Random problems offer the following advantages for empirically evaluating the performance of CSP algorithms:
Instance 99 17 19: (6 6) (2 0) (3 8) (5 7) (9 6) (2 7) (5 6) (8 2) (9 9) (4 8) 57 94: (0 3) (0 1) (8 0) (2 2) (7 6) (9 1) (8 4) (3 0) (9 2) (8 8) 10 28: (5 0) (4 6) (9 2) (8 2) (1 2) (3 5) (4 8) (1 1) (3 3) (4 0) 1 90: (1 4) (4 5) (5 3) (7 8) (7 2) (7 1) (0 0) (0 4) (0 5) (1 9) 55 64: (2 0) (5 9) (0 8) (0 2) (9 0) (5 1) (5 4) (2 7) (1 6) (5 0) 9 32: (0 5) (1 1) (6 3) (1 8) (2 4) (5 6) (3 5) (2 8) (9 9) (5 3) 3 12: (0 7) (3 6) (8 8) (0 8) (6 1) (1 4) (2 0) (3 2) (4 1) (3 0) 52 69: (5 5) (7 8) (8 2) (1 8) (9 7) (9 2) (9 3) (3 1) (9 9) (4 8) 11 59: (9 0) (0 1) (8 7) (5 8) (7 4) (2 2) (2 1) (8 4) (9 8) (6 9) 14 44: (9 0) (2 4) (3 3) (5 0) (2 7) (1 4) (3 9) (9 6) (6 8) (7 0)At a minimum, your program should duplicate this result.
/* urbcsp.c -- generates uniform random binary constraint satisfaction problems
*/
#include <stdio.h>
#include <math.h>
/* function declarations */
float ran2(long *idum);
void StartCSP(int N, int K, int instance);
void EndCSP();
void AddConstraint(int var1, int var2);
void AddNogood(int val1, int val2);
/*********************************************************************
This file has 5 parts:
0. This introduction.
1. A main() function, which can be used to demonstrate MakeURBCSP().
2. MakeURBCSP().
3. ran2(), a random number generator.
4. The four functions StartCSP(), AddConstraint(), AddNogood(), and
EndCSP(), which are called by MakeURBCSP(). The versions
of these functions given here print out each instance, listing
the incompatible value pairs of each constraint. You will need
to replace these functions with versions that mesh with your
system and data structures.
*********************************************************************/
/*********************************************************************
1. A simple main() function which reads in command line parameters
and generates CSPs.
*********************************************************************/
int main(int argc, char* argv[])
{
int N, D, C, T, I, i;
long S;
if (argc != 7)
{
printf("usage: urbcsp #vars #vals #constraints #nogoods seed "
"instances\n");
return 0;
}
N = atoi(argv[1]);
D = atoi(argv[2]);
C = atoi(argv[3]);
T = atoi(argv[4]);
S = atoi(argv[5]);
I = atoi(argv[6]);
/* Seed passed to ran2() must initially be negative. */
if (S > 0)
S = -S;
for (i=0; i<I; ++i)
if (!MakeURBCSP(N, D, C, T, &S))
return 0;
return 1;
}
/*********************************************************************
2. MakeURBCSP() creates a uniform binary constraint satisfaction
problem with a specified number of variables, domain size,
tightness, and number of constraints. MakeURBCSP() calls
four functions, StartCSP(), AddConstraint(), AddNogood(), and
EndCSP(), which actually create the CSP (that is, build a data
structure). Feel free to change the signatures of these functions.
Note that numbering starts from 0: the variables are numbered 0..N-1,
and the values are numbered 0..K-1.
INPUT PARAMETERS:
N: number of variables
D: size of each variable's domain
C: number of constraints
T: number of incompatible value pairs in each constraint
Seed: a negative number means start a new sequence of
pseudo-random numbers; a positive number means continue
with the same sequence. S is turned positive by ran2().
RETURN VALUE:
Returns 0 if there is a problem; 1 for normal completion.
*********************************************************************/
int MakeURBCSP(int N, int D, int C, int T, long *Seed)
{
int PossibleCTs, PossibleNGs; /* CT means "constraint" */
unsigned long *CTarray, *NGarray; /* NG means "nogood pair" */
long selectedCT, selectedNG;
int i, c, r, t;
int var1, var2, val1, val2;
static int instance;
/* Check for valid values of N, D, C, and T. */
if (N < 2)
{
printf("MakeURBCSP: ***Illegal value for N: %d\n", N);
return 0;
}
if (D < 2)
{
printf("MakeURBCSP: ***Illegal value for D: %d\n", D);
return 0;
}
if (C < 0 || C > N * (N - 1) / 2)
{
printf("MakeURBCSP: ***Illegal value for C: %d\n", C);
return 0;
}
if (T < 1 || T > ((D * D) - 1))
{
printf("MakeURBCSP: ***Illegal value for T: %d\n", T);
return 0;
}
if (*Seed < 0) /* starting a new sequence of random numbers */
instance = 0;
else
++instance; /* increment static variable */
StartCSP(N, D, instance);
/* The program has to choose randomly and uniformly m values from
n possibilities. It uses the following logic for both constraints
and nogood value pairs:
1. Let t[] be an array of the n possibilities
2. for i = 0 to m-1
3. r = random(i, n-1) ; random() returns an int in [i,n-1]
4. swap t[i] and t[r]
5. end-for
At the end of the for loop, the elements from t[0] to t[m-1] are
the m randomly selected elements.
*/
/* Create an array for each possible binary constraint. */
PossibleCTs = N * (N - 1) / 2;
CTarray = (unsigned long*) malloc(PossibleCTs * 4);
/* Create an array for each possible value pair. */
PossibleNGs = D * D;
NGarray = (unsigned long*) malloc(PossibleNGs * 4);
/* Initialize the CTarray. Each entry has one var in the high two
bytes, and the other in the low two bytes. */
i=0;
for (var1=0; var1<(N-1); ++var1)
for (var2=var1+1; var2<N; ++var2)
CTarray[i++] = (var1 << 16) | var2;
/* Select C constraints. */
for (c=0; c<C; ++c)
{
/* Choose a random number between c and PossibleCTs - 1, inclusive. */
r = c + (int) (ran2(Seed) * (PossibleCTs - c));
/* Swap elements [c] and [r]. */
selectedCT = CTarray[r];
CTarray[r] = CTarray[c];
CTarray[c] = selectedCT;
/* Broadcast the constraint. */
AddConstraint((int)(CTarray[c] >> 16), (int)(CTarray[c] & 0x0000FFFF));
/* For each constraint, select T illegal value pairs. */
/* Initialize the NGarray. */
for (i=0; i<(D*D); ++i)
NGarray[i] = i;
/* Select T incompatible pairs. */
for (t=0; t<T; ++t)
{
/* Choose a random number between t and PossibleNGs - 1, inclusive.*/
r = t + (int) (ran2(Seed) * (PossibleNGs - t));
selectedNG = NGarray[r];
NGarray[r] = NGarray[t];
NGarray[t] = selectedNG;
/* Broadcast the nogood value pair. */
AddNogood((int)(NGarray[t] / D), (int)(NGarray[t] % D));
}
}
EndCSP();
free(CTarray);
free(NGarray);
return 1;
}
/*********************************************************************
3. This random number generator is from William H. Press, et al.,
_Numerical Recipes in C_, Second Ed. with corrections (1994),
p. 282. This excellent book is available through the
WWW at http://nr.harvard.edu/nr/bookc.html.
The specific section concerning ran2, Section 7.1, is in
http://cfatab.harvard.edu/nr/bookc/c7-1.ps
*********************************************************************/
#define IM1 2147483563
#define IM2 2147483399
#define AM (1.0/IM1)
#define IMM1 (IM1-1)
#define IA1 40014
#define IA2 40692
#define IQ1 53668
#define IQ2 52774
#define IR1 12211
#define IR2 3791
#define NTAB 32
#define NDIV (1+IMM1/NTAB)
#define EPS 1.2e-7
#define RNMX (1.0 - EPS)
/* ran2() - Return a random floating point value between 0.0 and
1.0 exclusive. If idum is negative, a new series starts (and
idum is made positive so that subsequent calls using an unchanged
idum will continue in the same sequence). */
float ran2(long *idum)
{
int j;
long k;
static long idum2 = 123456789;
static long iy = 0;
static long iv[NTAB];
float temp;
if (*idum <= 0) { /* initialize */
if (-(*idum) < 1) /* prevent idum == 0 */
*idum = 1;
else
*idum = -(*idum); /* make idum positive */
idum2 = (*idum);
for (j = NTAB + 7; j >= 0; j--) { /* load the shuffle table */
k = (*idum) / IQ1;
*idum = IA1 * (*idum - k*IQ1) - k*IR1;
if (*idum < 0)
*idum += IM1;
if (j < NTAB)
iv[j] = *idum;
}
iy = iv[0];
}
k = (*idum) / IQ1;
*idum = IA1 * (*idum - k*IQ1) - k*IR1;
if (*idum < 0)
*idum += IM1;
k = idum2/IQ2;
idum2 = IA2 * (idum2 - k*IQ2) - k*IR2;
if (idum2 < 0)
idum2 += IM2;
j = iy / NDIV;
iy = iv[j] - idum2;
iv[j] = *idum;
if (iy < 1)
iy += IMM1;
if ((temp = AM * iy) > RNMX)
return RNMX; /* avoid endpoint */
else
return temp;
}
/*********************************************************************
4. An implementation of StartCSP, AddConstraint, AddNogood, and EndCSP
which prints out the CSP, just listing incompatible value pairs.
Each constraint starts one a new line, and the id-numbers of the
variables appear before the colon. For instance, the output of
urbcsp 10 5 4 3 9999 10
begins
Instance 0
8 9: (1 1) (4 0) (0 4)
2 4: (0 3) (3 1) (4 0)
6 9: (4 1) (2 0) (0 3)
1 5: (0 3) (4 0) (0 0)
*********************************************************************/
void StartCSP(int N, int D, int instance)
{
printf("\nInstance %d", instance);
}
void AddConstraint(int var1, int var2)
{
printf("\n%3d %3d: ", var1, var2);
}
void AddNogood(int val1, int val2)
{
printf("(%d %d) ", val1, val2);
}
void EndCSP()
{
printf("\n");
}