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Scan of complicated 14-vertex graph

newscan7

If I’m not mistaken, there are 33 edges.

If we remove the vertex M and the four edges incident on M, this leaves 29 edges. The 13-point configuration has bilateral symmetry across a line through the points J, H, and I. In the 13-point configuration where M is removed, by symmetry, edges have mirror images different from themselves, except for the edge BF, which is its own mirror image across an axis through J, H, and I.

====

Added: Thu Mar 2 21:11:34 EST 2017

The solver for 15 vertices that starts from a 7-vertex Moser spindle isn’t going very far very fast.

$ cat data1232a.txt
adjacency matrix:
0 0 1 1 0 0 1 0 0 0 0 0 0 0 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 1
1 0 0 0 1 0 1 1 0 0 0 0 0 1 0
1 1 0 0 0 1 0 0 0 0 0 0 1 0 0
0 1 1 0 0 1 1 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 1 0 0 0 0 1 0 0
1 0 1 0 1 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 1 0 0 1 0 1 0 0 1 0
0 0 0 0 0 0 0 1 0 0 1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 1 1 0 0 1
0 0 0 0 0 0 0 1 1 1 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0 0 1 0 0
0 0 0 1 0 1 0 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 1 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0 0 1 0 0 0 1 0

post adjacency matrix:
0 0 1 1 0 0 1 0 0 0 0 0 0 0 0
0 0 0 1 1 1 0 0 0 0 0 0 0 1 1
1 0 0 0 1 0 1 1 0 0 0 0 0 1 0
1 1 0 0 0 1 0 0 0 1 1 0 1 0 0
0 1 1 0 0 1 1 0 0 0 0 0 0 0 0
0 1 0 1 1 0 0 1 0 0 0 0 1 0 0
1 0 1 0 1 0 0 0 0 0 0 0 0 0 1
0 0 1 0 0 1 0 0 1 0 1 0 0 1 0
0 0 0 0 0 0 0 1 0 0 1 1 1 0 0
0 0 0 1 0 0 0 0 0 0 1 1 0 0 1
0 0 0 1 0 0 0 1 1 1 0 0 0 1 0
0 0 0 0 0 0 0 0 1 1 0 0 1 0 0
0 0 0 1 0 1 0 0 1 0 0 1 0 0 0
0 1 1 0 0 0 0 1 0 0 1 0 0 0 1
0 1 0 0 0 0 1 0 0 1 0 0 0 1 0
total_finds = 92
Tests count = 13 has_converged_step = 1600 max_has_converged_step = 1600
rec_diff1 = 39.325534
rec_diff25 = 32.270247
rec_diff50 = 16.837123
rec_diff100 = 13.714747
rec_diff200 = 9.446856
rec_diff400 = 0.019220
rec_diff800 = 0.0000007856360233
rec_diff1200 = 0.0000000000793501
probable_unit_lengths = 33
graph is 3-colorable:no.
count_4_colorings = 1232 num_4_colorings_mod_24 = 0
Matrix of distances vertex to vertex:
A B C D E F G H I J K L M N O
A 0.00 0.74 1.00 1.00 1.73 1.57 1.00 0.58 1.29 1.57 0.74 2.29 1.98 0.46 0.58
B 0.74 0.00 0.58 1.00 1.00 1.00 0.46 0.46 1.44 1.91 1.37 2.35 1.73 1.00 1.00
C 1.00 0.58 0.00 1.57 1.00 1.46 1.00 1.00 2.00 2.43 1.73 2.93 2.29 1.00 1.46
D 1.00 1.00 1.57 0.00 1.73 1.00 0.74 0.58 0.46 1.00 1.00 1.37 1.00 1.46 0.58
E 1.73 1.00 1.00 1.73 0.00 1.00 1.00 1.37 2.18 2.73 2.35 2.89 2.00 1.91 1.95
F 1.57 1.00 1.46 1.00 1.00 0.00 0.58 1.00 1.37 1.95 1.91 1.91 1.00 1.95 1.46
G 1.00 0.46 1.00 0.74 1.00 0.58 0.00 0.46 1.19 1.73 1.44 2.00 1.29 1.37 1.00
H 0.58 0.46 1.00 0.58 1.37 1.00 0.46 0.00 1.00 1.46 1.00 1.95 1.46 1.00 0.58
I 1.29 1.44 2.00 0.46 2.18 1.37 1.19 1.00 0.00 0.58 1.00 1.00 1.00 1.73 0.74
J 1.57 1.91 2.43 1.00 2.73 1.95 1.73 1.46 0.58 0.00 1.00 1.00 1.46 1.95 1.00
K 0.74 1.37 1.73 1.00 2.35 1.91 1.44 1.00 1.00 1.00 0.00 1.91 1.95 1.00 0.46
L 2.29 2.35 2.93 1.37 2.89 1.91 2.00 1.95 1.00 1.00 1.91 0.00 1.00 2.73 1.73
M 1.98 1.73 2.29 1.00 2.00 1.00 1.29 1.46 1.00 1.46 1.95 1.00 0.00 2.43 1.57
N 0.46 1.00 1.00 1.46 1.91 1.95 1.37 1.00 1.73 1.95 1.00 2.73 2.43 0.00 1.00
O 0.58 1.00 1.46 0.58 1.95 1.46 1.00 0.58 0.74 1.00 0.46 1.73 1.57 1.00 0.00

The UDG it has found has 33 edges and 1232 4-colorings, up to permutation of the 4 colors (and no 3-colorings).

I’ll check that the 33-edge 14-vertex UDG in the picture does indeed have bilateral symmetry for an axis of symmetry through the points J , H, and I.

Maybe as 15th point I can add the mirror image of point M in the axis of symmetry through J, H, and I.

It’s getting complicated.

=====

Added: Thu Mar 2 22:07:18 EST 2017

Indeed, there is an axis of symmetry through points J, H, and I. 14 points minus 3 points equals 11 points, but point M has no mirror image, so subract one again to get 10 points in 5 pairs of mirror image points:

D and E  ( pair number 1)

L and N ( pair number 2)

B and F (pair number 3)

G and K (pair number 4)

A and C (pair number 5)

image:

scan22

=====

Added:  Thu Mar 2 23:10:13 EST 2017

Please note that the line through points J, H, and I above is only to show the axis of symmetry, and no graph edges are part of this line…

My enumeration of the 33 edges follows. Please contact me at

david250 at videotron dot ca if you find mistakes.

A F
A G
A H
A M
B C
B E
B F
B N
C H
C K
D J
D L
D H
D F
D K
E J
E N
E H
E G
F M
F L
G H
G L
G I
H K
I L
I N
I K
I M
J L
J N
K N
K M

=====

Added: Fri Mar 3 03:56:16 EST 2017

Point “O” is the mirror image of point M, and therefore there are edges BO and CO, mirror images of edges FM and AM.

Result:

adjacency matrix:
0 0 0 0 0 1 1 0 0 0 0 0 1 0 0
0 0 1 0 0 1 0 0 0 0 0 0 0 1 1
0 1 0 0 0 0 0 1 0 0 1 0 0 0 1
0 0 0 0 0 1 0 1 0 1 0 1 0 0 0
0 0 0 0 0 0 1 1 0 1 0 0 0 1 0
1 1 0 1 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 0 0 1 0 0 0 0 0 0 0
0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 1 1 0 0
0 0 0 1 1 0 0 0 0 0 0 1 0 1 0
0 0 1 0 0 0 0 0 1 0 0 0 1 1 0
0 0 0 1 0 1 0 0 1 1 0 0 0 0 0
1 0 0 0 0 0 0 0 1 0 1 0 0 0 0
0 1 0 0 1 0 0 0 0 1 1 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0 0 0 0

post adjacency matrix:
0 0 0 0 0 1 1 1 0 0 0 0 1 0 0
0 0 1 0 1 1 0 0 0 0 0 0 0 1 1
0 1 0 0 0 0 0 1 0 0 1 0 0 0 1
0 0 0 0 0 1 0 1 0 1 1 1 0 0 0
0 1 0 0 0 0 1 1 0 1 0 0 0 1 0
1 1 0 1 0 0 0 0 0 0 0 1 1 0 0
1 0 0 0 1 0 0 1 1 0 0 1 0 0 1
1 0 1 1 1 0 1 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0 1 1 1 1 1
0 0 0 1 1 0 0 0 0 0 0 1 0 1 0
0 0 1 1 0 0 0 1 1 0 0 0 1 1 0
0 0 0 1 0 1 1 0 1 1 0 0 0 0 0
1 0 0 0 0 1 0 0 1 0 1 0 0 0 0
0 1 0 0 1 0 0 0 1 1 1 0 0 0 0
0 1 1 0 0 0 1 0 1 0 0 0 0 0 0
total_finds = 4
Tests count = 1 has_converged_step = 2540 max_has_converged_step = 2540
rec_diff1 = 64.481510
rec_diff25 = 1.995834
rec_diff50 = 1.403561
rec_diff100 = 1.203674
rec_diff200 = 0.626094
rec_diff400 = 0.150774
rec_diff800 = 0.0118507527986628
rec_diff1200 = 0.0010902257621921
probable_unit_lengths = 37
graph is 3-colorable:no.
count_4_colorings = 364 num_4_colorings_mod_24 = 0
Matrix of distances vertex to vertex:
A B C D E F G H I J K L M N O
A 0.00 0.74 0.46 1.91 1.73 1.00 1.00 1.00 0.46 2.35 1.37 1.37 1.00 1.44 0.58
B 0.74 0.00 1.00 1.57 1.00 1.00 0.46 0.58 0.58 1.73 1.46 0.74 1.57 1.00 1.00
C 0.46 1.00 0.00 1.73 1.91 0.74 1.37 1.00 0.46 2.35 1.00 1.44 0.58 1.37 1.00
D 1.91 1.57 1.73 0.00 1.46 1.00 1.95 1.00 1.46 1.00 1.00 1.00 1.95 0.58 2.43
E 1.73 1.00 1.91 1.46 0.00 1.57 1.00 1.00 1.46 1.00 1.95 0.58 2.43 1.00 1.95
F 1.00 1.00 0.74 1.00 1.57 0.00 1.46 0.58 0.58 1.73 0.46 1.00 1.00 0.74 1.57
G 1.00 0.46 1.37 1.95 1.00 1.46 0.00 1.00 1.00 1.91 1.91 1.00 1.95 1.37 1.00
H 1.00 0.58 1.00 1.00 1.00 0.58 1.00 0.00 0.58 1.37 1.00 0.46 1.46 0.46 1.46
I 0.46 0.58 0.46 1.46 1.46 0.58 1.00 0.58 0.00 1.95 1.00 1.00 1.00 1.00 1.00
J 2.35 1.73 2.35 1.00 1.00 1.73 1.91 1.37 1.95 0.00 1.91 1.00 2.73 1.00 2.73
K 1.37 1.46 1.00 1.00 1.95 0.46 1.91 1.00 1.00 1.91 0.00 1.37 1.00 1.00 1.95
L 1.37 0.74 1.44 1.00 0.58 1.00 1.00 0.46 1.00 1.00 1.37 0.00 1.91 0.46 1.73
M 1.00 1.57 0.58 1.95 2.43 1.00 1.95 1.46 1.00 2.73 1.00 1.91 0.00 1.73 1.46
N 1.44 1.00 1.37 0.58 1.00 0.74 1.37 0.46 1.00 1.00 1.00 0.46 1.73 0.00 1.91
O 0.58 1.00 1.00 2.43 1.95 1.57 1.00 1.46 1.00 2.73 1.95 1.73 1.46 1.91 0.00

15 vertices, 37 edges, 364 4-colorings.

Source code used = /home/david/graphs/golomb23/udgraph15_solver43a.c

#include <stdio.h>
#include <math.h>
#define NUMSTEPS 10000
#define MAXDIFFAT100 ((long double) 18)/((long double) 1)
#define MAXDIFFAT50 ((long double) 18)/((long double) 1)
#define MAXDIFFAT25 ((long double) 40)/((long double) 1)
#define MAXDIFFAT1 ((long double) 400)/((long double) 1)
#define MAXDIFFAT200 ((long double) 96)/((long double) 10)
#define MAXDIFFAT400 ((long double) 67)/((long double) 1000)
#define MAXDIFFAT800 ((long double) 79)/((long double) 100000000)
#define MAXDIFFAT1200 ((long double) 84)/((long double)1000000000000)
#define VERBOSE
#define VERTEX 15

/**********************************************
rec_diff1 = 28.852841 40.0
rec_diff25 = 39.668785 40.0
rec_diff50 = 17.967935 18.0
rec_diff100 = 17.856958 18.0
rec_diff200 = 9.573263 9.6
rec_diff400 = 0.066982 6.7e-2
rec_diff800 = 0.0000007832212564 7.9e-7
rec_diff1200 = 0.0000000000839841 8.4e-11
************************************************/

static unsigned long long Q[2097152],carry=0;

unsigned long long B64MWC(void)
{ unsigned long long t,x; static int j=2097151;
j=(j+1)&2097151;
x=Q[j]; t=(x<<28)+carry;
carry=(x>>36)-(t<x);
return (Q[j]=t-x);
}

#define CNG ( cng=6906969069LL*cng+13579 )
#define XS ( xs^=(xs<<13), xs^=(xs>>17), xs^=(xs<<43) )
#define KISS ( B64MWC()+CNG+XS )
/********************* README SECTION *********************

10-point non-singular solutions to the unit
graph problem are found numerically at a rate of
57.9 solutions per second on a dual core Athlon
5000+ processor.

The solutions are expected to be isometric as a
10-point metric space to the soltion depicted in
the graph in my blog post :

Sketch of 10-vertex unit distance graph, 2013
at URL =

meditationatae.wordpress.com/2017/02/06/sketch-of-10-vertex-unit-distance-graph-2013
The sci dot math posts:

mathforum.org/kb/message.jspa?messageID=10081388

and earlier:

mathforum.org/kb/message.jspa?messageID=10074716

This solver for a particular graph has been optimized
to run in as little time as possible for the given graph,
decribed by the 10×10 adjacency matrix.

To compile, I type:

$ gcc -lm -O3 -o udgraph_solver201a.out udgraph_solver201a.c

at the shell command line in Linux.

The executable is then udgraph_solver201a.out .
In C pre-processor terms, if VERBOSE is defined by
a pre-processor directive,
Number-Sign define VERBOSE
say on line 7 above after the other
Number-sign defines,
then the solution count and the 10×10 matrix of vertex to vertex
distances for a solution will be printed.

As above VERBOSE is not defined, the program will run with
minimal output until it finishes after about 9 minutes
with my system.

This README is based on file
Slash home slash david slash graphs slash golomb6
slash udgraph_solver201a dot c,

will serve to write the local file:

Slash home slash david slash graphs slash golomb6
slash udgraph_solver301a dot c ,

and will go by the Moniker or alias
“unit distance graph solver draft 101”

a hexadecimal dump will be posted to my blog

meditationatae.wordpress.com
David Bernier

********************* README END *************************/

int main(void)
{
unsigned long long i,cng=123456789987654321LL, xs=362436069362436069LL;
unsigned long long randx;
unsigned long long mask = 2147483647LL;
int B;
int j;
int k;
int quit;
int is_singular;
int graph_found;
int total_edges;
int degree_test_passed;
int l, m;
int n, p;
int has_k4;
int is_3colorable;
int count;
int total_finds;
int probable_unit_lengths;
int solution_found;
int coloring_found;
char alphabet[VERTEX];
unsigned long long maxi_ull;
long double xcoord[VERTEX];
long double diff;
long double diff25;
long double diff50;
long double diff100;
long double diff200;
long double diff400;
long double diff800;
long double diff1200;
long double diff1;
long double rec_diff25;
long double rec_diff50;
long double rec_diff100;
long double rec_diff200;
long double rec_diff400;
long double rec_diff800;
long double rec_diff1200;
long double rec_diff1;
int ru1;
int ru2;
long double epsilon;
int co1;
int co2;
int colors[VERTEX];
int num_4_colorings;
int num_4_colorings_mod_24;
int count_4_colorings;
int n_colors;
int degrees[VERTEX];
int v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14;
int has_failed;
int numedges;
long double diff_record;
long double maxdiffat400;
long double one;
long double ycoord[VERTEX];
long double forces[VERTEX][2];
long double C;
int sum_of_degrees;
long double vector[2];
long double xgood[VERTEX];
long double ygood[VERTEX];
int four_colouring_failed;
int has_converged_flag;
int has_converged_step;
int max_has_converged_step;
long double scaling;
long double dmatrix[VERTEX][VERTEX];
int adjmat[VERTEX][VERTEX];
int testmat[VERTEX][VERTEX];
int blog_mat[14][14];
FILE *in;
int post_adjmat[VERTEX][VERTEX];
int spindle[7][7] = {{0,0,1,1,0,0,1},{0,0,0,1,1,1,0},{1,0,0,0,1,0,1},{1,1,0,0,0,1,0},{0,1,1,0,0,1,1},{0,1,0,1,1,0,0},{1,0,1,0,1,0,0}};
int base_mat[8][8];

/************************************************************************

udgraph_solver3401a.c : user 22m50.198s w/
MAXDIFFAT100 ((long double) 38)/((long double) 1)

newtestz746a.out 345 : 8m 34.631s for 30k solns. , using -O3
newtestz745a.out 340 : 8m 35s for 30000 solutions, with -O3
newtestz585a.c: 8m 51s for 30000 solutions, using -O3 optimization
newtest83a.c: 9m 57s for 30000 solutions, using -O3 optimization option
newtest81a.c: 9m 57s for 30000 solutions, using -O3 optimization option
newtest73a.c: 8m 49s for 30000 solutions, using -O3 optimization option
newtest66a.c: 10m 25s for 30000 solutions, using -O3 optimization option
newtest65a.c: 11m 30s for 30000 solutions
newtest64a.c: 11m 30s for 30000 solutions
newtest63a.c: 11m 33s for 30000 solutions
newtest62a.c: 11m 33s for 30000 solutions
newtest61a.c: 3m 51s for 10000 solutions
newtest57a.c: 6m 27s for 10000 solutions
newtest56a.c: 6m 37s for 10000 solutions
newtest55a.c: 6m 43s for 10000 solutions
newtest54a.c: 6m 48s for 10000 solutions
newtest53a.c: 6m 46s for 10000 solutions
newtest48a.c: 62 seconds for 1600 solutions
newtest47a.c: 14 seconds for 400 solutions
newtest46a.c: 66 seconds for 400 solutions
newtest39a.c: 67 seconds for 400 solutions
newtest37a.c: 70 seconds for 400 solutions
newtest35a.c: 79 seconds for 400 solutions
newtest34a.c: 72 seconds for 400 solutions
newtest33a.c: 91 seconds for 400 solutions
newtest30a.c: 16 seconds for 100 solutions
newtest29a.c: 18 seconds for 100 solutions
newtest28a.c: 25 seconds for 100 solutions
newtest27a.c: 50 seconds for 100 solutions
newtest26a.c: 99 seconds for 100 solutions
newtest25a.c: 3000 solutions per hour
for 100 solutions, 2 minutes …
808 solutions per minute for 4-point diamond shape.
gtest230a.c :
2600 solutions per minute for 7-point 4-colour
graph
gtest980a.c :
98000 solutions per minute for 7-point 4-colour
graph, Mosers’ spindle.
en.wikipedia.org slash wiki slash Moser_spindle
*************************************************/
B = 340;
total_edges = 27 ;

total_finds = 0;

maxi_ull = ((unsigned long long)6700417)*((unsigned long
long)2753074036095);
scaling = ((long double) 57)/((long double) 10);
one = (long double) 1;
diff_record = ((long double) 4100)/((long double) 100);

diff_record = MAXDIFFAT1;
maxdiffat400 = ((long double)1)/((long double)100000);
maxdiffat400 = (((long double)1)/((long double)100000))*maxdiffat400;

// maxdiffat400 = (((long double)1)/((long double)100000))*maxdiffat400;

epsilon = ((long double)1)/((long double)10000000);

rec_diff25 = (long double) 0;
rec_diff50 = (long double) 0;
rec_diff100 = (long double) 0;
rec_diff1 = (long double) 0;
rec_diff200 = (long double) 0;
rec_diff400 = (long double) 0;
rec_diff800 = (long double) 0;
rec_diff1200 = (long double) 0;
alphabet[0] = ‘A’;
alphabet[1] = ‘B’;
alphabet[2] = ‘C’;
alphabet[3] = ‘D’;
alphabet[4] = ‘E’;
alphabet[5] = ‘F’;
alphabet[6] = ‘G’;
alphabet[7] = ‘H’;
alphabet[8] = ‘I’;
alphabet[9] = ‘J’;
alphabet[10] = ‘K’;
alphabet[11] = ‘L’;
alphabet[12] = ‘M’;
alphabet[13] = ‘N’;
alphabet[14] = ‘O’;
in=fopen(“/home/david/graphs/golomb23/base_mat_from_blog01a.txt”, “r”);
for(l=0; l< 14 ; l++)
{
for(m=0; m < 14; m++)
{
fscanf(in, “%d”, &blog_mat[l][m]);
}
}

fclose(in);
for(l=0; l< VERTEX ; l++)
{
for(m=0; m < VERTEX ; m++)
{
testmat[l][m] = 0;
}
}

for(l=0; l< 14 ; l++)
{
for(m=0; m < 14; m++)
{
testmat[l][m] = blog_mat[l][m];
}
}
/***************************************************

add edges:

BO
CO

*********************************************************/

testmat[1][14] = 1;
testmat[2][14] = 1;
testmat[14][1] = 1;
testmat[14][2] = 1;

sum_of_degrees = 0;

for(l=0; l< VERTEX ; l++)
{
for(m=0; m < VERTEX ; m++)
{
if(testmat[l][m] == 1)
{
sum_of_degrees = sum_of_degrees +1;
}
}
}

printf(“\n sum_of_degrees = %d\n\n”, sum_of_degrees);
/* First seed Q[] with CNG+XS: */
for(i=0;i<2097152;i++)
{
Q[i]=CNG+XS;
Q[i] = Q[i]^14502779422240352273ULL;
Q[i] = Q[i]^9440806654508920842ULL;
Q[i] = Q[i]^11231778222269950461ULL;
}

for(l=0; l< VERTEX ; l++)
{
dmatrix[l][l] = (long double) 0;
}

while( total_finds < 5000000000 )
{

graph_found = 0;

while( graph_found == 0)
{

numedges = 27;
for(l=0; l< VERTEX ; l++)
{
for(m=0; m < VERTEX; m++)
{
adjmat[l][m] = 0;
}
}

for(l=0; l< VERTEX ; l++)
{
for(m=0; m < VERTEX; m++)
{
adjmat[l][m] = testmat[l][m] ;
}
}

while(numedges < total_edges )
{
ru1 = (int) (KISS&mask);
co1 = ru1/143165577 ;
ru2 = (int) (KISS&mask);
co2 = ru2/143165577 ;
if( (co1 != co2) && (adjmat[co1][co2] == 0) )
{
if( (co1 > 13) || (co2 > 13) )
{
adjmat[co1][co2] = 1;
adjmat[co2][co1] = 1;
numedges++;
}
}
}

/*** compute degrees[] ***/
/*** each 3 or more ***/

degree_test_passed = 1;
/*********************************************************************
for(l=0; l< VERTEX ; l++)
{
degrees[l] = 0;

for(m=0; m < VERTEX; m++)
{
degrees[l] = degrees[l] + adjmat[l][m];
}

if( degrees[l] < 3 )
{
degree_test_passed = 0;
break;
}
}
********************************************************************/

if(degree_test_passed == 1)
{
graph_found = 1;
}

}
count = 0;
max_has_converged_step = 0;
while( count < 1 )
{
solution_found = 0;

while( 0 == solution_found )
{
for( j=0; j< VERTEX ; j++)
{
randx = KISS;
xcoord[j] = ((long double) randx)/((long double) maxi_ull);
xcoord[j] = scaling*xcoord[j];
randx = KISS;
ycoord[j] = ((long double) randx)/((long double) maxi_ull);
ycoord[j] = scaling*ycoord[j];
}
for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l ; m++)
{
dmatrix[l][m] = (xcoord[l]-xcoord[m])*(xcoord[l]-xcoord[m]);
dmatrix[l][m] = dmatrix[l][m] +
(ycoord[l]-ycoord[m])*(ycoord[l]-ycoord[m]);
dmatrix[l][m] = sqrtl(dmatrix[l][m]);
}
for(m= l+1 ; m< VERTEX ; m++)
{
dmatrix[l][m] = dmatrix[m][l];
}
}
diff = (long double) 0;
for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l; m++)
{
if( 1 == adjmat[l][m] )
{
diff = diff + fabsl(one-dmatrix[l][m]);
}
}
}

diff1 = diff;

if(diff < diff_record)
{
solution_found = 1;

for( j =0; j< VERTEX ; j++)
{
xgood[j] = xcoord[j];
ygood[j] = ycoord[j];
}
}
}

/*****************************************************************

have solution …

*****************************************************************/
has_converged_flag = 0;
quit = 0;
count = count + 1;
/*************** BEGIN ITERATIONS TO CONVERGE **************/
for( k = 0; k < NUMSTEPS ; k++)
{
// if( quit == 1)
// {
// break;
// }

if( (k+1) < 100)
{
C = ((long double) 200)/((long double) 1000);
}
else
{
C = ((long double) 200 )/((long double) 1000);
}

for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l ; m++)
{
dmatrix[l][m] = (xgood[l]-xgood[m])*(xgood[l]-xgood[m]);
dmatrix[l][m] = dmatrix[l][m] +
(ygood[l]-ygood[m])*(ygood[l]-ygood[m]);
dmatrix[l][m] = sqrtl(dmatrix[l][m]);
}
for(m= l+1 ; m< VERTEX ; m++)
{
dmatrix[l][m] = dmatrix[m][l];
}
}
if( (k+1) == 25 )
{
diff = (long double) 0;
for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l; m++)
{
if( 1 == adjmat[l][m] )
{
diff = diff + fabsl(one-dmatrix[l][m]);
}
}
}

diff25 = diff;

if( diff > MAXDIFFAT25 )
{
quit = 1;
}
}
if( (k+1) == 50 )
{
diff = (long double) 0;
for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l; m++)
{
if( 1 == adjmat[l][m] )
{
diff = diff + fabsl(one-dmatrix[l][m]);
}
}
}

diff50 = diff;

if( diff > MAXDIFFAT50 )
{
quit = 1;
}
}
if( (k+1) == 100 )
{
diff = (long double) 0;
for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l; m++)
{
if( 1 == adjmat[l][m] )
{
diff = diff + fabsl(one-dmatrix[l][m]);
}
}
}

diff100 = diff;

if( diff > MAXDIFFAT100 )
{
quit = 1;
}
}

if( (k+1) == 200 )
{
diff = (long double) 0;
for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l; m++)
{
if( 1 == adjmat[l][m] )
{
diff = diff + fabsl(one-dmatrix[l][m]);
}
}
}

diff200 = diff;

if( diff > MAXDIFFAT200 )
{
quit = 1;
}
}
if( (k+1) == 400 )
{
diff = (long double) 0;
for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l; m++)
{
if( 1 == adjmat[l][m] )
{
diff = diff + fabsl(one-dmatrix[l][m]);
}
}
}

diff400 = diff;

if( diff > MAXDIFFAT400 )
{
quit = 1;
}
}
if( (k+1) == 800 )
{
diff = (long double) 0;
for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l; m++)
{
if( 1 == adjmat[l][m] )
{
diff = diff + fabsl(one-dmatrix[l][m]);
}
}
}

diff800 = diff;

if( diff > MAXDIFFAT800 )
{
quit = 1;
}

}
if( (k+1) == 1200 )
{
diff = (long double) 0;
for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l; m++)
{
if( 1 == adjmat[l][m] )
{
diff = diff + fabsl(one-dmatrix[l][m]);
}
}
}

diff1200 = diff;

if( diff > MAXDIFFAT1200 )
{
quit = 1;
}

}
diff = (long double) 0;

for(l=0; l< VERTEX ; l++)
{
for(m=0; m< l; m++)
{
if( 1 == adjmat[l][m] )
{
diff = diff + fabsl(one-dmatrix[l][m]);
}
}
}

if( (diff < maxdiffat400) && (has_converged_flag == 0) )
{
has_converged_flag = 1;
has_converged_step = k+1;

if( has_converged_step > max_has_converged_step )
{
max_has_converged_step = has_converged_step;
}

quit = 1;

/***********************

int is_singular;

**********************/
is_singular = 0;

for(l=0; l < VERTEX; l++)
{
for(m = 0; m < l; m++)
{
if( dmatrix[l][m] < epsilon )
{
is_singular = 1;
}
}
}
if( is_singular == 0)
{

total_finds = total_finds + 1;

if( (diff25 > rec_diff25) && (has_converged_step > 25))
{
rec_diff25 = diff25;
}

if( (diff50 > rec_diff50) && (has_converged_step > 50))
{
rec_diff50 = diff50;
}
if( (diff100 > rec_diff100) && (has_converged_step > 100))
{
rec_diff100 = diff100;
}

if( diff1 > rec_diff1)
{
rec_diff1 = diff1;
}

if( (diff200 > rec_diff200) && (has_converged_step > 200) )
{
rec_diff200 = diff200;
}

if( (diff400 > rec_diff400 ) && (has_converged_step > 400))
{
rec_diff400 = diff400;
}
if( (diff800 > rec_diff800) && (has_converged_step > 800))
{
rec_diff800 = diff800;
}
if( (diff1200 > rec_diff1200) && (has_converged_step > 1200))
{
rec_diff1200 = diff1200;
}
#ifdef VERBOSE
for(l = 0; l< VERTEX; l++)
{
for(m=0; m< VERTEX; m++)
{
post_adjmat[l][m] = 0;
}
}
probable_unit_lengths = 0;

for(l = 0; l<VERTEX; l++)
{
for(m = 0; m < l; m++)
{
if( fabsl(dmatrix[l][m]-one) < epsilon )
{
probable_unit_lengths++ ;
post_adjmat[l][m] = 1;
post_adjmat[m][l] = 1;
}
}
}
/**** TEST post_adjmat[][] for 3-coloring BEGIN ****/

n_colors = 3;
coloring_found = 0;
for(v0 = 0; v0< 1 ; v0++)
{
for(v1 = 0; v1< 2 ; v1++)
{
for(v2 = 0; v2< n_colors ; v2++)
{
for(v3 = 0; v3< n_colors ; v3++)
{
for(v4 = 0; v4< n_colors ; v4++)
{
for(v5 = 0; v5< n_colors ; v5++)
{
for(v6 = 0; v6< n_colors ; v6++)
{
for(v7 = 0; v7< n_colors ; v7++)
{
for(v8 = 0; v8< n_colors ; v8++)
{
for(v9 = 0; v9< n_colors ; v9++)
{
for(v10 = 0; v10< n_colors ; v10++)
{
for(v11 = 0; v11< n_colors ; v11++)
{
for(v12 = 0; v12< n_colors ; v12++)
{
for(v13 = 0; v13< n_colors ; v13++)
{
for(v14 = 0; v14< n_colors ; v14++)
{

colors[0] = v0;
colors[1] = v1;
colors[2] = v2;
colors[3] = v3;
colors[4] = v4;
colors[5] = v5;
colors[6] = v6;
colors[7] = v7;
colors[8] = v8;
colors[9] = v9;
colors[10] = v10;
colors[11] = v11;
colors[12] = v12;
colors[13] = v13;
colors[14] = v14;

has_failed = 0;

for(l=0; l< VERTEX ; l++)
{
for(m=0; m < l; m++)
{
if( (post_adjmat[l][m]==1)&& (colors[l]==colors[m]) )
{
has_failed = 1;
}
}
}

if( has_failed == 0 )
{
coloring_found = 1;
}

if( coloring_found == 1 )
{
break;
}

}

if( coloring_found == 1 )
{
break;
}
}

if( coloring_found == 1 )
{
break;
}
}
if( coloring_found == 1 )
{
break;
}
}

if( coloring_found == 1 )
{
break;
}
}

if( coloring_found == 1 )
{
break;
}

}

if( coloring_found == 1 )
{
break;
}
}

if( coloring_found == 1 )
{
break;
}

}

if( coloring_found == 1 )
{
break;
}

}

if( coloring_found == 1 )
{
break;
}
}

if( coloring_found == 1 )
{
break;
}

}

if( coloring_found == 1 )
{
break;
}
}

if( coloring_found == 1 )
{
break;
}
}

if( coloring_found == 1 )
{
break;
}
}

if( coloring_found == 1 )
{
break;
}
}

if( coloring_found == 1 )
{
is_3colorable = 1;
}
else
{
is_3colorable = 0;
}

/**** TEST post_adjmat[][] for 3-coloring END ****/

printf(“adjacency matrix:\n”);

for(l=0; l< VERTEX ; l++)
{
for(m=0; m < VERTEX; m++)
{
printf(“%d “, adjmat[l][m]) ;
}
printf(“\n”);
}

printf(“\n”);
printf(“post adjacency matrix:\n”);

for(l=0; l< VERTEX ; l++)
{
for(m=0; m < VERTEX; m++)
{
printf(“%d “, post_adjmat[l][m]) ;
}
printf(“\n”);
}

if( is_3colorable == 0)
{

n_colors = 4;
coloring_found = 0;
num_4_colorings = 0;

for(v0 = 0; v0< n_colors ; v0++)
{
for(v1 = 0; v1< n_colors ; v1++)
{
for(v2 = 0; v2< n_colors ; v2++)
{
for(v3 = 0; v3< n_colors ; v3++)
{
for(v4 = 0; v4< n_colors ; v4++)
{
for(v5 = 0; v5< n_colors ; v5++)
{
for(v6 = 0; v6< n_colors ; v6++)
{
for(v7 = 0; v7< n_colors ; v7++)
{
for(v8 = 0; v8< n_colors ; v8++)
{
for(v9 = 0; v9< n_colors ; v9++)
{
for(v10 = 0; v10< n_colors ; v10++)
{
for(v11 = 0; v11< n_colors ; v11++)
{
for(v12 = 0; v12< n_colors ; v12++)
{
for(v13 = 0; v13< n_colors ; v13++)
{
for(v14 = 0; v14< n_colors ; v14++)
{
colors[0] = v0;
colors[1] = v1;
colors[2] = v2;
colors[3] = v3;
colors[4] = v4;
colors[5] = v5;
colors[6] = v6;
colors[7] = v7;
colors[8] = v8;
colors[9] = v9;
colors[10] = v10;
colors[11] = v11;
colors[12] = v12;
colors[13] = v13;
colors[14] = v14;

has_failed = 0;
four_colouring_failed = 0;

for(l=0; l< VERTEX ; l++)
{
for(m=0; m < l; m++)
{
if( (post_adjmat[l][m]==1)&& (colors[l]==colors[m]) )
{
has_failed = 1;
four_colouring_failed = 1;
}
if( four_colouring_failed == 1)
{
break;
}
}

if( four_colouring_failed == 1)
{
break;
}
}

if( has_failed == 0 )
{
coloring_found = 1;
num_4_colorings++ ;
}
}
}
}
}
}
}
}
}
}
}
}
}
}
}
}

num_4_colorings_mod_24 = num_4_colorings%24 ;

count_4_colorings = num_4_colorings/24;

}
printf(“total_finds = %d\n”, total_finds);
printf(“Tests count = %d “, count);
printf(“has_converged_step = %d “, has_converged_step);
printf(“max_has_converged_step = %d\n”, max_has_converged_step);
printf(“rec_diff1 = %.6Lf\n”, rec_diff1);
printf(“rec_diff25 = %.6Lf\n”, rec_diff25);
printf(“rec_diff50 = %.6Lf\n”, rec_diff50);
printf(“rec_diff100 = %.6Lf\n”, rec_diff100);
printf(“rec_diff200 = %.6Lf\n”, rec_diff200);
printf(“rec_diff400 = %.6Lf\n”, rec_diff400);
printf(“rec_diff800 = %.16Lf\n”, rec_diff800);
printf(“rec_diff1200 = %.16Lf\n”, rec_diff1200);
printf(“probable_unit_lengths = %d\n”, probable_unit_lengths);

printf(“graph is 3-colorable:”);
if(is_3colorable == 1)
{
printf(“yes. \n”);
}
else
{
printf(“no. \n”);
}
if( is_3colorable == 0 )
{
printf(“count_4_colorings = %d “, count_4_colorings);
printf(“num_4_colorings_mod_24 = %d\n”, num_4_colorings_mod_24);
}

printf(“Matrix of distances vertex to vertex:\n”);
printf(” “);
for(m=0; m<VERTEX; m++)
{
printf(” %c “, alphabet[m]);
}
printf(“\n”);
for(l=0; l< VERTEX ; l++)
{
printf(“%c “, alphabet[l]);
for(m=0; m< VERTEX ; m++)
{
printf(“%.2Lf “, dmatrix[l][m]);
}
printf(“\n”);
}

printf(“\n”);
fflush(stdout);
#endif

}
}
for(l=0; l< VERTEX ; l++)
{
forces[l][0] = (long double) 0;
forces[l][1] = (long double) 0;

for(m=0; m< VERTEX ; m++)
{
if( 1 == adjmat[l][m] )
{
vector[0] = xgood[m]-xgood[l];
vector[1] = ygood[m]-ygood[l];
vector[0] = vector[0]/dmatrix[l][m];
vector[1] = vector[1]/dmatrix[l][m];
vector[0] = vector[0]*C;
vector[1] = vector[1]*C;
vector[0] = vector[0]*(dmatrix[l][m]-one);
vector[1] = vector[1]*(dmatrix[l][m]-one);

forces[l][0] = forces[l][0] + vector[0];
forces[l][1] = forces[l][1] + vector[1];
}
}
}

for( j =0; j< VERTEX ; j++)
{
xgood[j] = xgood[j] + forces[j][0];
ygood[j] = ygood[j] + forces[j][1];
}
}
/******************************************************
Below, post-convergence algorithm or heuristic:
******************************************************/
}
/*****************************************
while( count < 1 ) end Block
*****************************************/
}
/********************************************
end of while( 1 == 1 ) Block
********************************************/
return 0;
}

 

 

The file  base_mat_from_blog01a.txt :

0 0 0 0 0 1 1 0 0 0 0 0 1 0
0 0 1 0 0 1 0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 1 0 0 1 0 0 0
0 0 0 0 0 1 0 1 0 1 0 1 0 0
0 0 0 0 0 0 1 1 0 1 0 0 0 1
1 1 0 1 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 0 0 1 0 0 0 0 0 0
0 0 1 1 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 1 1 0
0 0 0 1 1 0 0 0 0 0 0 1 0 1
0 0 1 0 0 0 0 0 1 0 0 0 1 1
0 0 0 1 0 1 0 0 1 1 0 0 0 0
1 0 0 0 0 0 0 0 1 0 1 0 0 0
0 1 0 0 1 0 0 0 0 1 1 0 0 0

 

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Written by meditationatae

February 27, 2017 at 9:30 pm

Posted in History

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