/***************************************************************************** * * * Vertex-invariants source file for nauty 1.7. * * * * Copyright (1989) 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 as version 1.7, no changes to this file * * * *****************************************************************************/ #define EXTDEFS 1 #include "naututil.h" #if MAXM==1 #define M 1 #else #define M m #endif #define ACCUM(x,y) x = (((x) + (y)) & 077777) static int fuzz1[] = {037541,061532,005257,026416}; static int fuzz2[] = {006532,070236,035523,062437}; #define FUZZ1(x) ((x) ^ fuzz1[(x)&3]) #define FUZZ2(x) ((x) ^ fuzz2[(x)&3]) #define MAXCLIQUE 7 /* max clique size for cliques() */ #if MAXCLIQUE >= MAXN/2 **** error: MAXCLIQUE too big #endif #define MAXINDSET 7 /* max independent set size for indsets() */ #if MAXINDSET >= MAXN/2 **** error: MAXINDSET too big #endif static set workset[MAXM]; /* used for scratch work */ static short workshort[MAXN+2]; /* used for scratch work */ /***************************************************************************** * * * 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 NILFUNCTION. * * 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. * * * * A vertex-invariant must be declared thus: * * UPROC 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 * * (,g,,level, * * invararg,digraph) * * Note that invar[] is declared as a permutation. 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. * * * * 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. * * * *****************************************************************************/ UPROC twopaths(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i,v,w; register short 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. * * * *****************************************************************************/ UPROC quadruples(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i,pc; register setword sw; register set *gw; register short wt; int v,iv,v1,v2,v3; set *gv; set ws1[MAXM]; long wv,wv1,wv2,wv3; for (i = n; --i >= 0;) invar[i] = 0; 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]) /* not == */ 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. * * * *****************************************************************************/ UPROC triples(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i,pc; register setword sw; register set *gw; register short wt; int v,iv,v1,v2; set *gv; long wv,wv1,wv2; for (i = n; --i >= 0;) invar[i] = 0; 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]) /* not == */ 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. * * * *****************************************************************************/ UPROC adjtriang(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int j,pc; register setword sw; register set *gi; register short wt; int i,v1,v2; boolean v1v2; set *gv1,*gv2; for (i = n; --i >= 0;) invar[i] = 0; wt = 1; for (i = 0; i < n; ++i) { workshort[lab[i]] = FUZZ1(wt); if (ptn[i] <= level) ++wt; } for (v1 = 0, gv1 = g; v1 < n; ++v1, gv1 += M) { for (v2 = (digraph ? 0 : v1+1); v2 < n; ++v2) { if (v2 == v1) continue; v1v2 = (ISELEMENT(gv1,v2) != 0); if (invararg == 0 && !v1v2 || invararg == 1 && v1v2) continue; wt = workshort[v1]; ACCUM(wt,workshort[v2]); ACCUM(wt,v1v2); 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]) /* not == */ 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(ptn,level,minsize,bigcells,cellstart,cellsize,n) nvector *ptn; int level,minsize,*bigcells,n; short *cellstart,*cellsize; { register int cell1,cell2,j; register short si,st; int bc,i,h; bc = 0; for (cell1 = 0; cell1 < n; cell1 = cell2 + 1) { for (cell2 = cell1; ptn[cell2] > level; ++cell2) {} if (cell2 >= cell1 + 3) { cellstart[bc] = cell1; cellsize[bc] = cell2 - cell1 + 1; ++bc; } } *bigcells = bc; 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. * * * *****************************************************************************/ UPROC celltrips(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i,pc; register setword sw; register set *gw; register short wt; int v,iv,v1,iv1,v2,iv2; int icell,bigcells,cell1,cell2; short *cellstart,*cellsize; set *gv; for (i = n; --i >= 0;) invar[i] = 0; cellstart = workshort; cellsize = workshort + (MAXN/2); getbigcells(ptn,level,3,&bigcells,cellstart,cellsize,n); 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]) /* not == */ 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. * * * *****************************************************************************/ UPROC cellquads(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i,pc; register setword sw; register set *gw; register short wt; int v,iv,v1,iv1,v2,iv2,v3,iv3; int icell,bigcells,cell1,cell2; short *cellstart,*cellsize; set *gv; set ws1[MAXM]; for (i = n; --i >= 0;) invar[i] = 0; cellstart = workshort; cellsize = workshort + (MAXN/2); getbigcells(ptn,level,4,&bigcells,cellstart,cellsize,n); 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]) /* not == */ 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. * * * *****************************************************************************/ UPROC cellquins(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i,pc; register setword sw; register set *gw; register short wt; int v,iv,v1,iv1,v2,iv2,v3,iv3,v4,iv4; int icell,bigcells,cell1,cell2; short *cellstart,*cellsize; set *gv; set ws1[MAXM],ws2[MAXM]; for (i = n; --i >= 0;) invar[i] = 0; cellstart = workshort; cellsize = workshort + (MAXN/2); getbigcells(ptn,level,5,&bigcells,cellstart,cellsize,n); 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]) /* not == */ 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; } } /***************************************************************************** * * * 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. * * * *****************************************************************************/ UPROC distances(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i; register set *gw; register short wt; int d,cell1,cell2,iv,v,w; boolean success; set sofar[MAXM],frontier[MAXM]; for (i = n; --i >= 0;) invar[i] = 0; wt = 1; for (i = 0; i < n; ++i) { workshort[lab[i]] = FUZZ1(wt); if (ptn[i] <= level) ++wt; } 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(sofar,m); ADDELEMENT(sofar,v); EMPTYSET(frontier,m); ADDELEMENT(frontier,v); for (d = 1; d < n; ++d) { EMPTYSET(workset,m); wt = 0; w = -1; while ((w = nextelement(frontier,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;) { frontier[i] = workset[i] & ~sofar[i]; sofar[i] |= frontier[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 largest of invararg and MAXINDSET. * * * *****************************************************************************/ UPROC indsets(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i; register short wt; register set *gv; int ss,setsize; int v[MAXINDSET]; long wv[MAXINDSET]; set s[MAXINDSET-1][MAXM],*s0; for (i = n; --i >= 0;) invar[i] = 0; if (invararg <= 1 || digraph) return; if (invararg > MAXINDSET) setsize = MAXINDSET; else setsize = invararg; 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*)s[0]; 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; } else if ((v[ss] = nextelement(s[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); for (i = M; --i >= 0;) s[ss-1][i] = s[ss-2][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 largest of invararg and MAXCLIQUE. * * * *****************************************************************************/ UPROC cliques(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i; register short wt; register set *gv; int ss,setsize; int v[MAXCLIQUE]; long wv[MAXCLIQUE]; set nset[MAXCLIQUE-1][MAXM]; for (i = n; --i >= 0;) invar[i] = 0; if (invararg <= 1 || digraph) return; if (invararg > MAXCLIQUE) setsize = MAXCLIQUE; else setsize = invararg; 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); for (i = M; --i >= 0;) nset[0][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; } else if ((v[ss] = nextelement(nset[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); for (i = M; --i >= 0;) nset[ss-1][i] = nset[ss-2][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 largest of invararg and MAXCLIQUE. We try the * * cells in increasing order of size and stop as soon as any cell splits. * * * *****************************************************************************/ UPROC cellcliq(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i; register short wt; register set *gv; int ss,setsize; int v[MAXCLIQUE]; set nset[MAXCLIQUE-1][MAXM]; short *cellstart,*cellsize; int iv,icell,bigcells,cell1,cell2; int pc; setword sw; for (i = n; --i >= 0;) invar[i] = 0; if (invararg <= 1 || digraph) return; if (invararg > MAXCLIQUE) setsize = MAXCLIQUE; else setsize = invararg; cellstart = workshort; cellsize = workshort + (MAXN/2); getbigcells(ptn,level,setsize > 6 ? setsize : 6,&bigcells, cellstart,cellsize,n); for (icell = 0; icell < bigcells; ++icell) { cell1 = cellstart[icell]; cell2 = cell1 + cellsize[icell] - 1; 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); pc = 0; for (i = M; --i >= 0;) { nset[0][i] = gv[i] & workset[i]; if (sw = nset[0][i]) /* not == */ 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; } else if ((v[ss] = nextelement(nset[ss-1],M,v[ss])) < 0) --ss; else { ++ss; if (ss < setsize) { gv = GRAPHROW(g,v[ss-1],m); for (i = M; --i >= 0;) nset[ss-1][i] = nset[ss-2][i] & gv[i]; v[ss] = v[ss-1]; } } } } wt = invar[lab[cell1]]; for (iv = cell1; iv <= cell2; ++iv) if (invar[lab[i]] != 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 largest of invararg and MAXCLIQUE. * * We try the cells in increasing order of size and stop as soon as any * * cell splits. * * * *****************************************************************************/ UPROC cellind(g,lab,ptn,level,numcells,tvpos,invar,invararg,digraph,m,n) graph *g; nvector *lab,*ptn; int level,numcells,tvpos,invararg,m,n; permutation *invar; boolean digraph; { register int i; register short wt; register set *gv; int ss,setsize; int v[MAXCLIQUE]; set nset[MAXCLIQUE-1][MAXM]; short *cellstart,*cellsize; int iv,icell,bigcells,cell1,cell2; int pc; setword sw; for (i = n; --i >= 0;) invar[i] = 0; if (invararg <= 1 || digraph) return; if (invararg > MAXCLIQUE) setsize = MAXCLIQUE; else setsize = invararg; cellstart = workshort; cellsize = workshort + (MAXN/2); getbigcells(ptn,level,setsize > 6 ? setsize : 6,&bigcells, cellstart,cellsize,n); for (icell = 0; icell < bigcells; ++icell) { cell1 = cellstart[icell]; cell2 = cell1 + cellsize[icell] - 1; 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); pc = 0; for (i = M; --i >= 0;) { nset[0][i] = ~gv[i] & workset[i]; if (sw = nset[0][i]) /* not == */ 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; } else if ((v[ss] = nextelement(nset[ss-1],M,v[ss])) < 0) --ss; else { ++ss; if (ss < setsize) { gv = GRAPHROW(g,v[ss-1],m); for (i = M; --i >= 0;) nset[ss-1][i] = nset[ss-2][i] & ~gv[i]; v[ss] = v[ss-1]; } } } } wt = invar[lab[cell1]]; for (iv = cell1; iv <= cell2; ++iv) if (invar[lab[i]] != wt) return; } } /***************************************************************************** * * * nautinv_null() does nothing. See dreadnaut.c for its purpose. * * * *****************************************************************************/ void nautinv_null() { }