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nautinv.c
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/*****************************************************************************
* *
* Vertex-invariants source file for nauty 2.6. *
* *
* Copyright (1989-2013) 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. */
static const int fuzz1[] = {037541,061532,005257,026416};
static const int fuzz2[] = {006532,070236,035523,062437};
#define FUZZ1(x) ((x) ^ fuzz1[(x)&3])
#define FUZZ2(x) ((x) ^ fuzz2[(x)&3])
#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;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"twopaths");
DYNALLOC1(int,workshort,workshort_sz,n+2,"twopaths");
#endif
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;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"quadruples");
DYNALLOC1(set,ws1,ws1_sz,m,"quadruples");
DYNALLOC1(set,workset,workset_sz,m,"quadruples");
#endif
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]) != 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;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"triples");
DYNALLOC1(int,workshort,workshort_sz,n+2,"triples");
#endif
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]) != 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;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"adjtriang");
DYNALLOC1(int,workshort,workshort_sz,n+2,"adjtriang");
#endif
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]) != 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) {}
if (cell2 >= cell1 + minsize - 1)
{
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. *
* *
*****************************************************************************/
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;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"celltrips");
DYNALLOC1(int,workshort,workshort_sz,n+2,"celltrips");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/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]) != 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;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"cellquads");
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellquads");
DYNALLOC1(set,ws1,ws1_sz,m,"cellquads");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/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]) != 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;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"cellquins");
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellquins");
DYNALLOC1(set,ws1,ws1_sz,m,"cellquins");
DYNALLOC1(set,ws2,ws2_sz,m,"cellquins");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/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]) != 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. *
*****************************************************************************/
static int
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;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellfano2");
DYNALLOC1(int,vv,vv_sz,n,"cellfano2");
DYNALLOC1(int,ww,ww_sz,n,"cellfano2");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/2);
getbigcells(ptn,level,4,&bigcells,cellstart,cellsize,n);
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1;
for (iv0 = cell1; iv0 <= cell2 - 3; ++iv0)
{
v0 = lab[iv0];
gv0 = GRAPHROW(g,v0,m);
nw = 0;
for (iv1 = iv0 + 1; iv1 <= cell2; ++iv1)
{
v1 = lab[iv1];
if (ISELEMENT(gv0,v1)) continue;
if ((x01 = uniqinter(gv0,GRAPHROW(g,v1,m),m)) < 0) continue;
vv[nw] = v1;
ww[nw] = x01;
++nw;
}
for (iv1 = 0; iv1 < nw-2; ++iv1)
{
v1 = vv[iv1];
gv1 = GRAPHROW(g,v1,m);
x01 = ww[iv1];
for (iv2 = iv1 + 1; iv2 < nw-1; ++iv2)
{
x02 = ww[iv2];
if (x02 == x01) continue;
v2 = vv[iv2];
if (ISELEMENT(gv1,v2)) continue;
gv2 = GRAPHROW(g,v2,m);
if ((x12 = uniqinter(gv1,gv2,m)) < 0) continue;
for (iv3 = iv2 + 1; iv3 < nw; ++iv3)
{
x03 = ww[iv3];
if (x03 == x01 || x03 == x02) continue;
v3 = vv[iv3];
if (ISELEMENT(gv1,v3) || ISELEMENT(gv2,v3))
continue;
gv3 = GRAPHROW(g,v3,m);
if ((x13 = uniqinter(gv1,gv3,m)) < 0) continue;
if ((x23 = uniqinter(gv2,gv3,m)) < 0
|| x23 == x13) continue;
if ((pnt0 = uniqinter(GRAPHROW(g,x01,m),
GRAPHROW(g,x23,m),m)) < 0)
continue;
if ((pnt1 = uniqinter(GRAPHROW(g,x02,m),
GRAPHROW(g,x13,m),m)) < 0)
continue;
if ((pnt2 = uniqinter(GRAPHROW(g,x03,m),
GRAPHROW(g,x12,m),m)) < 0)
continue;
gp0 = GRAPHROW(g,pnt0,m);
gp1 = GRAPHROW(g,pnt1,m);
gp2 = GRAPHROW(g,pnt2,m);
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;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellfano");
DYNALLOC1(set,w01,w01_sz,m,"cellfano");
DYNALLOC1(set,w02,w02_sz,m,"cellfano");
DYNALLOC1(set,w03,w03_sz,m,"cellfano");
DYNALLOC1(set,w12,w12_sz,m,"cellfano");
DYNALLOC1(set,w13,w13_sz,m,"cellfano");
DYNALLOC1(set,w23,w23_sz,m,"cellfano");
DYNALLOC1(set,pt0,pt0_sz,m,"cellfano");
DYNALLOC1(set,pt1,pt1_sz,m,"cellfano");
DYNALLOC1(set,pt2,pt2_sz,m,"cellfano");
DYNALLOC1(set,workset,workset_sz,m,"cellfano");
#else
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/2);
getbigcells(ptn,level,4,&bigcells,cellstart,cellsize,n);
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1;
for (iv0 = cell1; iv0 <= cell2 - 3; ++iv0)
{
v0 = lab[iv0];
gv0 = GRAPHROW(g,v0,m);
for (iv1 = iv0 + 1; iv1 <= cell2 - 2; ++iv1)
{
v1 = lab[iv1];
if (ISELEMENT(gv0,v1)) continue;
gv1 = GRAPHROW(g,v1,m);
for (i = M; --i >= 0;) workset[i] = gv0[i] & gv1[i];
setnbhd(g,m,n,workset,w01);
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;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"distances");
DYNALLOC1(int,workshort,workshort_sz,n+2,"distances");
DYNALLOC1(set,ws1,ws1_sz,m,"distances");
DYNALLOC1(set,ws2,ws2_sz,m,"distances");
#endif
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;
}
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;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"indsets");
DYNALLOC2(set,wss,wss_sz,m,MAXCLIQUE-1,"indsets");
#endif
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]];
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;
}
else if ((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
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);
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;
}
else if ((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;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"cellcliq");
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellcliq");
DYNALLOC2(set,wss,wss_sz,m,MAXCLIQUE-1,"cellcliq");
#endif
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 + (n/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);
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;
}
else if ((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;
#if !MAXN
DYNALLOC1(set,workset,workset_sz,m,"cellind");
DYNALLOC1(int,workshort,workshort_sz,n+2,"cellind");
DYNALLOC2(set,wss,wss_sz,m,MAXCLIQUE-1,"cellind");
#endif
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 + (n/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);
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;
}
else if ((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;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"adjacencies");
#endif
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 *
* *
*****************************************************************************/
void
nautinv_freedyn(void)
{
#if !MAXN
DYNFREE(workset,workset_sz);
DYNFREE(workshort,workshort_sz);
DYNFREE(ws1,ws1_sz);
DYNFREE(ws2,ws2_sz);
DYNFREE(vv,vv_sz);
DYNFREE(ww,ww_sz);
DYNFREE(w01,w01_sz);
DYNFREE(w02,w02_sz);
DYNFREE(w03,w03_sz);
DYNFREE(w12,w12_sz);
DYNFREE(w13,w13_sz);
DYNFREE(w23,w23_sz);
DYNFREE(pt0,pt0_sz);
DYNFREE(pt1,pt1_sz);
DYNFREE(pt2,pt2_sz);
DYNFREE(wss,wss_sz);
#endif
}
/*===================================================================*/
/*****************************************************************************
* *
* 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. *
* *
*****************************************************************************/
static int
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;
#if !MAXN
DYNALLOC1(int,workperm,workperm_sz,n,"refine");
DYNALLOC1(set,workset,workset_sz,m,"refine");
DYNALLOC1(int,bucket,bucket_sz,n+2,"refine");
DYNALLOC1(int,count,count_sz,n,"refine");
#endif
longcode = *numcells;
split1 = -1;
hint = 0;
while (*numcells < n && ((split1 = hint, ISELEMENT(active,split1))
|| (split1 = nextelement(active,M,split1)) >= 0
|| (split1 = nextelement(active,M,-1)) >= 0))
{
DELELEMENT(active,split1);
for (split2 = split1; ptn[split2] > level; ++split2) {}
longcode = MASH(longcode,split1+split2);
if (split1 == split2) /* trivial splitting cell */
{
gptr = GRAPHROW(g,lab[split1],M);
for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{
for (cell2 = cell1; ptn[cell2] > level; ++cell2) {}
if (cell1 == cell2) continue;
c1 = cell1;
c2 = cell2;
while (c1 <= c2)
{
labc1 = lab[c1];
if (ISELEMENT(gptr,labc1))
++c1;
else
{
lab[c1] = lab[c2];
lab[c2] = labc1;
--c2;
}
}
if (c2 >= cell1 && c1 <= cell2)
{
ptn[c2] = level;
longcode = MASH(longcode,FUZZ1(c2));
++*numcells;
if (ISELEMENT(active,cell1) || c2-cell1 >= cell2-c1)
{
ADDELEMENT(active,c1);
if (c1 == cell2) hint = c1;
}
else
{
ADDELEMENT(active,cell1);
if (c2 == cell1) hint = cell1;
}
}
}
}
else /* nontrivial splitting cell */
{
EMPTYSET(workset,m);
for (i = split1; i <= split2; ++i)
ADDELEMENT(workset,lab[i]);
longcode = MASH(longcode,FUZZ2(split2-split1+1));
for (cell1 = 0; cell1 < n; cell1 = cell2 + 1)
{
for (cell2 = cell1; ptn[cell2] > level; ++cell2) {}
if (cell1 == cell2) continue;
i = cell1;
set1 = workset;
set2 = GRAPHROW(g,lab[i],m);
cnt = 0;
for (c1 = m; --c1 >= 0;)
if ((x = ((*set1++) & (*set2++))) != 0)
cnt += POPCOUNT(x);
count[i] = bmin = bmax = cnt;
bucket[cnt] = 1;
while (++i <= cell2)
{
set1 = workset;
set2 = GRAPHROW(g,lab[i],m);
cnt = 0;
for (c1 = m; --c1 >= 0;)
if ((x = ((*set1++) & (*set2++))) != 0)
cnt += POPCOUNT(x);
while (bmin > cnt) bucket[--bmin] = 0;
while (bmax < cnt) bucket[++bmax] = 0;
++bucket[cnt];
count[i] = cnt;
}
if (bmin == bmax)
{
longcode = MASH(longcode,FUZZ1(bmin+cell1));
continue;
}
c1 = cell1;
maxcell = -1;
for (i = bmin; i <= bmax; ++i)
if (bucket[i])
{
c2 = c1 + bucket[i];
bucket[i] = c1;
longcode = MASH(longcode,i+c1);
if (c2-c1 > maxcell)
{
maxcell = c2-c1;
maxpos = c1;
}
if (c1 != cell1)
{
ADDELEMENT(active,c1);
if (c2-c1 == 1) hint = c1;
++*numcells;
}
if (c2 <= cell2) ptn[c2-1] = level;
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 (!ISELEMENT(active,cell1))
{
ADDELEMENT(active,cell1);
DELELEMENT(active,maxpos); /* check maxpos is alwas defined */
}
}
}
if (--strength == 0) break; /* negative is fine! */
}
longcode = MASH(longcode,FUZZ2(*numcells));
return CLEANUP(longcode);
}
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;
#if !MAXN
DYNALLOC1(int,workshort,workshort_sz,n+2,"refinvar");
DYNALLOC1(int,vv,vv_sz,n,"refinvar");
DYNALLOC1(int,ww,ww_sz,n,"refinvar");
DYNALLOC1(set,ws1,ws1_sz,n,"refinvar");
#endif
for (i = n; --i >= 0;) invar[i] = 0;
cellstart = workshort;
cellsize = workshort + (n/2);
getbigcells(ptn,level,2,&bigcells,cellstart,cellsize,n);
for (icell = 0; icell < bigcells; ++icell)
{
cell1 = cellstart[icell];
cell2 = cell1 + cellsize[icell] - 1;
for (i = cell1; i <= cell2; ++i)
{
for (j = 0; j < n; ++j)
{
vv[j] = lab[j];
ww[j] = ptn[j];
}
newnumcells = numcells + 1;
ww[cell1] = level;
EMPTYSET(ws1,m);
ADDELEMENT(ws1,cell1);
vv[i] = lab[cell1];
vv[cell1] = lab[i];
invar[lab[i]] = semirefine(g,vv,ww,level,&newnumcells,
invararg,ws1,m,n);
}
wt = invar[lab[cell1]];
for (i = cell1 + 1; i <= cell2; ++i)
if (invar[lab[i]] != wt) return;
}
}

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