ResidualDigraph< DGR, CM, FM, TL > Class Template Reference

Detailed Description

template<typename DGR, typename CM, typename FM, typename TL>
class lemon::ResidualDigraph< DGR, CM, FM, TL >

ResidualDigraph can be used for composing the residual digraph for directed flow and circulation problems. Let \( G=(V, A) \) be a directed graph and let \( F \) be a number type. Let \( flow, cap: A\to F \) be functions on the arcs. This adaptor implements a digraph structure with node set \( V \) and arc set \( A_{forward}\cup A_{backward} \), where \( A_{forward}=\{uv : uv\in A, flow(uv)<cap(uv)\} \) and \( A_{backward}=\{vu : uv\in A, flow(uv)>0\} \), i.e. the so called residual digraph. When the union \( A_{forward}\cup A_{backward} \) is taken, multiplicities are counted, i.e. the adaptor has exactly \( |A_{forward}| + |A_{backward}|\) arcs (it may have parallel arcs). This class conforms to the Digraph concept.

This class provides only linear time counting for nodes and arcs.

Template Parameters

DGR	The type of the adapted digraph. It must conform to the Digraph concept. It is implicitly const.
CM	The type of the capacity map. It must be an arc map of some numerical type, which defines the capacities in the flow problem. It is implicitly const. The default type is GR::ArcMap<int>.
FM	The type of the flow map. It must be an arc map of some numerical type, which defines the flow values in the flow problem. The default type is CM.
TL	The tolerance type for handling inexact computation. The default tolerance type depends on the value type of the capacity map.

Note

This adaptor is implemented using Undirector and FilterArcs adaptors.

The Node type of this adaptor and the adapted digraph are convertible to each other, moreover the Arc type of the adaptor is convertible to the Arc type of the adapted digraph.

#include <lemon/adaptors.h>

Classes
class	ResidualCapacity
	Residual capacity map. More...

Public Types
typedef DGR	Digraph
	The type of the underlying digraph.
typedef CM	CapacityMap
	The type of the capacity map.
typedef FM	FlowMap
	The type of the flow map.
typedef TL	Tolerance
	The tolerance type.

Public Member Functions
	ResidualDigraph (const DGR &digraph, const CM &capacity, FM &flow, const TL &tolerance=Tolerance())
	Constructor.
Value	residualCapacity (const Arc &a) const
void	augment (const Arc &a, const Value &v) const
	Augments on the given arc in the residual digraph.
ResidualCapacity	residualCapacity () const
	Returns a residual capacity map.

Static Public Member Functions
static bool	forward (const Arc &a)
	Returns true if the given residual arc is a forward arc.
static bool	backward (const Arc &a)
	Returns true if the given residual arc is a backward arc.
static Arc	forward (const typename Digraph::Arc &a)
	Returns the forward oriented residual arc.
static Arc	backward (const typename Digraph::Arc &a)
	Returns the backward oriented residual arc.

Related Functions
(Note that these are not member functions.)
template<typename DGR , typename CM , typename FM >
ResidualDigraph< DGR, CM, FM >	residualDigraph (const DGR &digraph, const CM &capacity_map, FM &flow_map)
	Returns a (read-only) Residual adaptor.

Constructor & Destructor Documentation

ResidualDigraph ( const DGR &  digraph, const CM &  capacity, FM &  flow, const TL &  tolerance = Tolerance()  )

inline

Constructor of the residual digraph adaptor. The parameters are the digraph, the capacity map, the flow map, and a tolerance object.

Member Function Documentation

Value residualCapacity ( const Arc &  a ) const

inline

Returns the residual capacity of the given arc.

void augment ( const Arc &  a, const Value &  v  ) const

inline

Augments on the given arc in the residual digraph. It increases or decreases the flow value on the original arc according to the direction of the residual arc.

static bool forward ( const Arc &  a )

inlinestatic

Returns true if the given residual arc has the same orientation as the original arc, i.e. it is a so called forward arc.

static bool backward ( const Arc &  a )

inlinestatic

Returns true if the given residual arc has the opposite orientation than the original arc, i.e. it is a so called backward arc.

static Arc forward ( const typename Digraph::Arc &  a )

inlinestatic

Returns the forward oriented residual arc related to the given arc of the underlying digraph.

static Arc backward ( const typename Digraph::Arc &  a )

inlinestatic

Returns the backward oriented residual arc related to the given arc of the underlying digraph.

ResidualCapacity residualCapacity ( ) const

inline

This function just returns a residual capacity map.