MinCostMaxFlow< Graph, CapacityMap, CostMap > Class Template Reference
[Minimum Cost Flow algorithms]

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Detailed Description

template<typename Graph, typename CapacityMap = typename Graph::template EdgeMap<int>, typename CostMap = typename Graph::template EdgeMap<int>>
class lemon::MinCostMaxFlow< Graph, CapacityMap, CostMap >

MinCostMaxFlow implements an efficient algorithm for finding a maximum flow having minimal total cost from a given source node to a given target node in a directed graph.

MinCostMaxFlow uses Preflow for finding the maximum flow value and NetworkSimplex for finding a minimum cost flow of that value. According to our benchmark tests Preflow is generally the most efficient algorithm for the maximum flow problem and NetworkSimplex is the most efficient for the minimum cost flow problem in LEMON.

Template Parameters:

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

Warning:

• Edge capacities and costs should be non-negative integers.
• CapacityMap::Value must be convertible to CostMap::Value.
• CostMap::Value must be signed type.

Author:

Peter Kovacs

#include <lemon/min_cost_max_flow.h>

List of all members.

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
	MinCostMaxFlow (const Graph &graph, const CapacityMap &capacity, const CostMap &cost, Node s, Node t)
	Constructor.
	~MinCostMaxFlow ()
	Destructor.
MinCostMaxFlow &	flowMap (FlowMap &map)
	Set the flow map.
MinCostMaxFlow &	potentialMap (PotentialMap &map)
	Set the potential map.
Execution control
void	run ()
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.

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Constructor & Destructor Documentation

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

Constructor.

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.

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Member Function Documentation

MinCostMaxFlow& flowMap

(

FlowMap &

map

)

[inline]

Set the flow map.

Returns:

(*this)

MinCostMaxFlow& potentialMap

(

PotentialMap &

map

)

[inline]

Set the potential map.

Returns:

(*this)

void run

(

)

[inline]

Run the algorithm.

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.