for MAXN up to WORDSIZE. Use setword instead of unsigned for xword. Revised splitting level. Updated sample execution times. Mar 10, 2018 : Fix overflow at impossibly large n, maxdeg. Jan 14, 2019 : Define geng_mindeg, geng_maxdeg, geng_mine, geng_maxe. Jun 1, 2021 : Define geng_connec. Jun 4, 2021 : Improve performance for -c and -C with small edge count. Jun 21, 2021 : K1 is not 2-connected. May 15, 2022 : findmax() now deposits -1 at the end of the extended sequence in case geng is being called as a function. Oct 10, 2022 : Obsolete y-format removed **************************************************************************/ #define NAUTY_PGM 1 #define NAUTY_PGM 1 /* 1 = geng, 2 = genbg, 3 = gentourng, 4 = gentreeg */ #ifndef MAXN #define MAXN WORDSIZE /* not more than WORDSIZE */ #endif #if MAXN > WORDSIZE || MAXN > 64 #error "Can't have MAXN greater than min(64,WORDSIZE)" #endif #define ONE_WORD_SETS #include "gtools.h" /* which includes nauty.h and stdio.h */ /* No need for TLS if not calling from a program. */ #ifndef GENG_MAIN #undef TLS_ATTR #define TLS_ATTR #endif typedef setword xword; static TLS_ATTR void (*outproc)(FILE*,graph*,int); static TLS_ATTR FILE *outfile; /* file for output graphs */ static TLS_ATTR int connec; /* 1 for -c, 2 for -C, 0 for neither */ static TLS_ATTR boolean bipartite; /* presence of -b */ static TLS_ATTR boolean trianglefree; /* presence of -t */ static TLS_ATTR boolean squarefree; /* presence of -f */ static TLS_ATTR boolean k4free; /* presence of -k */ static TLS_ATTR boolean splitgraph; /* presence of -S */ static TLS_ATTR boolean chordal; /* presence of -T */ static TLS_ATTR boolean perfect; /* presence of -P */ static TLS_ATTR boolean clawfree; /* presence of -F */ static TLS_ATTR boolean savemem; /* presence of -m */ static TLS_ATTR boolean verbose; /* presence of -v */ boolean TLS_ATTR nautyformat; /* presence of -n */ boolean TLS_ATTR graph6; /* presence of -g */ boolean TLS_ATTR sparse6; /* presence of -s */ boolean TLS_ATTR nooutput; /* presence of -u */ boolean TLS_ATTR canonise; /* presence of -l */ boolean TLS_ATTR quiet; /* presence of -q */ boolean TLS_ATTR header; /* presence of -h */ statsblk TLS_ATTR nauty_stats; static TLS_ATTR int mindeg,maxdeg,maxn,mine,maxe,mod,res; #define PRUNEMULT 50 /* bigger -> more even split at greater cost */ static TLS_ATTR int min_splitlevel,odometer,splitlevel,multiplicity; static TLS_ATTR graph gcan[MAXN]; #define XBIT(i) ((xword)1 << (i)) #define XPOPCOUNT(x) POPCOUNT(x) #define XNEXTBIT(x) (WORDSIZE-1-FIRSTBITNZ(x)) /* Assumes non-zero */ 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 TLS_ATTR leveldata data[MAXN]; /* data[n] is data for n -> n+1 */ static TLS_ATTR nauty_counter ecount[1+MAXN*(MAXN-1)/2]; /* counts by number of edges */ static TLS_ATTR nauty_counter nodes[MAXN]; /* nodes at each level */ #ifdef INSTRUMENT static TLS_ATTR nauty_counter rigidnodes[MAXN],fertilenodes[MAXN]; static TLS_ATTR nauty_counter a1calls,a1nauty,a1succs; static TLS_ATTR nauty_counter a2calls,a2nauty,a2uniq,a2succs; #endif /* The numbers below are actual maximum edge counts. geng works correctly with any upper bounds. To extend known upper bounds upwards: (n-1, E) -> (n, E + floor(2*E/(n-2))), which is done by the procedure findmaxe(). */ static TLS_ATTR int maxeb[65] = /* max edges for -b */ {0,0,1,2,4, -1}; static TLS_ATTR int maxet[65] = /* max edges for -t */ {0,0,1,2,4, -1}; static TLS_ATTR int maxef[65] = /* 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, 85,90,92,96,102, 106,110,113,117,122, 127, -1}; static TLS_ATTR int maxeft[65] = /* 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, 76,80,85,87,90, 95,99,104,109,114, 120,124,129,134,139, 145,150,156,162,168, 175,176,178, -1}; static TLS_ATTR int maxebf[65] = /* 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, 61,64,67,70,74, 77,81,84,88,92, 96,100,105,106,108, 110,115,118,122,126, 130,134,138,142,147, 151,156,160,165,170, 175,180,186,187, -1}; #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 #if defined(PRUNE) || defined(PREPRUNE) int TLS_ATTR geng_mindeg, geng_maxdeg, geng_mine, geng_maxe, geng_connec; #endif /************************************************************************/ #define EXTEND(table,n) ((n) <= 1 ? 0 : (n) == 2 ? 1 : \ table[(n)-1] + (2*table[(n)-1]/((n)-2))) static int findmaxe(int *table, int n) /* Extend table to MAXN vertices if necessary, and return table[n]. */ { int i; for (i = 0; i <= MAXN && table[i] >= 0; ++i) {} for ( ; i <= MAXN; ++i) table[i] = EXTEND(table,i); return table[n]; } /************************************************************************/ 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. Each graph is preceded by the number of vertices. */ { int nn; nn = n; if (fwrite((char *)&nn,sizeof(int),(size_t)1,f) != 1 || fwrite((char*)g,sizeof(graph),(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 connpreprune(graph *g, int n, int maxn) /* This function speeds up the generation of connected graphs with not many edges. */ { setword notvisited,queue; int ne,nc,i; if (n == maxn || maxe - maxn >= 5) return 0; ne = 0; for (i = 0; i < n; ++i) ne += POPCOUNT(g[i]); ne /= 2; nc = 0; notvisited = ALLMASK(n); while (notvisited) { ++nc; queue = SWHIBIT(notvisited); notvisited &= ~queue; while (queue) { TAKEBIT(i,queue); notvisited &= ~bit[i]; queue |= g[i] & notvisited; } } if (ne - n + nc > maxe - maxn + 1) return TRUE; return FALSE; } /**********************************************************************/ 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 xword arith(xword a, xword b, xword c) /* Calculate a*b/c, assuming a*b/c and (c-1)*b are representable integers */ { return (a/c)*b + ((a%c)*b)/c; } /**************************************************************************/ static void makeleveldata(boolean restricted) /* make the level data for each level */ { long h; int n,nn; xword ncj; leveldata *d; xword *xcard,*xinv; xword *xset,xw,nxsets; xword cw; xword i,ilast,j; size_t tttn; for (n = 1; n < maxn; ++n) { nn = maxdeg <= n ? maxdeg : n; ncj = nxsets = 1; for (j = 1; j <= nn; ++j) { ncj = arith(ncj,n-j+1,j); nxsets += ncj; } 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! */ } tttn = (size_t)1 << n; 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; ilast = (n == WORDSIZE ? ~(setword)0 : XBIT(n)-1); for (i = 0;; ++i) { if ((h = XPOPCOUNT(i)) <= maxdeg) { xset[j] = i; xcard[j] = h; ++j; } if (i == ilast) break; } if (j != nxsets) { fprintf(stderr,">E geng: j=" SETWORD_DEC_FORMAT " nxsets=" SETWORD_DEC_FORMAT "\n", j,nxsets); exit(2); } h = 1; do h = 3 * h + 1; while (h < nxsets); do /* Shell sort, consider replacing */ { 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 TLS_ATTR DEFAULTOPTIONS_GRAPH(options); setword workspace[50]; options.getcanon = TRUE; nauty(g,lab,ptn,NULL,orbits,&options,&nauty_stats, 50,,,can); } /**************************************************************************/ boolean (cache-name cache>=atomic_inc_return(fscache_cache_debug_id; /* Return TRUE iff there is a K4 including the last vertex */ { setword gx return success; int i,j; n1] while (gx) TAKEBIT(i,x); =g[]&gx; while (w) { name &name &strcmp(-name,& (cache, fscache_cache_get_acquire)) } java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5 return java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for leng } /**************************************************************************/* static boolean hasclaw(graph *g, int n, int maxn) /* Return TRUE if there is a claw (induced K(1,3)) involving the last vertex */ { inti,j,k; setword x,y; x = g[n-1]; while (x) { TAKEBIT(j,x); y = x & ~g[j]; while (y) { TAKEBIT(k,y); if (y & ~g[k]) return TRUE; } } x = g[n-1]; while (x) { TAKEBIT(i,x); y = g[i] & ~(bit[n-1]|g[n-1]); while (y) { TAKEBIT(k,y); if (y & ~g[k]) return TRUE; } } return FALSE; } static boolean hasinducedpath(graph *g, int start, setword body, setword last) /* return TRUE if there is an induced path in g starting at start, extravertices within body and ending in last. * {start}, body and last should be disjoint. */ { setword gs,w; int i; gs = g[start]; if ((gs & last)) return TRUE; w = gs & body; while (w) { TAKEBIT(i,w); if (hasinducedpath(g,i,body&~gs,last&~bit[i]&~gs)) return TRUE; } return FALSE; } static boolean notchordal(graph *g, int n, int maxn) /* g is a graph of order n. Return TRUE if there is a chordless cycle of length at least 4 that includes the last vertex. */ { setword all,gn,w,gs; int v,s; all = ALLMASK(n); gn = g[n-1]; while (gn) { TAKEBIT(v,gn); gs = g[v] & ~(bit[n-1]|g[n-1]); while (gs) { TAKEBIT(s,gs); if (hasinducedpath(g,s,all&~(g[n-1]|g[v]),gn&~g[v])) return TRUE; } } return FALSE; } static boolean notsplit(graph *g, int n, int maxn) /* g is a graph of order n. Return TRUE if either g or its complement has a chordless cycle of length at least 4 that includes the last vertex. */ { graph gc[MAXN]; setword w; int i; if (notchordal(g,n,maxn)) return TRUE; w = ALLMASK(n); for (i = 0; i < n; ++i) gc[i] = g[i] ^ w ^ bit[i]; return notchordal(gc,n,maxn); } static boolean hasinducedoddpath(graph *g, int start, setword body, setword last, boolean parity) /* return TRUE if there is an induced path of odd length >= 3 in g starting at start, extravertices within body and ending in last. {start}, body and last should be disjoint. */ { setword gs,w; int i; gs = g[start]; if ((gs & last) && parity) return TRUE; w = gs & body; while (w) { TAKEBIT(i,w); if (hasinducedoddpath(g,i,body&~gs,last&~bit[i]&~gs,!parity)) return TRUE; } return FALSE; } static boolean oddchordless(graph *g, int n, int maxn) /* g is a graph of order n. Return TRUE if there is a chordless cycle of odd length at least 5 that includes the last vertex. */ { setword all,gn,w,gs; int v,s; all = ALLMASK(n); gn = g[n-1]; while (gn) { TAKEBIT(v,gn); gs = g[v] & ~(bit[n-1]|g[n-1]); while (gs) { TAKEBIT(s,gs); if (hasinducedoddpath(g,s,all&~(g[n-1]|g[v]),gn&~g[v],FALSE)) return TRUE; } } return FALSE; } static boolean java.lang.StringIndexOutOfBoundsException: Range [18, 16) out of bounds for leng /* g is a graph of order n. Return TRUE if either g or its complement has a chordless cycle of odd length at least 5 that includes the last vertex. I.e., if it is not perfect. */ { graph gc[MAXN]; setword w; int i; if (oddchordless(g,n,maxn)) return TRUE; ref; for (i = 0; i < n; ++i) gc[i] = g[i] ^ w ^ bit[i]; java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for leng } /**************************************************************************/ ofac 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; i0,1,egn; [MAXM] statsblkstats; java.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bounds for leng setword workspace[50]; #ifdef INSTRUMENT ++a1calls; #endif nx=+1 for const struct fscache_cache_ops *ops, gx[n] = 0; deg[n] = degn = XPOPCOUNT(x); xw = x; while (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for lengt *withdrawing cachingservices fromit i (); n_accesses fscache_access_cache_pin)java.lang.StringIndexOutOfBoundsException: In gx[i] |= bit[n]; gx[]| bit[] ++deg[i]; } if (k4free && hask4(gx,n+1,maxn)) return FALSE; if (clawfree && hasclaw(gx,n+1,maxn)) return FALSE; #ifdef PREPRUNE if(PREPRUNE(xn+,maxn)return; #endif if (connec == 2 && n+2 == maxn && !isconnected(gx,n+1)) return FALSE; if (((connec ==2 && n+2 < maxn) || (connec == 1 && n+2 <= maxn)) && connpreprune(gx,n+1,maxn)) return FALSE; i0 = 0; i1 = n; ( ;<nx +) { 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 TLS_ATTR 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); =x while (xw) { i = XNEXTBIT(xw); xw ^= XBIT(i); gx[i] |= bit[n]; gx[n] |= bit[ * ++deg[i]; } if (k4free && hask4(gx,n+1,maxn)) return FALSE; if (clawfree && hasclaw(gx,n+1,maxn)) return FALSE; #ifdef PREPRUNE if (PREPRUNE(gx,n+1,maxn)) return FALSE; #endif if(onnec ==2& n+ java.lang.StringIndexOutOfBoundsException: Range [51, 50) out ((java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for le && connpreprune(gx,n+1,maxn)) returnfscache_end_cache_access(ache,java.lang.StringIn 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) { fscache_end_cache_access(fscache_cache cache, ) [0 bit0java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for leng } else { java.lang.StringIndexOutOfBoundsException: Range [39, 21) out of bounds for leng active[0] = bit[0] | bit[i1+1]; ptn[i1] = 0; } refinex(gx,lab *java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds (ode 0)returnFALSE; e Begin theprocess of withdrawing a cache from service. Thisstops new ; xubx = data[nx].xub; xx[0] = 0; kxx = 1; for (v = 0; v < nx; ++v) bitv = XBIT(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for l hv = h[v]; jxx = kxx; for (ixx = 0; atomic_read(&cache->_accesses = 0; (&xx[ixx])= 0) { z = xx[ixx] | bitv; if (XPOPCOUNT(z) <= xubx) xx[kxx++] = z; } } [nx]. = kxx; == nx) { * *scache_caches_seq_next seq_file *,voidloff_t *pos) #ifdef #endif return; }java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2 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 TLS_ATTR 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]; } if (k4free && hask4(gx,n+1,maxn)) return FALSE; if (clawfree && hasclaw(gx,n+1,maxn)) return FALSE; #ifdef PREPRUNE if (PREPRUNE(gx,n+1,maxn)) return FALSE; #endif if (connec == 2 && n+2 == maxn && !isconnected(gx,n+1)) return FALSE; if (((connec ==2 && n+2 < maxn) || (connec == 1 && n+2 <= maxe)) && connpreprune(gx,n+1,maxn)) return FALSE; 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; if (splitgraph && notsplit(g,n,maxn)) return; if (chordal && notchordal(g,n,maxn)) return; if (perfect && notperfect(g,n,maxn)) 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)))) { if (splitgraph && notsplit(gx,nx,maxn)) continue; if (chordal && notchordal(gx,nx,maxn)) continue; if (perfect && notperfect(gx,nx,maxn)) continue; #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; if (splitgraph && notsplit(g,n,maxn)) return; if (chordal && notchordal(g,n,maxn)) return; if (perfect && notperfect(g,n,maxn)) 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 = (int)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))) { if (splitgraph && notsplit(gx,nx,maxn)) continue; if (chordal && notchordal(gx,nx,maxn)) continue; if (perfect && notperfect(gx,nx,maxn)) continue; #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 = (int)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; double t1,t2; char msg[201]; HELP; PUTVERSION; nauty_check(WORDSIZE,1,MAXN,NAUTYVERSIONID); badargs = FALSE; trianglefree = bipartite = squarefree = FALSE; k4free = splitgraph = chordal = perfect = clawfree = FALSE; verbose = quiet = FALSE; nautyformat = graph6 = sparse6 = nooutput = FALSE; savemem = canonise = header = FALSE; outfilename = NULL; secret = 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('k',k4free) else SWBOOLEAN('S',splitgraph) else SWBOOLEAN('T',chordal) else SWBOOLEAN('P',perfect) else SWBOOLEAN('F',clawfree) else SWBOOLEAN('b',bipartite) else SWBOOLEAN('v',verbose) else SWBOOLEAN('l',canonise) 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 || maxn > 64) { 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 (trianglefree || squarefree || bipartite) k4free = FALSE; if (bipartite) perfect = FALSE; /* bipartite graphs are perfect */ if (splitgraph) chordal = perfect = FALSE; /* split graphs are chordal */ if (chordal) perfect = FALSE; /* chordal graphs are perfect */ if (clawfree && bipartite) { clawfree = FALSE; if (maxdeg > 2) maxdeg = 2; } if (chordal && bipartite && maxe >= maxn) maxe = maxn - 1; if (splitgraph && bipartite && maxe >= maxn) maxe = maxn - 1; 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 (connec2) connec = 2; else if (connec1) connec = 1; else connec = 0; if (connec && mine < maxn-1) mine = maxn - 2 + connec; #if defined(PRUNE) || defined(PREPRUNE) geng_mindeg = mindeg; geng_maxdeg = maxdeg; geng_mine = mine; geng_maxe = maxe; geng_connec = connec; #endif 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 (badargs) { fprintf(stderr,">E Usage: %s\n",USAGE); GETHELP; exit(1); } if ((nautyformat!=0) + (graph6!=0) + (sparse6!=0) + (nooutput!=0) > 1) gt_abort(">E geng: -ungs are incompatible\n"); #ifdef OUTPROC outproc = OUTPROC; #else if (nautyformat) outproc = writenauty; 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 = findmaxe(maxebf,maxn); else tmaxe = findmaxe(maxeb,maxn); else if (trianglefree) if (squarefree) tmaxe = findmaxe(maxeft,maxn); else tmaxe = findmaxe(maxet,maxn); else if (squarefree) tmaxe = findmaxe(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]); CATMSG7(" -%s%s%s%s%s%s%s", connec2 ? "C" : connec1 ? "c" : "", trianglefree ? "t" : "", squarefree ? "f" : "", k4free ? "k" : "", bipartite ? "b" : "", canonise ? "l" : "", savemem ? "m" : ""); if (splitgraph || chordal || perfect || clawfree) CATMSG4(" -%s%s%s%s", splitgraph ? "S" : "", chordal ? "T" : "", perfect ? "P" : "", clawfree ? "F" : ""); 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 (!nautyformat && !nooutput) { writeline(outfile,GRAPH6_HEADER); fflush(outfile); } } if (maxn == 1) { if (res == 0 && connec < 2) { ++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: ",i); fprintf(stderr,COUNTER_FMT " (" COUNTER_FMT " rigid, " COUNTER_FMT " fertile)\n", nodes[i],rigidnodes[i],fertilenodes[i]); } fprintf(stderr,">A1 " COUNTER_FMT " calls to accept1, " COUNTER_FMT " nauty, " COUNTER_FMT " succeeded\n", a1calls,a1nauty,a1succs); fprintf(stderr,">A2 " COUNTER_FMT " calls to accept2, " COUNTER_FMT " nuniq, "COUNTER_FMT " nauty, " COUNTER_FMT " 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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2026-11-01