/***************************************************************************** * * * Vertex-invariants source file for nauty 2.8. * * * * Copyright (1989-2022) Brendan McKay. All rights reserved. * * Subject to waivers and disclaimers in nauty.h. * * * * CHANGE HISTORY * * 13-Mar-90 : initial release for version 1.5 * * 10-Nov-90 : changes for version 1.6 : * * - added dummy routine nautinv_null() * * 27-Aug-92 : renamed to version 1.7, no changes to this file * * 5-Jun-93 : renamed to version 1.7+, no changes to this file * * 18-Aug-93 : renamed to version 1.8, no changes to this file * * 17-Sep-93 : changes for version 1.9 : * * - added invariant routine adjacencies() * * 20-Jun-96 : changes for version 2.0 : * * - added invariants cellfano() and cellfano2() * * 11-Jul-96 - added dynamic allocation * * 21-Oct-98 - use shortish in place of short for BIGNAUTY * * 9-Jan-00 - added nautinv_check() * * 12-Feb-00 - minor code formatting * * 16-Nov-00 - made changes listed in nauty.h * * 22-Apr-01 : changes for version 2.1 : * * - made all large dynamic memory external to routines * * - added nautinv_freedyn() to free all such memory * * - include nautinv.h rather than naututil.h * * - removed nautinv_null() * * - added code to facilitate compilation into Magma * * - removed EXTDEFS * * 12-Jul-01 - use invararg in distances() * * - fixed comments in ind and cliq routines * * 21-Nov-01 : use NAUTYREQUIRED in nautinv_check() * * 10-Dec-06 : remove BIGNAUTY * * 10-Nov-09 : remove types shortish and permutation * * 23-Nov-09 : add refinvar() * * 12-Jun-10 : fixed identical errors in cellcliq() and cellind() * * 15-Jan-12 : add TLS_ATTR attributes * * 23-Aug-12 : fix getbigcells(), thanks to Fatih Demirkale * * 23-Jan-13 : add some parens to satisfy icc * * *
*****************************************************************************/
#define ONE_WORD_SETS #include"nautinv.h"
#if MAXM==1 #define M 1 #else #define M m #endif
#define MASH(l,i) ((((l) ^ 056345) + (i)) & 077777) /* : expression whose long value depends only on long l and int/long i.
Anything goes, preferably non-commutative. */
#define CLEANUP(l) ((int)((l) % 077777)) /* : expression whose value depends on long l and is less than 077777
when converted to int then short. Anything goes. */
#define ACCUM(x,y) x = (((x) + (y)) & 077777) /* : must be commutative. */
#define MAXCLIQUE 10 /* max clique size for cliques() and maxindset() */
#if MAXN static TLS_ATTR int workshort[MAXN+2]; static TLS_ATTR int vv[MAXN],ww[MAXN]; static TLS_ATTR int workperm[MAXN]; static TLS_ATTR int bucket[MAXN+2]; static TLS_ATTR int count[MAXN]; static TLS_ATTR set workset[MAXM]; static TLS_ATTR set w01[MAXM],w02[MAXM],w03[MAXM],w12[MAXM],w13[MAXM],w23[MAXM]; static TLS_ATTR set pt0[MAXM],pt1[MAXM],pt2[MAXM]; static TLS_ATTR set wss[MAXCLIQUE-1][MAXM]; static TLS_ATTR set ws1[MAXM],ws2[MAXM]; #else
DYNALLSTAT(int,workshort,workshort_sz);
DYNALLSTAT(int,vv,vv_sz);
DYNALLSTAT(int,ww,ww_sz);
DYNALLSTAT(int,workperm,workperm_sz);
DYNALLSTAT(int,bucket,bucket_sz);
DYNALLSTAT(int,count,count_sz);
DYNALLSTAT(set,ws1,ws1_sz);
DYNALLSTAT(set,ws2,ws2_sz);
DYNALLSTAT(set,workset,workset_sz);
DYNALLSTAT(set,w01,w01_sz);
DYNALLSTAT(set,w02,w02_sz);
DYNALLSTAT(set,w03,w03_sz);
DYNALLSTAT(set,w12,w12_sz);
DYNALLSTAT(set,w13,w13_sz);
DYNALLSTAT(set,w23,w23_sz);
DYNALLSTAT(set,pt0,pt0_sz);
DYNALLSTAT(set,pt1,pt1_sz);
DYNALLSTAT(set,pt2,pt2_sz);
DYNALLSTAT(set,wss,wss_sz); #endif
/* aproto: header new_nauty_protos.h */
/***************************************************************************** * * * This file contains a number of procedures which compute vertex-invariants * * for stronger partition refinement. Since entirely different * * vertex-invariants seem to work better for different types of graph, we * * cannot do more than give a small collection of representative examples. * * Any serious computations with difficult graphs may well need to use * * specially-written vertex-invariants. The use of vertex-invariants * * procedures is supported by nauty from version 1.5 onwards, via the * * options userinvarproc, mininvarlevel, maxinvarlevel and invararg. * * The meaning of these fields in detail are as follows: * * userinvarproc is the address of the vertex-invariant procedure. If * * no vertex-invariants is required, this field should * * have the value NULL. * * maxinvarlevel The absolute value of this is the maximum level in the * * search tree at which the vertex-invariant will be * * computed. The root of the tree is at level 1, so the * * vertex-invariant will not be invoked at all if * * maxinvarlevel==0. Negative values of maxinvarlevel * * request nauty to not compute the vertex-invariant at * * a level greater than that of the earliest node (if any) * * on the path to the first leaf of the search tree at * * which the vertex-invariant refines the partition. * * mininvarlevel The absolute value of this is the minimum level in the * * search tree at which the vertex-invariant will be * * computed. The root of the tree is at level 1, so there * * is no effective limit if mininvarlevel is -1, 0 or 1. * * Negative values of mininvarlevel request nauty to not * * compute the vertex-invariant at a level less than * * that of the earliest node (if any) on the path to the * * first leaf of the search tree at which the * * vertex-invariant refines the partition. * * invararg is passed to the vertex-invariant procedure via the * * argument of the same name. It can be used by the * * procedure for any purpose. * * Note that negative values of maxinvarlevel and mininvarlevel make the * * canonical labelling invalid, but can speed automorphism group finding. * * Nauty already knows this and takes their absolute values. * * * * A vertex-invariant must be declared thus: * * void invarproc(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) * * All of these arguments must be treated as read-only except for invar. * * g : the graph, exactly as passed to nauty() * * lab,ptn : the current partition nest (see nauty.h for the format) * * level : the level of this node in the search tree. * * numcells : the number of cells in the partition at this node. * * tvpos : the index in (lab,ptn) of one cell in the partition. * * If level <= 1, the cell will be the first fragment of the * * first active cell (as provided by the initial call to nauty), * * or the first cell, if there were no active cells. * * If level > 1, the cell will be the singleton cell which was * * created to make this node of the search tree from its parent. * * invararg : a copy of options.invararg * * digraph : a copy of options.digraph * * m,n : size parameters as passed to nauty() * * invar : an array to return the answer in. The procedure must put in * * each invar[i] (0 <= i < n) an invariant of the 6-tuple * * (<vertex i>,g,<the partition nest to this level>,level, * * invararg,digraph) * * Note that invar[] is declared as an int array. Since the * * absolute value of the invariant is irrelevant, only the * * comparative values, any short, int or long value can be * * assigned to the entries of invar[] without fear. However, * * you should assign a value less than 077777 to ensure machine- * * independence of the canonical labelling. * * * * The refinement procedure has already been called before the invariant * * procedure is called. That means that the partition is equitable if * * digraph==FALSE. * * *
*****************************************************************************/
/***************************************************************************** * * * twopaths() assigns to each vertex v the sum of the weights of each vertex * * which can be reached from v along a walk of length two (including itself * * usually). The weight of each vertex w is defined as the ordinal number * * of the cell containing w, starting at 1 for the first cell. * * *
*****************************************************************************/
void
twopaths(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,v,w; int wt;
set *gv,*gw;
wt = 1; for (i = 0; i < n; ++i)
{
workshort[lab[i]] = wt; if (ptn[i] <= level) ++wt;
}
for (v = 0, gv = (set*)g; v < n; ++v, gv += M)
{
EMPTYSET(workset,m);
w = -1; while ((w = nextelement(gv,M,w)) >= 0)
{
gw = GRAPHROW(g,w,m); for (i = M; --i >= 0;) UNION(workset[i],gw[i]);
}
wt = 0;
w = -1; while ((w = nextelement(workset,M,w)) >= 0) ACCUM(wt,workshort[w]);
invar[v] = wt;
}
}
/***************************************************************************** * * * quadruples() assigns to each vertex v a value depending on the set of * * weights w(v,v1,v2,v3), where w(v,v1,v2,v3) depends on the number of * * vertices adjacent to an odd number of {v,v1,v2,v3}, and to the cells * * that v,v1,v2,v3 belong to. {v,v1,v2,v3} are permitted to range over all * * distinct 4-tuples which contain at least one member in the cell tvpos. * * *
*****************************************************************************/
void
quadruples(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,pc;
setword sw;
set *gw; int wt; int v,iv,v1,v2,v3;
set *gv; long wv,wv1,wv2,wv3;
wt = 1; for (i = 0; i < n; ++i)
{
workshort[lab[i]] = FUZZ2(wt); if (ptn[i] <= level) ++wt;
}
iv = tvpos - 1; do
{
v = lab[++iv];
gv = GRAPHROW(g,v,m);
wv = workshort[v]; for (v1 = 0; v1 < n-2; ++v1)
{
wv1 = workshort[v1]; if (wv1 == wv && v1 <= v) continue;
wv1 += wv;
gw = GRAPHROW(g,v1,m); for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i]; for (v2 = v1+1; v2 < n-1; ++v2)
{
wv2 = workshort[v2]; if (wv2 == wv && v2 <= v) continue;
wv2 += wv1;
gw = GRAPHROW(g,v2,m); for (i = M; --i >= 0;) ws1[i] = workset[i] ^ gw[i]; for (v3 = v2+1; v3 < n; ++v3)
{
wv3 = workshort[v3]; if (wv3 == wv && v3 <= v) continue;
wv3 += wv2;
gw = GRAPHROW(g,v3,m);
pc = 0; for (i = M; --i >= 0;) if ((sw = ws1[i] ^ gw[i]) != 0) pc += POPCOUNT(sw);
wt = (FUZZ1(pc)+wv3) & 077777;
wt = FUZZ2(wt);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
ACCUM(invar[v3],wt);
}
}
}
} while (ptn[iv] > level);
}
/***************************************************************************** * * * triples() assigns to each vertex v a value depending on the set of * * weights w(v,v1,v2), where w(v,v1,v2) depends on the number of vertices * * adjacent to an odd number of {v,v1,v2}, and to the cells that * * v,v1,v2 belong to. {v,v1,v2} are permitted to range over all distinct * * triples which contain at least one member in the cell tvpos. * * *
*****************************************************************************/
void
triples(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,pc;
setword sw;
set *gw; int wt; int v,iv,v1,v2;
set *gv; long wv,wv1,wv2;
wt = 1; for (i = 0; i < n; ++i)
{
workshort[lab[i]] = FUZZ1(wt); if (ptn[i] <= level) ++wt;
}
iv = tvpos - 1; do
{
v = lab[++iv];
gv = GRAPHROW(g,v,m);
wv = workshort[v]; for (v1 = 0; v1 < n-1; ++v1)
{
wv1 = workshort[v1]; if (wv1 == wv && v1 <= v) continue;
wv1 += wv;
gw = GRAPHROW(g,v1,m); for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i]; for (v2 = v1+1; v2 < n; ++v2)
{
wv2 = workshort[v2]; if (wv2 == wv && v2 <= v) continue;
wv2 += wv1;
gw = GRAPHROW(g,v2,m);
pc = 0; for (i = M; --i >= 0;) if ((sw = workset[i] ^ gw[i]) != 0) pc += POPCOUNT(sw);
wt = (FUZZ1(pc)+wv2) & 077777;
wt = FUZZ2(wt);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
}
}
} while (ptn[iv] > level);
}
/***************************************************************************** * * * adjtriang() assigns to each vertex v a value depending on the numbers * * of common neighbours between each pair {v1,v2} of neighbours of v, and * * which cells v1 and v2 lie in. The vertices v1 and v2 must be adjacent * * if invararg == 0 and not adjacent if invararg == 1. * * *
*****************************************************************************/
void
adjtriang(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int j,pc;
setword sw;
set *gi; int wt; int i,v1,v2;
boolean v1v2;
set *gv1,*gv2;
gv2 = GRAPHROW(g,v2,m); for (i = M; --i >= 0;) workset[i] = gv1[i] & gv2[i];
i = -1; while ((i = nextelement(workset,M,i)) >= 0)
{
pc = 0;
gi = GRAPHROW(g,i,m); for (j = M; --j >= 0;) if ((sw = workset[j] & gi[j]) != 0) pc += POPCOUNT(sw);
pc = (pc + wt) & 077777;
ACCUM(invar[i],pc);
}
}
}
}
/***************************************************************************** * * * getbigcells(ptn,level,minsize,bigcells,cellstart,cellsize,n) is an * * auxiliary procedure to make a list of all the large cells in the current * * partition. On entry, ptn, level and n have their usual meanings, * * while minsize is the smallest size of an interesting cell. On return, * * bigcells is the number of cells of size at least minsize, cellstart[0...] * * contains their starting positions in ptn, and cellsize[0...] contain * * their sizes. These two arrays are in increasing order of cell size, * * then position. * * *
*****************************************************************************/
void
getbigcells(int *ptn, int level, int minsize, int *bigcells, int *cellstart, int *cellsize, int n)
{ int cell1,cell2,j; int si,st; int bc,i,h;
bc = 0; for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{ for (cell2 = cell1; ptn[cell2] > level; ++cell2) {}
j = bc / 3;
h = 1; do
h = 3 * h + 1; while (h < j);
do/* shell sort */
{ for (i = h; i < bc; ++i)
{
st = cellstart[i];
si = cellsize[i]; for (j = i; cellsize[j-h] > si ||
(cellsize[j-h] == si && cellstart[j-h] > st); )
{
cellsize[j] = cellsize[j-h];
cellstart[j] = cellstart[j-h]; if ((j -= h) < h) break;
}
cellsize[j] = si;
cellstart[j] = st;
}
h /= 3;
} while (h > 0);
}
/***************************************************************************** * * * celltrips() assigns to each vertex v a value depending on the set of * * weights w(v,v1,v2), where w(v,v1,v2) depends on the number of vertices * * adjacent to an odd number of {v,v1,v2}. {v,v1,v2} are constrained to * * belong to the same cell. We try the cells in increasing order of size, * * and stop as soon as any cell splits. * * *
*****************************************************************************/
void
celltrips(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,pc;
setword sw;
set *gw; int wt; int v,iv,v1,iv1,v2,iv2; int icell,bigcells,cell1,cell2; int *cellstart,*cellsize;
set *gv;
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1; for (iv = cell1; iv <= cell2 - 2; ++iv)
{
v = lab[iv];
gv = GRAPHROW(g,v,m); for (iv1 = iv + 1; iv1 <= cell2 - 1; ++iv1)
{
v1 = lab[iv1];
gw = GRAPHROW(g,v1,m); for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i]; for (iv2 = iv1 + 1; iv2 <= cell2; ++iv2)
{
v2 = lab[iv2];
gw = GRAPHROW(g,v2,m);
pc = 0; for (i = M; --i >= 0;) if ((sw = workset[i] ^ gw[i]) != 0)
pc += POPCOUNT(sw);
wt = FUZZ1(pc);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
}
}
}
wt = invar[lab[cell1]]; for (i = cell1 + 1; i <= cell2; ++i) if (invar[lab[i]] != wt) return;
}
}
/***************************************************************************** * * * cellquads() assigns to each vertex v a value depending on the set of * * weights w(v,v1,v2,v3), where w(v,v1,v2,v3) depends on the number of * * vertices adjacent to an odd number of {v,v1,v2,v3}. {v,v1,v2,v3} are * * constrained to belong to the same cell. We try the cells in increasing * * order of size, and stop as soon as any cell splits. * * *
*****************************************************************************/
void
cellquads(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,pc;
setword sw;
set *gw; int wt; int v,iv,v1,iv1,v2,iv2,v3,iv3; int icell,bigcells,cell1,cell2; int *cellstart,*cellsize;
set *gv;
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1; for (iv = cell1; iv <= cell2 - 3; ++iv)
{
v = lab[iv];
gv = GRAPHROW(g,v,m); for (iv1 = iv + 1; iv1 <= cell2 - 2; ++iv1)
{
v1 = lab[iv1];
gw = GRAPHROW(g,v1,m); for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i]; for (iv2 = iv1 + 1; iv2 <= cell2 - 1; ++iv2)
{
v2 = lab[iv2];
gw = GRAPHROW(g,v2,m); for (i = M; --i >= 0;) ws1[i] = workset[i] ^ gw[i]; for (iv3 = iv2 + 1; iv3 <= cell2; ++iv3)
{
v3 = lab[iv3];
gw = GRAPHROW(g,v3,m);
pc = 0; for (i = M; --i >= 0;) if ((sw = ws1[i] ^ gw[i]) != 0)
pc += POPCOUNT(sw);
wt = FUZZ1(pc);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
ACCUM(invar[v3],wt);
}
}
}
}
wt = invar[lab[cell1]]; for (i = cell1 + 1; i <= cell2; ++i) if (invar[lab[i]] != wt) return;
}
}
/***************************************************************************** * * * cellquins() assigns to each vertex v a value depending on the set of * * weights w(v,v1,v2,v3,v4), where w(v,v1,v2,v3,v4) depends on the number * * of vertices adjacent to an odd number of {v,v1,v2,v3,v4}. * * {v,v1,v2,v3,v4} are constrained to belong to the same cell. We try the * * cells in increasing order of size, and stop as soon as any cell splits. * * *
*****************************************************************************/
void
cellquins(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,pc;
setword sw;
set *gw; int wt; int v,iv,v1,iv1,v2,iv2,v3,iv3,v4,iv4; int icell,bigcells,cell1,cell2; int *cellstart,*cellsize;
set *gv;
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1; for (iv = cell1; iv <= cell2 - 4; ++iv)
{
v = lab[iv];
gv = GRAPHROW(g,v,m); for (iv1 = iv + 1; iv1 <= cell2 - 3; ++iv1)
{
v1 = lab[iv1];
gw = GRAPHROW(g,v1,m); for (i = M; --i >= 0;) workset[i] = gv[i] ^ gw[i]; for (iv2 = iv1 + 1; iv2 <= cell2 - 2; ++iv2)
{
v2 = lab[iv2];
gw = GRAPHROW(g,v2,m); for (i = M; --i >= 0;) ws1[i] = workset[i] ^ gw[i]; for (iv3 = iv2 + 1; iv3 <= cell2 - 1; ++iv3)
{
v3 = lab[iv3];
gw = GRAPHROW(g,v3,m); for (i = M; --i >= 0;) ws2[i] = ws1[i] ^ gw[i]; for (iv4 = iv3 + 1; iv4 <= cell2; ++iv4)
{
v4 = lab[iv4];
gw = GRAPHROW(g,v4,m);
pc = 0; for (i = M; --i >= 0;) if ((sw = ws2[i] ^ gw[i]) != 0)
pc += POPCOUNT(sw);
wt = FUZZ1(pc);
ACCUM(invar[v],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
ACCUM(invar[v3],wt);
ACCUM(invar[v4],wt);
}
}
}
}
}
wt = invar[lab[cell1]]; for (i = cell1 + 1; i <= cell2; ++i) if (invar[lab[i]] != wt) return;
}
}
/***************************************************************************** * * * uniqinter(s1,s2,m) returns the number in both sets if it is unique, * * or -1 if there is none or it is not unique. *
*****************************************************************************/
staticint
uniqinter(set *s1, set *s2, int m)
{ int i,j;
setword w;
for (i = 0; i < M; ++i)
{ if ((w = s1[i] & s2[i]) != 0)
{
j = FIRSTBITNZ(w); if (w != BITT[j]) return -1;
j += TIMESWORDSIZE(i); for (++i; i < M; ++i) if (s1[i] & s2[i]) return -1; return j;
}
} return -1;
}
/***************************************************************************** * * * cellfano2() assigns to each vertex v a value depending on the set of * * weights w(v,v1,v2,v3), where w(v,v1,v2,v3) depends on the number of * * fano-plane analogues containing {v,v1,v2,v3}. {v,v1,v2,v3} are * * constrained to belong to the same cell and being independent and * * non-collinear. We try the cells in increasing order of size, and stop * * as soon as any cell splits. * * *
*****************************************************************************/
void
cellfano2(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,pc;
setword sw; int wt; int v0,v1,v2,v3,iv0,iv1,iv2,iv3; int icell,bigcells,cell1,cell2; int *cellstart,*cellsize; int nw,x01,x02,x03,x12,x13,x23; int pnt0,pnt1,pnt2;
set *gv0,*gv1,*gv2,*gv3;
set *gp0,*gp1,*gp2;
pc = 0; for (i = M; --i >= 0;)
{
sw = gp0[i] & gp1[i] & gp2[i]; if (sw) pc += POPCOUNT(sw);
}
wt = FUZZ1(pc);
ACCUM(invar[v0],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
ACCUM(invar[v3],wt);
}
}
}
}
wt = invar[lab[cell1]]; for (i = cell1 + 1; i <= cell2; ++i) if (invar[lab[i]] != wt) return;
}
}
/***************************************************************************** * * * setnbhd(g,m,n,w,wn) is an auxiliary routine that sets wn to the union * * of the neighbours of the vertices in w. * * *
*****************************************************************************/
void
setnbhd(graph *g, int m, int n, set *w, set *wn)
{ int i,j;
set *gi;
i = nextelement(w,M,-1); if (i < 0)
{
EMPTYSET(wn,M); return;
}
gi = GRAPHROW(g,i,M); for (j = M; --j >= 0;) wn[j] = gi[j];
while ((i = nextelement(w,M,i)) >= 0)
{
gi = GRAPHROW(g,i,M); for (j = M; --j >= 0;) wn[j] |= gi[j];
}
}
/***************************************************************************** * * * cellfano() assigns to each vertex v a value depending on the set of * * weights w(v,v1,v2,v3), where w(v,v1,v2,v3) depends on the number of * * fano-plane analogues containing {v,v1,v2,v3}. {v,v1,v2,v3} are * * constrained to belong to the same cell and being independent. We try * * the cells in increasing order of size, and stop as soon as any cell * * splits. * * *
*****************************************************************************/
void
cellfano(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,pc;
setword sw; int wt; int v0,v1,v2,v3,iv0,iv1,iv2,iv3; int icell,bigcells,cell1,cell2; int *cellstart,*cellsize;
set *gv0,*gv1,*gv2,*gv3;
for (iv2 = iv1 + 1; iv2 <= cell2 - 1; ++iv2)
{
v2 = lab[iv2]; if (ISELEMENT(gv0,v2) || ISELEMENT(gv1,v2)) continue;
gv2 = GRAPHROW(g,v2,m); for (i = M; --i >= 0;) workset[i] = gv0[i] & gv2[i];
setnbhd(g,m,n,workset,w02); for (i = M; --i >= 0;) workset[i] = gv1[i] & gv2[i];
setnbhd(g,m,n,workset,w12);
for (iv3 = iv2 + 1; iv3 <= cell2; ++iv3)
{
v3 = lab[iv3]; if (ISELEMENT(gv0,v3) || ISELEMENT(gv1,v3) ||
ISELEMENT(gv2,v3)) continue;
gv3 = GRAPHROW(g,v3,m); for (i = M; --i >= 0;) workset[i] = gv0[i] & gv3[i];
setnbhd(g,m,n,workset,w03); for (i = M; --i >= 0;) workset[i] = gv1[i] & gv3[i];
setnbhd(g,m,n,workset,w13); for (i = M; --i >= 0;) workset[i] = gv2[i] & gv3[i];
setnbhd(g,m,n,workset,w23);
for (i = M; --i >= 0;) workset[i] = w01[i] & w23[i];
setnbhd(g,m,n,workset,pt0); for (i = M; --i >= 0;) workset[i] = w03[i] & w12[i];
setnbhd(g,m,n,workset,pt1); for (i = M; --i >= 0;) workset[i] = w02[i] & w13[i];
setnbhd(g,m,n,workset,pt2);
pc = 0; for (i = M; --i >= 0;)
{
sw = pt0[i] & pt1[i] & pt2[i]; if (sw) pc += POPCOUNT(sw);
}
wt = FUZZ1(pc);
ACCUM(invar[v0],wt);
ACCUM(invar[v1],wt);
ACCUM(invar[v2],wt);
ACCUM(invar[v3],wt);
}
}
}
}
wt = invar[lab[cell1]]; for (i = cell1 + 1; i <= cell2; ++i) if (invar[lab[i]] != wt) return;
}
}
/***************************************************************************** * * * distances() assigns to each vertex v a value depending on the number of * * vertices at each distance from v, and what cells they lie in. * * If we find any cell which is split in this manner, we don't try any * * further cells. * * *
*****************************************************************************/
void
distances(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i;
set *gw; int wt; int d,dlim,cell1,cell2,iv,v,w;
boolean success;
wt = 1; for (i = 0; i < n; ++i)
{
workshort[lab[i]] = FUZZ1(wt); if (ptn[i] <= level) ++wt;
}
if (invararg > n || invararg == 0) dlim = n; else dlim = invararg+1;
success = FALSE; for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{ for (cell2 = cell1; ptn[cell2] > level; ++cell2) {} if (cell2 == cell1) continue;
for (iv = cell1; iv <= cell2; ++iv)
{
v = lab[iv];
EMPTYSET(ws1,m);
ADDELEMENT(ws1,v);
EMPTYSET(ws2,m);
ADDELEMENT(ws2,v); for (d = 1; d < dlim; ++d)
{
EMPTYSET(workset,m);
wt = 0;
w = -1; while ((w = nextelement(ws2,M,w)) >= 0)
{
gw = GRAPHROW(g,w,m);
ACCUM(wt,workshort[w]); for (i = M; --i >= 0;) workset[i] |= gw[i];
} if (wt == 0) break;
ACCUM(wt,d);
wt = FUZZ2(wt);
ACCUM(invar[v],wt); for (i = M; --i >= 0;)
{
ws2[i] = workset[i] & ~ws1[i];
ws1[i] |= ws2[i];
}
} if (invar[v] != invar[lab[cell1]]) success = TRUE;
} if (success) break;
}
}
/***************************************************************************** * * * indsets() assigns to each vertex v a value depending on which cells the * * vertices which join v in an independent set lie in. The size of the * * independent sets which are used is the smallest of invararg and MAXCLIQUE.* * *
*****************************************************************************/
void
indsets(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i; int wt;
set *gv; int ss,setsize; int v[MAXCLIQUE]; long wv[MAXCLIQUE];
set *s0,*s1;
wt = 1; for (i = 0; i < n; ++i)
{
workshort[lab[i]] = FUZZ2(wt); if (ptn[i] <= level) ++wt;
}
for (v[0] = 0; v[0] < n; ++v[0])
{
wv[0] = workshort[v[0]];
s0 = (set*)wss;
EMPTYSET(s0,m); for (i = v[0]+1; i < n; ++i) ADDELEMENT(s0,i);
gv = GRAPHROW(g,v[0],m); for (i = M; --i >= 0;) s0[i] &= ~gv[i];
ss = 1;
v[1] = v[0]; while (ss > 0)
{ if (ss == setsize)
{
wt = FUZZ1(wv[ss-1]); for (i = ss; --i >= 0;) ACCUM(invar[v[i]],wt);
--ss;
} elseif ((v[ss] = nextelement((set*)wss+M*(ss-1),M,v[ss])) < 0)
--ss; else
{
wv[ss] = wv[ss-1] + workshort[v[ss]];
++ss; if (ss < setsize)
{
gv = GRAPHROW(g,v[ss-1],m);
s1 = (set*)wss + M*(ss-2); for (i = M; --i >= 0;) s1[i+M] = s1[i] & ~gv[i];
v[ss] = v[ss-1];
}
}
}
}
}
/***************************************************************************** * * * cliques() assigns to each vertex v a value depending on which cells the * * vertices which join v in a clique lie in. The size of the cliques used * * is the smallest of invararg and MAXCLIQUE. * * *
*****************************************************************************/
void
cliques(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i; int wt;
set *gv; int ss,setsize; int v[MAXCLIQUE]; long wv[MAXCLIQUE];
set *ns;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"cliques");
DYNALLOC2(set,wss,wss_sz,m,MAXCLIQUE-1,"cliques"); #else
set wss[MAXCLIQUE-1][MAXM]; #endif
wt = 1; for (i = 0; i < n; ++i)
{
workshort[lab[i]] = FUZZ2(wt); if (ptn[i] <= level) ++wt;
}
for (v[0] = 0; v[0] < n; ++v[0])
{
wv[0] = workshort[v[0]];
gv = GRAPHROW(g,v[0],m);
ns = (set*)wss; for (i = M; --i >= 0;) ns[i] = gv[i];
ss = 1;
v[1] = v[0]; while (ss > 0)
{ if (ss == setsize)
{
wt = FUZZ1(wv[ss-1]); for (i = ss; --i >= 0;) ACCUM(invar[v[i]],wt);
--ss;
} elseif ((v[ss] = nextelement((set*)wss+M*(ss-1),M,v[ss])) < 0)
--ss; else
{
wv[ss] = wv[ss-1] + workshort[v[ss]];
++ss; if (ss < setsize)
{
gv = GRAPHROW(g,v[ss-1],m);
ns = (set*)wss + M*(ss-2); for (i = M; --i >= 0;) ns[i+M] = ns[i] & gv[i];
v[ss] = v[ss-1];
}
}
}
}
}
/***************************************************************************** * * * cellcliq() assigns to each vertex v a value depending on the number of * * cliques which v lies in and which lie in the same cell as v. The size * * of clique counted is the smallest of invararg and MAXCLIQUE. We try the * * cells in increasing order of size and stop as soon as any cell splits. * * *
*****************************************************************************/
void
cellcliq(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i; int wt;
set *gv; int ss,setsize; int v[MAXCLIQUE];
set *ns; int *cellstart,*cellsize; int iv,icell,bigcells,cell1,cell2; int pc;
setword sw;
EMPTYSET(workset,m); for (iv = cell1; iv <= cell2; ++iv) ADDELEMENT(workset,lab[iv]);
for (iv = cell1; iv <= cell2; ++iv)
{
v[0] = lab[iv];
gv = GRAPHROW(g,v[0],m);
ns = (set*)wss;
pc = 0;
for (i = M; --i >= 0;)
{
ns[i] = gv[i] & workset[i]; if ((sw = ns[i]) != 0) pc += POPCOUNT(sw);
} if (pc <= 1 || pc >= cellsize[icell] - 2) continue;
ss = 1;
v[1] = v[0]; while (ss > 0)
{ if (ss == setsize)
{ for (i = ss; --i >= 0;) ++invar[v[i]];
--ss;
} elseif ((v[ss]
= nextelement((set*)wss+M*(ss-1),M,v[ss])) < 0)
--ss; else
{
++ss; if (ss < setsize)
{
gv = GRAPHROW(g,v[ss-1],m);
ns = (set*)wss + M*(ss-2); for (i = M; --i >= 0;) ns[i+M] = ns[i] & gv[i];
v[ss] = v[ss-1];
}
}
}
}
wt = invar[lab[cell1]]; for (iv = cell1 + 1; iv <= cell2; ++iv) if (invar[lab[iv]] != wt) return;
}
}
/***************************************************************************** * * * cellind() assigns to each vertex v a value depending on the number of * * independent sets which v lies in and which lie in the same cell as v. * * The size of clique counted is the smallest of invararg and MAXCLIQUE. * * We try the cells in increasing order of size and stop as soon as any * * cell splits. * * *
*****************************************************************************/
void
cellind(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i; int wt;
set *gv; int ss,setsize; int v[MAXCLIQUE];
set *ns; int *cellstart,*cellsize; int iv,icell,bigcells,cell1,cell2; int pc;
setword sw;
EMPTYSET(workset,m); for (iv = cell1; iv <= cell2; ++iv) ADDELEMENT(workset,lab[iv]);
for (iv = cell1; iv <= cell2; ++iv)
{
v[0] = lab[iv];
gv = GRAPHROW(g,v[0],m);
ns = (set*)wss;
pc = 0;
for (i = M; --i >= 0;)
{
ns[i] = ~gv[i] & workset[i]; if ((sw = ns[i]) != 0) pc += POPCOUNT(sw);
} if (pc <= 1 || pc >= cellsize[icell] - 2) continue;
ss = 1;
v[1] = v[0]; while (ss > 0)
{ if (ss == setsize)
{ for (i = ss; --i >= 0;) ++invar[v[i]];
--ss;
} elseif ((v[ss]
= nextelement((set*)wss+M*(ss-1),M,v[ss])) < 0)
--ss; else
{
++ss; if (ss < setsize)
{
gv = GRAPHROW(g,v[ss-1],m);
ns = (set*)wss + M*(ss-2); for (i = M; --i >= 0;) ns[i+M] = ns[i] & ~gv[i];
v[ss] = v[ss-1];
}
}
}
}
wt = invar[lab[cell1]]; for (iv = cell1 + 1; iv <= cell2; ++iv) if (invar[lab[iv]] != wt) return;
}
}
/***************************************************************************** * * * adjacencies() assigns to each vertex v a code depending on which cells * * it is joined to and from, and how many times. It is intended to provide * * better partitioning that the normal refinement routine for digraphs. * * It will not help with undirected graphs in nauty at all. * * *
*****************************************************************************/
void
adjacencies(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,v,w; int vwt,wwt;
set *gv;
vwt = 1; for (i = 0; i < n; ++i)
{
workshort[lab[i]] = vwt; if (ptn[i] <= level) ++vwt;
invar[i] = 0;
}
for (v = 0, gv = (set*)g; v < n; ++v, gv += M)
{
vwt = FUZZ1(workshort[v]);
wwt = 0;
w = -1; while ((w = nextelement(gv,M,w)) >= 0)
{
ACCUM(wwt,FUZZ2(workshort[w]));
ACCUM(invar[w],vwt);
}
ACCUM(invar[v],wwt);
}
}
/***************************************************************************** * * * nautinv_check() checks that this file is compiled compatibly with the * * given parameters. If not, call exit(1). * * *
*****************************************************************************/
void
nautinv_check(int wordsize, int m, int n, int version)
{ if (wordsize != WORDSIZE)
{
fprintf(ERRFILE,"Error: WORDSIZE mismatch in nautinv.c\n"); exit(1);
}
#if MAXN if (m > MAXM)
{
fprintf(ERRFILE,"Error: MAXM inadequate in nautinv.c\n"); exit(1);
}
if (n > MAXN)
{
fprintf(ERRFILE,"Error: MAXN inadequate in nautinv.c\n"); exit(1);
} #endif
if (version < NAUTYREQUIRED)
{
fprintf(ERRFILE,"Error: nautinv.c version mismatch\n"); exit(1);
}
}
/***************************************************************************** * * * nautinv_freedyn() - free the dynamic memory in this module * * *
*****************************************************************************/
/***************************************************************************** * * * semirefine(g,lab,ptn,level,numcells,strength,active,m,n) performs a * * refinement operation on the partition at the specified level of the * * partition nest (lab,ptn). *numcells is assumed to contain the number of * * cells on input, and is updated. The initial set of active cells (alpha * * in the paper) is specified in the set active. Precisely, x is in active * * iff the cell starting at index x in lab is active. * * *code is set to a value which depends on the fine detail of the * * algorithm, but which is independent of the labelling of the graph. * * *
*****************************************************************************/
staticint
semirefine(graph *g, int *lab, int *ptn, int level, int *numcells, int strength, set *active, int m, int n)
{ int i,c1,c2,labc1;
setword x;
set *set1,*set2; int split1,split2,cell1,cell2; int cnt,bmin,bmax; long longcode;
set *gptr; int maxcell,maxpos,hint;
void
refinvar(graph *g, int *lab, int *ptn, int level, int numcells, int tvpos, int *invar, int invararg, boolean digraph, int m, int n)
{ int i,j; int wt; int icell,bigcells,cell1,cell2; int *cellstart,*cellsize; int newnumcells;
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
