# OpenGraph DrawingFramework

v. 2022.02 (Dogwood)

abacus::Constraint Class Referenceabstract

Forms the virtual base class for all possible constraints given in pool format. More...

#include <ogdf/lib/abacus/constraint.h>

Inheritance diagram for abacus::Constraint:

## Public Member Functions

Constraint (const Constraint &rhs)
Copy constructor. More...

Constraint (Master *master)
Initializes an empty constraint. More...

Constraint (Master *master, const Sub *sub, CSense::SENSE sense, double rhs, bool dynamic, bool local, bool liftable)
Initializes a constraint. More...

virtual ~Constraint ()

ConClassclassification (Active< Variable, Constraint > *var=nullptr) const
Returns a pointer to the classification of the constraint. More...

virtual double coeff (const Variable *v) const =0
Returns the coefficient of the variable v in the constraint. More...

virtual double distance (double *x, Active< Variable, Constraint > *actVar) const
Returns the Euclidean distance of x associated with variable set actVar to the hyperplane induced by the constraint. More...

virtual int genRow (Active< Variable, Constraint > *var, Row &row) const
Generates the row format of the constraint associated with the variable set var. More...

bool liftable () const
Checks if the constraint is liftable. More...

void printRow (std::ostream &out, Active< Variable, Constraint > *var) const
Writes the row format of the constraint associated with the variable set var to output stream out. More...

virtual double rhs () const
Returns the right hand side of the constraint. More...

CSensesense ()
Returns a pointer to the sense of the constraint. More...

const CSensesense () const
Returns a const pointer to the sense of the constraint. More...

virtual double slack (Active< Variable, Constraint > *variables, double *x) const
Computes the slack of the vector x associated with the variable set variables. More...

virtual bool valid (Sub *sub) const
Checks if the constraint is valid for the subproblem sub. More...

virtual bool violated (Active< Variable, Constraint > *variables, double *x, double *sl=nullptr) const
Checks if a constraint is violated by a vector x associated with a variable set. More...

virtual bool violated (double slack) const
Checks if a constraint is violated given the slack of a vector. More...

Public Member Functions inherited from abacus::ConVar
ConVar (Master *master, const Sub *sub, bool dynamic, bool local)
Creates an instance of type ConVar. More...

virtual ~ConVar ()

bool active () const
Checks if the constraint/variable is active in at least one active subproblem. More...

virtual bool dynamic () const
Return true if the constraint/variable is dynamic. More...

bool global () const
Returns true if the constraint/variable is globally valid, false otherwise. More...

bool local () const
Returns true if the constraint/variable is only locally valid, false otherwise. More...

bool expanded () const
Returns true if the expanded format of a constraint/variable is available, false otherwise. More...

virtual void expand () const
Expands a constraint/variable. More...

virtual void compress () const
Compresses a constraint/variable. More...

virtual bool deletable () const
Returns true if the constraint/variable can be destructed. More...

virtual void print (std::ostream &out) const
Writes the constraint/variable to the output stream out. More...

const Subsub () const
Returns a const pointer to the subproblem associated with the constraint/variable. More...

void sub (Sub *sub)
Associates a new subproblem with the constraint/variable. More...

virtual unsigned hashKey () const
Should provide a key for the constraint/variable that can be used to insert it into a hash table. More...

virtual const char * name () const
Should return the name of the constraint/variable. More...

virtual bool equal (const ConVar *cv) const
Should compare if the constraint/variable is identical (in a mathematical sense) with the constraint/variable cv. More...

virtual double rank () const
The function should return a rank associated with the constraint/variable. More...

Public Member Functions inherited from abacus::AbacusRoot
virtual ~AbacusRoot ()
The destructor. More...

## Protected Member Functions

virtual ConClassclassify (Active< Variable, Constraint > *var) const
The default implementation returns a 0 pointer. More...

virtual InfeasCon::INFEAS voidLhsViolated (double newRhs) const
Can be called if after variable elimination the left hand side of the constraint has become void and the right hand side has been adapted to newRhs. More...

## Protected Attributes

ConClassconClass_

bool liftable_
This member is true if also coefficients of variables which have been inactive at generation time can be computed, false otherwise. More...

double rhs_
The right hand side of the constraint. More...

CSense sense_
The sense of the constraint. More...

Protected Attributes inherited from abacus::ConVar
Mastermaster_
A pointer to the corresponding master of the optimization. More...

const Subsub_
A pointer to the subproblem associated with the constraint/variable. More...

bool expanded_
true, if expanded version of constraint/variables available. More...

int nReferences_
The number of references to the pool slot the constraint is stored in. More...

bool dynamic_
If this member is true then the constraint/variable can be also removed from the active formulation after it is added the first time. More...

int nActive_
The number of active subproblems of which the constraint/variable belongs to the set of active constraints/variables. More...

int nLocks_
The number of locks which have been set on the constraint/variable. More...

bool local_
true if the constraint/variable is only locally valid More...

## Private Member Functions

const Constraintoperator= (const Constraint &rhs)

## Friends

class LpSub

Static Public Member Functions inherited from abacus::AbacusRoot
static bool ascii2bool (const string &str)
Converts the string str to a boolean value. More...

static bool endsWith (const string &str, const string &end)
Returns true if str ends with end, false otherwise. More...

static double fracPart (double x)
Returns the absolute value of the fractional part of x. More...

static const char * onOff (bool value)
Converts a boolean variable to the strings "on" and "off". More...

## Detailed Description

Forms the virtual base class for all possible constraints given in pool format.

Constraints are one of the central items in a linear-programming based branch-and-bound algorithm. This class forms the virtual base class for all possible constraints given in pool format and is derived from the common base class ConVar of all constraints and variables.

Definition at line 56 of file constraint.h.

## ◆ Constraint() [1/3]

 abacus::Constraint::Constraint ( Master * master, const Sub * sub, CSense::SENSE sense, double rhs, bool dynamic, bool local, bool liftable )
inline

Initializes a constraint.

Parameters
 master A pointer to the corresponding master of the optimization. sub A pointer to the subproblem associated with the constraint. This can be also a 0-pointer. sense The sense of the constraint. rhs The right hand side of the constraint. dynamic If this parameter is true, then the constraint can be removed from the active constraint set during the cutting plane phase of the subproblem optimization. local If this parameter is true, then the constraint is considered to be only locally valid. In this case the paramument sub must not be 0 as each locally valid constraint is associated with a subproblem. liftable If this parameter is true, then a lifting procedure must be available, i.e., that the coefficients of variables which have not been active at generation time of the constraint can be computed.

Definition at line 288 of file constraint.h.

## ◆ Constraint() [2/3]

 abacus::Constraint::Constraint ( Master * master )
inline

Initializes an empty constraint.

This constructor is, e.g., useful if parallel separation is applied. In this case the constraint can be constructed and receive later its data by message passing.

Parameters
 master A pointer to the corresponding master of the optimization.

Definition at line 305 of file constraint.h.

## ◆ Constraint() [3/3]

 abacus::Constraint::Constraint ( const Constraint & rhs )
inline

Copy constructor.

Parameters
 rhs The constraint being copied.

Definition at line 104 of file constraint.h.

## ◆ ~Constraint()

 virtual abacus::Constraint::~Constraint ( )
inlinevirtual

Definition at line 111 of file constraint.h.

## ◆ classification()

 ConClass* abacus::Constraint::classification ( Active< Variable, Constraint > * var = nullptr ) const

Returns a pointer to the classification of the constraint.

If no classification is available then we try to classify the constraint. In this case var must not be a 0-pointer.

A constraint classification can only be generated if the function classify() is redefined in a derived class.

## ◆ classify()

 virtual ConClass* abacus::Constraint::classify ( Active< Variable, Constraint > * var ) const
inlineprotectedvirtual

The default implementation returns a 0 pointer.

Definition at line 260 of file constraint.h.

## ◆ coeff()

 virtual double abacus::Constraint::coeff ( const Variable * v ) const
pure virtual

Returns the coefficient of the variable v in the constraint.

Parameters
 v A pointer to a variable.
Returns
The coefficient of the variable v in the constraint.

## ◆ distance()

 virtual double abacus::Constraint::distance ( double * x, Active< Variable, Constraint > * actVar ) const
virtual

Returns the Euclidean distance of x associated with variable set actVar to the hyperplane induced by the constraint.

The distance of a point $$\overline{x}$$ and a hyperplane $$a^T x = \beta$$ can be computed in the following way: Let $$y$$ be the intersection of the hyperplane $$a^T x = \beta$$ and the line defined by $$\overline{x}$$ and the vector $$a$$. Then the distance $$d$$ is the length of the vector $$||\overline{x} - y||$$.

Parameters
 x The point for which the distance should be computed. actVar The variables associated with x.
Returns
The Euclidean distance of the vector x associated with the variable set actVar to the hyperplane induced by the constraint.

## ◆ genRow()

 virtual int abacus::Constraint::genRow ( Active< Variable, Constraint > * var, Row & row ) const
virtual

Generates the row format of the constraint associated with the variable set var.

This function is declared virtual since faster constraint specific implementations might be desirable.

All nonzero coefficients are added to the row format. Before we generate the coefficients we try to expand the constraint, afterwards it is compressed again.

Parameters
 var The variable set for which the row format should be computed. row Stores the row format after calling this function.
Returns
The number of nonzero elements in the row format row.

Reimplemented in abacus::SRowCon.

## ◆ liftable()

 bool abacus::Constraint::liftable ( ) const
inline

Checks if the constraint is liftable.

I.e., if the coefficients of variables inactive at generation time of the constraint can be computed later.

Returns
true If the constraint can be lifted, false otherwise.

Definition at line 140 of file constraint.h.

## ◆ operator=()

 const Constraint& abacus::Constraint::operator= ( const Constraint & rhs )
private

## ◆ printRow()

 void abacus::Constraint::printRow ( std::ostream & out, Active< Variable, Constraint > * var ) const

Writes the row format of the constraint associated with the variable set var to output stream out.

Parameters
 out The output stream. var The variables for which the row format should be written.

## ◆ rhs()

 virtual double abacus::Constraint::rhs ( ) const
inlinevirtual

Returns the right hand side of the constraint.

Definition at line 130 of file constraint.h.

## ◆ sense() [1/2]

 CSense* abacus::Constraint::sense ( )
inline

Returns a pointer to the sense of the constraint.

Definition at line 115 of file constraint.h.

## ◆ sense() [2/2]

 const CSense* abacus::Constraint::sense ( ) const
inline

Returns a const pointer to the sense of the constraint.

Definition at line 118 of file constraint.h.

## ◆ slack()

 virtual double abacus::Constraint::slack ( Active< Variable, Constraint > * variables, double * x ) const
virtual

Computes the slack of the vector x associated with the variable set variables.

Parameters
 variables The variable set associated with the vector x. x The values of the variables.
Returns
The slack induced by the vector x.

Reimplemented in abacus::SRowCon.

## ◆ valid()

 bool abacus::Constraint::valid ( Sub * sub ) const
inlinevirtual

Checks if the constraint is valid for the subproblem sub.

Per default, this is the case if the constraint is globally valid, or the subproblem associated with the constraint is an ancestor of the subproblem sub in the enumeration tree.

Parameters
 sub The subproblem for which the validity is checked.
Returns
true If the constraint is valid for the subproblem sub, false otherwise.

Definition at line 309 of file constraint.h.

## ◆ violated() [1/2]

 virtual bool abacus::Constraint::violated ( Active< Variable, Constraint > * variables, double * x, double * sl = nullptr ) const
virtual

Checks if a constraint is violated by a vector x associated with a variable set.

Parameters
 variables The variables associated with the vector x. x The vector for which the violation is checked. sl If sl is nonzero, then *sl will store the value of the violation, i.e., the slack.
Returns
true If the constraint is violated, false otherwise.

## ◆ violated() [2/2]

 virtual bool abacus::Constraint::violated ( double slack ) const
virtual

Checks if a constraint is violated given the slack of a vector.

Parameters
 slack The slack of a vector.
Returns
true if the constraint is an equation and the slack is nonzero.
true if the constraint is a $$\le$$-inequality and the slack is negative.
true if the constraint is a $$\ge$$-inequality and the slack is positive.
false otherwise.

## ◆ voidLhsViolated()

 virtual InfeasCon::INFEAS abacus::Constraint::voidLhsViolated ( double newRhs ) const
protectedvirtual

Can be called if after variable elimination the left hand side of the constraint has become void and the right hand side has been adapted to newRhs.

Then this function checks if the constraint is violated.

Parameters
 newRhs The right hand side of the constraint after the elimination of the variables.
Returns
TooLarge or TooSmall if the newRhs violates the sense of the constraint, i.e, it is < / > / != 0 and the sense of the constraint is >= / <= / =,
Feasible otherwise.

## ◆ LpSub

 friend class LpSub
friend

Definition at line 58 of file constraint.h.

## ◆ conClass_

 ConClass* abacus::Constraint::conClass_
mutableprotected

Definition at line 269 of file constraint.h.

## ◆ liftable_

 bool abacus::Constraint::liftable_
protected

This member is true if also coefficients of variables which have been inactive at generation time can be computed, false otherwise.

Definition at line 275 of file constraint.h.

## ◆ rhs_

 double abacus::Constraint::rhs_
protected

The right hand side of the constraint.

Definition at line 267 of file constraint.h.

## ◆ sense_

 CSense abacus::Constraint::sense_
protected

The sense of the constraint.

Definition at line 265 of file constraint.h.

The documentation for this class was generated from the following file: