NetworkSimplex< 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::NetworkSimplex< Graph, LowerMap, CapacityMap, CostMap, SupplyMap >

NetworkSimplex implements the primal network simplex 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.

Note:

NetworkSimplex provides five different pivot rule implementations that significantly affect the efficiency of the algorithm. By default "Block Search" pivot rule is used, which proved to be by far the most efficient according to our benchmark tests. However another pivot rule can be selected using run() function with the proper parameter.

Author:

Peter Kovacs

#include <lemon/network_simplex.h>

Inheritance diagram for NetworkSimplex< Graph, LowerMap, CapacityMap, CostMap, SupplyMap >:

[legend]

List of all members.

Classes
class	AlteringListPivotRule
	Implementation of the "Altering Candidate List" pivot rule for the network simplex algorithm. More...
class	BestEligiblePivotRule
	Implementation of the "Best Eligible" pivot rule for the network simplex algorithm. More...
class	BlockSearchPivotRule
	Implementation of the "Block Search" pivot rule for the network simplex algorithm. More...
class	CandidateListPivotRule
	Implementation of the "Candidate List" pivot rule for the network simplex algorithm. More...
class	FirstEligiblePivotRule
	Implementation of the "First Eligible" pivot rule for the network simplex algorithm. More...
Public Types
enum	PivotRuleEnum
	Enum type to select the pivot rule used by run().
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
	NetworkSimplex (const Graph &graph, const LowerMap &lower, const CapacityMap &capacity, const CostMap &cost, const SupplyMap &supply)
	General constructor (with lower bounds).
	NetworkSimplex (const Graph &graph, const CapacityMap &capacity, const CostMap &cost, const SupplyMap &supply)
	General constructor (without lower bounds).
	NetworkSimplex (const Graph &graph, const LowerMap &lower, const CapacityMap &capacity, const CostMap &cost, Node s, Node t, Capacity flow_value)
	Simple constructor (with lower bounds).
	NetworkSimplex (const Graph &graph, const CapacityMap &capacity, const CostMap &cost, Node s, Node t, Capacity flow_value)
	Simple constructor (without lower bounds).
	~NetworkSimplex ()
	Destructor.
NetworkSimplex &	flowMap (FlowMap &map)
	Set the flow map.
NetworkSimplex &	potentialMap (PotentialMap &map)
	Set the potential map.
Execution control
bool	run (PivotRuleEnum pivot_rule=BLOCK_SEARCH_PIVOT)
	Runs 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 typename Graph::Edge &edge) const
	Return the flow on the given edge.
Cost	potential (const typename Graph::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

NetworkSimplex	(	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).

NetworkSimplex	(	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).

NetworkSimplex	(	const Graph &	graph,
		const LowerMap &	lower,
		const CapacityMap &	capacity,
		const CostMap &	cost,
		Node	s,
		Node	t,
		Capacity	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).

NetworkSimplex	(	const Graph &	graph,
		const CapacityMap &	capacity,
		const CostMap &	cost,
		Node	s,
		Node	t,
		Capacity	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

NetworkSimplex& flowMap

(

FlowMap &

map

)

[inline]

Set the flow map.

Returns:

(*this)

NetworkSimplex& potentialMap

(

PotentialMap &

map

)

[inline]

Set the potential map.

Returns:

(*this)

bool run

(

PivotRuleEnum

pivot_rule = BLOCK_SEARCH_PIVOT

)

[inline]

Runs the algorithm.

Parameters:

pivot_rule

The pivot rule that is used during the algorithm.

The available pivot rules:

• FIRST_ELIGIBLE_PIVOT The next eligible edge is selected in a wraparound fashion in every iteration (FirstEligiblePivotRule).

• BEST_ELIGIBLE_PIVOT The best eligible edge is selected in every iteration (BestEligiblePivotRule).

• BLOCK_SEARCH_PIVOT A specified number of edges are examined in every iteration in a wraparound fashion and the best eligible edge is selected from this block (BlockSearchPivotRule).

• CANDIDATE_LIST_PIVOT In a major iteration a candidate list is built from eligible edges in a wraparound fashion and in the following minor iterations the best eligible edge is selected from this list (CandidateListPivotRule).

• ALTERING_LIST_PIVOT It is a modified version of the "Candidate List" pivot rule. It keeps only the several best eligible edges from the former candidate list and extends this list in every iteration (AlteringListPivotRule).

According to our comprehensive benchmark tests the "Block Search" pivot rule proved to be the fastest and the most robust on various test inputs. Thus it is the default option.

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 typename Graph::Edge &

edge

)

const [inline]

Return the flow on the given edge.

Precondition:

run() must be called before using this function.

Cost potential

(

const typename Graph::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.