Random problems offer the following advantages for empirically evaluating the performance of CSP algorithms:
The solution we adopt is to give each instance in a sequence (after the first) its own unique seed. After each instance is created, the random number generator is called one additional time to generate a number that will be used as the seed for the next instance. Since each instance is created with random numbers that start from the beginning of the sequence defined by a particular seed, each instance can be created by using its own particular seed. Thus it is possible to write "The only instance we could not solve within our 24 CPU-hour time bound was the 768th in the series, which has seed 1996453." Subsequently, it will be easy to recreate the one instance of interest.
Instance 99 uses seed -2016279424 40 68: (3 4) (2 9) (8 9) (5 2) (3 9) (6 9) (9 5) (7 4) (8 5) (3 1) 15 52: (8 4) (3 7) (5 3) (6 1) (7 8) (5 2) (5 1) (1 4) (8 7) (2 3) 68 71: (1 5) (0 5) (2 1) (8 9) (4 4) (8 3) (9 9) (2 5) (0 0) (0 6) 49 66: (4 5) (4 8) (9 7) (5 3) (9 5) (8 2) (1 2) (0 5) (0 3) (3 5) 80 89: (7 1) (8 5) (5 8) (7 2) (2 1) (7 8) (1 9) (8 8) (0 6) (0 7) 64 86: (7 3) (7 9) (4 9) (6 1) (2 8) (8 9) (8 4) (4 6) (0 2) (9 5) 21 26: (0 5) (4 0) (5 4) (4 1) (2 0) (7 1) (3 3) (8 8) (3 9) (2 1) 39 86: (7 1) (2 7) (1 2) (2 8) (2 9) (6 0) (4 1) (3 4) (3 6) (1 8) 12 53: (6 2) (3 9) (5 2) (4 5) (2 1) (9 8) (9 5) (5 6) (2 7) (8 2) 75 96: (1 4) (7 1) (8 0) (1 6) (2 8) (7 0) (8 3) (4 1) (0 1) (1 7)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 *idnum);
void StartCSP(int N, int K, int instance, long seed);
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]);
/* Note that to generate I instances, MakeURBCSP is called once with
the supplied seed, and then I-1 times with 0 instead of the seed. */
if (!MakeURBCSP(N, D, C, T, S))
return 0;
for (i=1; i<I; ++i)
if (!MakeURBCSP(N, D, C, T, 0))
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
S: seed; 0 means use seed generated from previous call to
MakeURBCSP(). The actual seed passed to ran2() is
negative; if S is positive its sign is reversed.
RETURN VALUE:
Returns 0 if there is a problem; 1 for normal completion.
*********************************************************************/
int MakeURBCSP(int N, int D, int C, int T, long S)
{
static int instance = 0;
static long default_seed = -12345;
static long next_seed;
long seed;
int PossibleCTs, PossibleNGs;
unsigned long *CTarray, *NGarray;
long selectedCT, selectedNG;
int i, c, r, t;
int var1, var2, val1, val2;
/* 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 (S == 0) /* no seed specified */
{
if (instance == 0) /* first instance, really should supply */
seed = default_seed; /* a seed, but just in case . . . */
else
seed = next_seed; /* this is the typical case */
}
else /* seed specified */
seed = (S < 0 ? S : -S); /* so use it, but it must be negative */
StartCSP(N, D, instance, seed);
++instance;
/* The program has to choose randomly and uniformly m values from
n possibilities. It uses the following logic for both constraints
and nogoods:
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 D illegal value pairs. */
/* Initialize the NGarray. */
for (i=0; i<(D*D); ++i)
NGarray[i] = i;
/* Select T nogoods. */
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. */
AddNogood((int)(NGarray[t] / D), (int)(NGarray[t] % D));
}
}
EndCSP();
free(CTarray);
free(NGarray);
next_seed = (long) (ran2(&seed) * -2147483646);
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 is an excellent book and 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; /* initialized below */
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 */
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];
idum2 = iv[NTAB/2]; /* Added for urbcsp so that a negative */
} /* idum always starts the same sequence. */
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 5 3 1514849 10
begins
Instance 0 uses seed -1514849
4 8: (4 4) (2 2) (0 3) (3 2) (4 1)
3 4: (3 4) (1 3) (3 0) (1 2) (0 2)
7 9: (2 4) (4 1) (0 2) (4 3) (3 1)
*********************************************************************/
void StartCSP(int N, int D, int instance, long seed)
{
printf("\nInstance %d uses seed %d", instance, seed);
}
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");
}