CapacityScaling< Graph, LowerMap, CapacityMap, CostMap, SupplyMap > Class Template Reference
[Minimum Cost Flow algorithms]

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Detailed Description

template<typename Graph, typename LowerMap = typename Graph::template EdgeMap<int>, typename CapacityMap = typename Graph::template EdgeMap<int>, typename CostMap = typename Graph::template EdgeMap<int>, typename SupplyMap = typename Graph::template NodeMap<int>>
class lemon::CapacityScaling< Graph, LowerMap, CapacityMap, CostMap, SupplyMap >

CapacityScaling implements the capacity scaling version of the successive shortest path algorithm for finding a minimum cost flow.

Template Parameters:

	Graph	The directed graph type the algorithm runs on.
	LowerMap	The type of the lower bound map.
	CapacityMap	The type of the capacity (upper bound) map.
	CostMap	The type of the cost (length) map.
	SupplyMap	The type of the supply map.

Warning:

• Edge capacities and costs should be non-negative integers.
• Supply values should be signed integers.
• The value types of the maps should be convertible to each other.
• CostMap::Value must be signed type.

Author:

Peter Kovacs

#include <lemon/capacity_scaling.h>

List of all members.

Classes
class	ResidualDijkstra
	Special implementation of the Dijkstra algorithm for finding shortest paths in the residual network. More...
Public Types
typedef Graph::template EdgeMap< Capacity >	FlowMap
	The type of the flow map.
typedef Graph::template NodeMap< Cost >	PotentialMap
	The type of the potential map.
Public Member Functions
	CapacityScaling (const Graph &graph, const LowerMap &lower, const CapacityMap &capacity, const CostMap &cost, const SupplyMap &supply)
	General constructor (with lower bounds).
	CapacityScaling (const Graph &graph, const CapacityMap &capacity, const CostMap &cost, const SupplyMap &supply)
	General constructor (without lower bounds).
	CapacityScaling (const Graph &graph, const LowerMap &lower, const CapacityMap &capacity, const CostMap &cost, Node s, Node t, Supply flow_value)
	Simple constructor (with lower bounds).
	CapacityScaling (const Graph &graph, const CapacityMap &capacity, const CostMap &cost, Node s, Node t, Supply flow_value)
	Simple constructor (without lower bounds).
	~CapacityScaling ()
	Destructor.
CapacityScaling &	flowMap (FlowMap &map)
	Set the flow map.
CapacityScaling &	potentialMap (PotentialMap &map)
	Set the potential map.
Execution control
bool	run (bool scaling=true)
	Run the algorithm.
Query Functions
The results of the algorithm can be obtained using these functions. run() must be called before using them.
const FlowMap &	flowMap () const
	Return a const reference to the edge map storing the found flow.
const PotentialMap &	potentialMap () const
	Return a const reference to the node map storing the found potentials (the dual solution).
Capacity	flow (const Edge &edge) const
	Return the flow on the given edge.
Cost	potential (const Node &node) const
	Return the potential of the given node.
Cost	totalCost () const
	Return the total cost of the found flow.
Private Member Functions
bool	init (bool scaling)
	Initialize the algorithm.
bool	startWithScaling ()
	Execute the capacity scaling algorithm.
bool	startWithoutScaling ()
	Execute the successive shortest path algorithm.

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Constructor & Destructor Documentation

CapacityScaling	(	const Graph &	graph,
		const LowerMap &	lower,
		const CapacityMap &	capacity,
		const CostMap &	cost,
		const SupplyMap &	supply
	)			[inline]

General constructor (with lower bounds).

Parameters:

	graph	The directed graph the algorithm runs on.
	lower	The lower bounds of the edges.
	capacity	The capacities (upper bounds) of the edges.
	cost	The cost (length) values of the edges.
	supply	The supply values of the nodes (signed).

CapacityScaling	(	const Graph &	graph,
		const CapacityMap &	capacity,
		const CostMap &	cost,
		const SupplyMap &	supply
	)			[inline]

General constructor (without lower bounds).

Parameters:

	graph	The directed graph the algorithm runs on.
	capacity	The capacities (upper bounds) of the edges.
	cost	The cost (length) values of the edges.
	supply	The supply values of the nodes (signed).

CapacityScaling	(	const Graph &	graph,
		const LowerMap &	lower,
		const CapacityMap &	capacity,
		const CostMap &	cost,
		Node	s,
		Node	t,
		Supply	flow_value
	)			[inline]

Simple constructor (with lower bounds).

Parameters:

	graph	The directed graph the algorithm runs on.
	lower	The lower bounds of the edges.
	capacity	The capacities (upper bounds) of the edges.
	cost	The cost (length) values of the edges.
	s	The source node.
	t	The target node.
	flow_value	The required amount of flow from node s to node t (i.e. the supply of s and the demand of t).

CapacityScaling	(	const Graph &	graph,
		const CapacityMap &	capacity,
		const CostMap &	cost,
		Node	s,
		Node	t,
		Supply	flow_value
	)			[inline]

Simple constructor (without lower bounds).

Parameters:

	graph	The directed graph the algorithm runs on.
	capacity	The capacities (upper bounds) of the edges.
	cost	The cost (length) values of the edges.
	s	The source node.
	t	The target node.
	flow_value	The required amount of flow from node s to node t (i.e. the supply of s and the demand of t).

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Member Function Documentation

CapacityScaling& flowMap

(

FlowMap &

map

)

[inline]

Set the flow map.

Returns:

(*this)

CapacityScaling& potentialMap

(

PotentialMap &

map

)

[inline]

Set the potential map.

Returns:

(*this)

bool run

(

bool

scaling = true

)

[inline]

This function runs the algorithm.

Parameters:

scaling

Enable or disable capacity scaling. If the maximum edge capacity and/or the amount of total supply is rather small, the algorithm could be slightly faster without scaling.

Returns:

true if a feasible flow can be found.

const FlowMap& flowMap

(

)

const [inline]

Return a const reference to the edge map storing the found flow.

Precondition:

run() must be called before using this function.

const PotentialMap& potentialMap

(

)

const [inline]

Return a const reference to the node map storing the found potentials (the dual solution).

Precondition:

run() must be called before using this function.

Capacity flow

(

const Edge &

edge

)

const [inline]

Return the flow on the given edge.

Precondition:

run() must be called before using this function.

Cost potential

(

const Node &

node

)

const [inline]

Return the potential of the given node.

Precondition:

run() must be called before using this function.

Cost totalCost

(

)

const [inline]

Return the total cost of the found flow. The complexity of the function is .

Precondition:

run() must be called before using this function.