Generated on Mon Aug 25 11:35:47 2008 for Gecode by doxygen 1.5.6

Linear constraints over integer variables
[Using finite domain integers]

Detailed Description

All variants for linear constraints over integer variables share the following properties:
  • Bounds consistency (over the real numbers) is supported for all constraints (actually, for disequlities always domain consistency is used as it is cheaper). Domain consistency is supported for all non-reified constraint. As bounds consistency for inequalities coincides with domain consistency, the only real variation is for linear equations. Domain consistent linear equations have exponential complexity, so use with care!
  • Variables occurring multiply in the argument arrays are replaced by a single occurrence: for example, $ax+bx$ becomes $(a+b)x$.
  • If in the above simplification the value for $(a+b)$ (or for $a$ and $b$) exceeds the limits for integers as defined in Int::Limits, an exception of type Int::OutOfLimits is thrown.
  • Assume the constraint $\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_r c$. If $|c|+\sum_{i=0}^{|x|-1}a_i\cdot x_i$ exceeds the maximal available precision (at least $2^{48}$), an exception of type Int::OutOfLimits is thrown.
  • In all other cases, the created propagators are accurate (that is, they will not silently overflow during propagation).


Functions

void Gecode::linear (Space *home, const IntVarArgs &x, IntRelType r, int c, IntConLevel icl=ICL_DEF, PropKind pk=PK_DEF)
 Post propagator for $\sum_{i=0}^{|x|-1}x_i\sim_r c$.
void Gecode::linear (Space *home, const IntVarArgs &x, IntRelType r, IntVar y, IntConLevel icl=ICL_DEF, PropKind pk=PK_DEF)
 Post propagator for $\sum_{i=0}^{|x|-1}x_i\sim_r y$.
void Gecode::linear (Space *home, const IntVarArgs &x, IntRelType r, int c, BoolVar b, IntConLevel icl=ICL_DEF, PropKind pk=PK_DEF)
 Post propagator for $\left(\sum_{i=0}^{|x|-1}x_i\sim_r c\right)\Leftrightarrow b$.
void Gecode::linear (Space *home, const IntVarArgs &x, IntRelType r, IntVar y, BoolVar b, IntConLevel icl=ICL_DEF, PropKind pk=PK_DEF)
 Post propagator for $\left(\sum_{i=0}^{|x|-1}x_i\sim_r y\right)\Leftrightarrow b$.
void Gecode::linear (Space *home, const IntArgs &a, const IntVarArgs &x, IntRelType r, int c, IntConLevel icl=ICL_DEF, PropKind pk=PK_DEF)
 Post propagator for $\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_r c$.
void Gecode::linear (Space *home, const IntArgs &a, const IntVarArgs &x, IntRelType r, IntVar y, IntConLevel icl=ICL_DEF, PropKind pk=PK_DEF)
 Post propagator for $\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_r y$.
void Gecode::linear (Space *home, const IntArgs &a, const IntVarArgs &x, IntRelType r, int c, BoolVar b, IntConLevel icl=ICL_DEF, PropKind pk=PK_DEF)
 Post propagator for $\left(\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_r c\right)\Leftrightarrow b$.
void Gecode::linear (Space *home, const IntArgs &a, const IntVarArgs &x, IntRelType r, IntVar y, BoolVar b, IntConLevel icl=ICL_DEF, PropKind pk=PK_DEF)
 Post propagator for $\left(\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_r y\right)\Leftrightarrow b$.

Function Documentation

void Gecode::linear ( Space *  home,
const BoolVarArgs &  x,
IntRelType  r,
int  c,
IntConLevel  icl,
PropKind  pk 
)

Post propagator for $\sum_{i=0}^{|x|-1}x_i\sim_r c$.

Definition at line 45 of file linear-bool.cc.

void Gecode::linear ( Space *  home,
const BoolVarArgs &  x,
IntRelType  r,
IntVar  y,
IntConLevel  icl,
PropKind  pk 
)

Post propagator for $\sum_{i=0}^{|x|-1}x_i\sim_r y$.

Definition at line 59 of file linear-bool.cc.

void Gecode::linear ( Space *  home,
const BoolVarArgs &  x,
IntRelType  r,
int  c,
BoolVar  b,
IntConLevel  icl,
PropKind  pk 
)

Post propagator for $\left(\sum_{i=0}^{|x|-1}x_i\sim_r c\right)\Leftrightarrow b$.

Definition at line 124 of file linear-bool.cc.

void Gecode::linear ( Space *  home,
const BoolVarArgs &  x,
IntRelType  r,
IntVar  y,
BoolVar  b,
IntConLevel  icl,
PropKind  pk 
)

Post propagator for $\left(\sum_{i=0}^{|x|-1}x_i\sim_r y\right)\Leftrightarrow b$.

Definition at line 138 of file linear-bool.cc.

void Gecode::linear ( Space *  home,
const IntArgs &  a,
const IntVarArgs &  x,
IntRelType  r,
int  c,
IntConLevel  icl = ICL_DEF,
PropKind  pk = PK_DEF 
)

Post propagator for $\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_r c$.

Throws an exception of type Int::ArgumentSizeMismatch, if a and x are of different size.

Definition at line 73 of file linear-bool.cc.

void Gecode::linear ( Space *  home,
const IntArgs &  a,
const IntVarArgs &  x,
IntRelType  r,
IntVar  y,
IntConLevel  icl = ICL_DEF,
PropKind  pk = PK_DEF 
)

Post propagator for $\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_r y$.

Throws an exception of type Int::ArgumentSizeMismatch, if a and x are of different size.

Definition at line 91 of file linear-bool.cc.

void Gecode::linear ( Space *  home,
const IntArgs &  a,
const IntVarArgs &  x,
IntRelType  r,
int  c,
BoolVar  b,
IntConLevel  icl = ICL_DEF,
PropKind  pk = PK_DEF 
)

Post propagator for $\left(\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_r c\right)\Leftrightarrow b$.

Throws an exception of type Int::ArgumentSizeMismatch, if a and x are of different size.

Definition at line 152 of file linear-bool.cc.

void Gecode::linear ( Space *  home,
const IntArgs &  a,
const IntVarArgs &  x,
IntRelType  r,
IntVar  y,
BoolVar  b,
IntConLevel  icl = ICL_DEF,
PropKind  pk = PK_DEF 
)

Post propagator for $\left(\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_r y\right)\Leftrightarrow b$.

Throws an exception of type Int::ArgumentSizeMismatch, if a and x are of different size.

Definition at line 169 of file linear-bool.cc.