Linear constraints over integer variables

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

linear() [1/8]

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

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

linear() [2/8]

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

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

linear() [3/8]

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

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

linear() [4/8]

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

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

linear() [5/8]

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.

linear() [6/8]

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.

linear() [7/8]

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.

linear() [8/8]

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.