Suurballe< GR, LEN, TR > Class Template Reference

Detailed Description

template<typename GR, typename LEN, typename TR>
class lemon::Suurballe< GR, LEN, TR >

Suurballe implements an algorithm for finding arc-disjoint paths having minimum total length (cost) from a given source node to a given target node in a digraph.

Note that this problem is a special case of the minimum cost flow problem. This implementation is actually an efficient specialized version of the successive shortest path algorithm directly for this problem. Therefore this class provides query functions for flow values and node potentials (the dual solution) just like the minimum cost flow algorithms.

Template Parameters

GR	The digraph type the algorithm runs on.
LEN	The type of the length map. The default value is GR::ArcMap<int>.

Warning

Length values should be non-negative.

Note

For finding node-disjoint paths, this algorithm can be used along with the SplitNodes adaptor.

#include <lemon/suurballe.h>

Classes
struct	SetFlowMap
struct	SetHeap
	Named parameter for setting Heap and HeapCrossRef types. More...
struct	SetPath
	Named parameter for setting Path type. More...
struct	SetPotentialMap

Public Types
typedef TR::Digraph	Digraph
	The type of the digraph.
typedef TR::LengthMap	LengthMap
	The type of the length map.
typedef TR::Length	Length
	The type of the lengths.
typedef TR::FlowMap	FlowMap
	The type of the flow map.
typedef TR::PotentialMap	PotentialMap
	The type of the potential map.
typedef TR::Path	Path
	The type of the path structures.
typedef TR::HeapCrossRef	HeapCrossRef
	The cross reference type used for the heap.
typedef TR::Heap	Heap
	The heap type used for internal Dijkstra computations.
typedef TR	Traits
	The traits class of the algorithm.

Public Member Functions
	Suurballe (const Digraph &graph, const LengthMap &length)
	Constructor.
	~Suurballe ()
	Destructor.
Suurballe &	flowMap (FlowMap &map)
	Set the flow map.
Suurballe &	potentialMap (PotentialMap &map)
	Set the potential map.
Execution Control
The simplest way to execute the algorithm is to call the run() function. If you need to execute the algorithm many times using the same source node, then you may call fullInit() once and start() for each target node. If you only need the flow that is the union of the found arc-disjoint paths, then you may call findFlow() instead of start().
int	run (const Node &s, const Node &t, int k=2)
	Run the algorithm.
void	init (const Node &s)
	Initialize the algorithm.
void	fullInit (const Node &s)
	Initialize the algorithm and perform Dijkstra.
int	start (const Node &t, int k=2)
	Execute the algorithm.
int	findFlow (const Node &t, int k=2)
	Execute the algorithm to find an optimal flow.
void	findPaths ()
	Compute the paths from the flow.
Query Functions
The results of the algorithm can be obtained using these functions. The algorithm should be executed before using them.
Length	totalLength () const
	Return the total length of the found paths.
int	flow (const Arc &arc) const
	Return the flow value on the given arc.
const FlowMap &	flowMap () const
	Return a const reference to an arc map storing the found flow.
Length	potential (const Node &node) const
	Return the potential of the given node.
const PotentialMap &	potentialMap () const
	Return a const reference to a node map storing the found potentials (the dual solution).
int	pathNum () const
	Return the number of the found paths.
const Path &	path (int i) const
	Return a const reference to the specified path.

Constructor & Destructor Documentation

Suurballe ( const Digraph &  graph, const LengthMap &  length  )

inline

Constructor.

Parameters

graph	The digraph the algorithm runs on.
length	The length (cost) values of the arcs.

Member Function Documentation

Suurballe& flowMap ( FlowMap &  map )

inline

This function sets the flow map. If it is not used before calling run() or init(), an instance will be allocated automatically. The destructor deallocates this automatically allocated map, of course.

The found flow contains only 0 and 1 values, since it is the union of the found arc-disjoint paths.

Returns

(*this)

Suurballe& potentialMap ( PotentialMap &  map )

inline

This function sets the potential map. If it is not used before calling run() or init(), an instance will be allocated automatically. The destructor deallocates this automatically allocated map, of course.

The node potentials provide the dual solution of the underlying minimum cost flow problem.

Returns

(*this)

int run ( const Node &  s, const Node &  t, int  k = 2  )

inline

This function runs the algorithm.

Parameters

s	The source node.
t	The target node.
k	The number of paths to be found.

Returns

k if there are at least k arc-disjoint paths from s to t in the digraph. Otherwise it returns the number of arc-disjoint paths found.

Note

Apart from the return value, s.run(s, t, k) is just a shortcut of the following code.

s.init(s);
s.start(t, k);

void init ( const Node &  s )

inline

This function initializes the algorithm with the given source node.

Parameters

s	The source node.

void fullInit ( const Node &  s )

inline

This function initializes the algorithm and performs a full Dijkstra search from the given source node. It makes consecutive executions of start(t, k) faster, since they have to perform Dijkstra only k-1 times.

This initialization is usually worth using instead of init() if the algorithm is executed many times using the same source node.

Parameters

s	The source node.

int start ( const Node &  t, int  k = 2  )

inline

This function executes the algorithm.

Parameters

t	The target node.
k	The number of paths to be found.

Returns

k if there are at least k arc-disjoint paths from s to t in the digraph. Otherwise it returns the number of arc-disjoint paths found.

Note

Apart from the return value, s.start(t, k) is just a shortcut of the following code.

s.findFlow(t, k);
s.findPaths();

int findFlow ( const Node &  t, int  k = 2  )

inline

This function executes the successive shortest path algorithm to find a minimum cost flow, which is the union of k (or less) arc-disjoint paths.

Parameters

t	The target node.
k	The number of paths to be found.

Returns

k if there are at least k arc-disjoint paths from the source node to the given node t in the digraph. Otherwise it returns the number of arc-disjoint paths found.

Precondition

init() must be called before using this function.

void findPaths ( )

inline

This function computes arc-disjoint paths from the found minimum cost flow, which is the union of them.

Precondition

init() and findFlow() must be called before using this function.

Length totalLength ( ) const

inline

This function returns the total length of the found paths, i.e. the total cost of the found flow. The complexity of the function is O(m).

Precondition

run() or findFlow() must be called before using this function.

int flow ( const Arc &  arc ) const

inline

This function returns the flow value on the given arc. It is 1 if the arc is involved in one of the found arc-disjoint paths, otherwise it is 0.

Precondition

run() or findFlow() must be called before using this function.

const FlowMap& flowMap ( ) const

inline

This function returns a const reference to an arc map storing the flow that is the union of the found arc-disjoint paths.

Precondition

run() or findFlow() must be called before using this function.

Length potential ( const Node &  node ) const

inline

This function returns the potential of the given node. The node potentials provide the dual solution of the underlying minimum cost flow problem.

Precondition

run() or findFlow() must be called before using this function.

const PotentialMap& potentialMap ( ) const

inline

This function returns a const reference to a node map storing the found potentials that provide the dual solution of the underlying minimum cost flow problem.

Precondition

run() or findFlow() must be called before using this function.

int pathNum ( ) const

inline

This function returns the number of the found paths.

Precondition

run() or findFlow() must be called before using this function.

const Path& path ( int  i ) const

inline

This function returns a const reference to the specified path.

Parameters

i	The function returns the i-th path. i must be between 0 and pathNum()-1.

Precondition

run() or findPaths() must be called before using this function.