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Linear constraints over integer variables
[Using integer variables and constraints]

Functions

void Gecode::linear (Home home, const IntVarArgs &x, IntRelType irt, int c, IntPropLevel ipl=IPL_DEF)
 Post propagator for $\sum_{i=0}^{|x|-1}x_i\sim_{irt} c$.
void Gecode::linear (Home home, const IntVarArgs &x, IntRelType irt, IntVar y, IntPropLevel ipl=IPL_DEF)
 Post propagator for $\sum_{i=0}^{|x|-1}x_i\sim_{irt} y$.
void Gecode::linear (Home home, const IntVarArgs &x, IntRelType irt, int c, Reify r, IntPropLevel ipl=IPL_DEF)
 Post propagator for $\left(\sum_{i=0}^{|x|-1}x_i\sim_{irt} c\right)\equiv r$.
void Gecode::linear (Home home, const IntVarArgs &x, IntRelType irt, IntVar y, Reify r, IntPropLevel ipl=IPL_DEF)
 Post propagator for $\left(\sum_{i=0}^{|x|-1}x_i\sim_{irt} y\right)\equiv r$.
void Gecode::linear (Home home, const IntArgs &a, const IntVarArgs &x, IntRelType irt, int c, IntPropLevel ipl=IPL_DEF)
 Post propagator for $\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_{irt} c$.
void Gecode::linear (Home home, const IntArgs &a, const IntVarArgs &x, IntRelType irt, IntVar y, IntPropLevel ipl=IPL_DEF)
 Post propagator for $\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_{irt} y$.
void Gecode::linear (Home home, const IntArgs &a, const IntVarArgs &x, IntRelType irt, int c, Reify r, IntPropLevel ipl=IPL_DEF)
 Post propagator for $\left(\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_{irt} c\right)\equiv r$.
void Gecode::linear (Home home, const IntArgs &a, const IntVarArgs &x, IntRelType irt, IntVar y, Reify r, IntPropLevel ipl=IPL_DEF)
 Post propagator for $\left(\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_{irt} y\right)\equiv r$.

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!
  • If the integer propagation level IPL_DEF is used as argument (hence, default propagation) and the linear constraint is sufficiently simple (two variables with unit coefficients), the domain consistent propagation is used.
  • 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 $\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_{irt} c$. 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).

Function Documentation

void Gecode::linear ( Home  home,
const IntVarArgs &  x,
IntRelType  irt,
int  c,
IntPropLevel  ipl 
)

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

void Gecode::linear ( Home  home,
const IntVarArgs &  x,
IntRelType  irt,
IntVar  y,
IntPropLevel  ipl 
)

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

void Gecode::linear ( Home  home,
const IntVarArgs &  x,
IntRelType  irt,
int  c,
Reify  r,
IntPropLevel   
)

Post propagator for $\left(\sum_{i=0}^{|x|-1}x_i\sim_{irt} c\right)\equiv r$.

void Gecode::linear ( Home  home,
const IntVarArgs &  x,
IntRelType  irt,
IntVar  y,
Reify  r,
IntPropLevel   
)

Post propagator for $\left(\sum_{i=0}^{|x|-1}x_i\sim_{irt} y\right)\equiv r$.

void Gecode::linear ( Home  home,
const IntArgs &  a,
const IntVarArgs &  x,
IntRelType  irt,
int  c,
IntPropLevel  ipl = IPL_DEF 
)

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

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

void Gecode::linear ( Home  home,
const IntArgs &  a,
const IntVarArgs &  x,
IntRelType  irt,
IntVar  y,
IntPropLevel  ipl = IPL_DEF 
)

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

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

void Gecode::linear ( Home  home,
const IntArgs &  a,
const IntVarArgs &  x,
IntRelType  irt,
int  c,
Reify  r,
IntPropLevel  ipl = IPL_DEF 
)

Post propagator for $\left(\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_{irt} c\right)\equiv r$.

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

void Gecode::linear ( Home  home,
const IntArgs &  a,
const IntVarArgs &  x,
IntRelType  irt,
IntVar  y,
Reify  r,
IntPropLevel  ipl = IPL_DEF 
)

Post propagator for $\left(\sum_{i=0}^{|x|-1}a_i\cdot x_i\sim_{irt} y\right)\equiv r$.

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