Detailed Description

template<typename Graph>
class operations_research::GenericMaxFlow< Graph >

Forward declaration.

Generic MaxFlow (there is a default MaxFlow specialization defined below) that works with StarGraph and all the reverse arc graphs from graph.h, see the end of max_flow.cc for the exact types this class is compiled for.

Definition at line 144 of file max_flow.h.

Public Types
typedef Graph::NodeIndex	NodeIndex

typedef Graph::ArcIndex	ArcIndex

typedef Graph::OutgoingArcIterator	OutgoingArcIterator

typedef Graph::OutgoingOrOppositeIncomingArcIterator	OutgoingOrOppositeIncomingArcIterator

typedef Graph::IncomingArcIterator	IncomingArcIterator

typedef ZVector< ArcIndex >	ArcIndexArray

typedef NodeIndex	NodeHeight
	The height of a node never excess 2 times the number of node, so we use the same type as a Node index. More...

typedef ZVector< NodeHeight >	NodeHeightArray

enum	Status { NOT_SOLVED, OPTIMAL, INT_OVERFLOW, BAD_INPUT, BAD_RESULT }

Public Member Functions
	GenericMaxFlow (const Graph *graph, NodeIndex source, NodeIndex sink)
	Initialize a MaxFlow instance on the given graph. More...

virtual	~GenericMaxFlow ()

const Graph *	graph () const
	Returns the graph associated to the current object. More...

Status	status () const
	Returns the status of last call to Solve(). More...

NodeIndex	GetSourceNodeIndex () const
	Returns the index of the node corresponding to the source of the network. More...

NodeIndex	GetSinkNodeIndex () const
	Returns the index of the node corresponding to the sink of the network. More...

void	SetArcCapacity (ArcIndex arc, FlowQuantity new_capacity)
	Sets the capacity for arc to new_capacity. More...

void	SetArcFlow (ArcIndex arc, FlowQuantity new_flow)
	Sets the flow for arc. More...

bool	Solve ()
	Returns true if a maximum flow was solved. More...

FlowQuantity	GetOptimalFlow () const
	Returns the total flow found by the algorithm. More...

FlowQuantity	Flow (ArcIndex arc) const
	Returns the flow on arc using the equations given in the comment on residual_arc_capacity_. More...

FlowQuantity	Capacity (ArcIndex arc) const
	Returns the capacity of arc using the equations given in the comment on residual_arc_capacity_. More...

void	GetSourceSideMinCut (std::vector< NodeIndex > *result)
	Returns the nodes reachable from the source in the residual graph, the outgoing arcs of this set form a minimum cut. More...

void	GetSinkSideMinCut (std::vector< NodeIndex > *result)
	Returns the nodes that can reach the sink in the residual graph, the outgoing arcs of this set form a minimum cut. More...

bool	CheckInputConsistency () const
	Checks the consistency of the input, i.e. More...

bool	CheckResult () const
	Checks whether the result is valid, i.e. More...

bool	AugmentingPathExists () const
	Returns true if there exists a path from the source to the sink with remaining capacity. More...

void	SetUseGlobalUpdate (bool value)
	Sets the different algorithm options. More...

void	SetUseTwoPhaseAlgorithm (bool value)

void	SetCheckInput (bool value)

void	SetCheckResult (bool value)

void	ProcessNodeByHeight (bool value)

FlowModel	CreateFlowModel ()
	Returns the protocol buffer representation of the current problem. More...

Protected Member Functions
bool	IsAdmissible (ArcIndex arc) const
	Returns true if arc is admissible. More...

bool	IsActive (NodeIndex node) const
	Returns true if node is active, i.e. More...

void	SetCapacityAndClearFlow (ArcIndex arc, FlowQuantity capacity)
	Sets the capacity of arc to 'capacity' and clears the flow on arc. More...

bool	CheckRelabelPrecondition (NodeIndex node) const
	Returns true if a precondition for Relabel is met, i.e. More...

std::string	DebugString (const std::string &context, ArcIndex arc) const
	Returns context concatenated with information about arc in a human-friendly way. More...

void	InitializeActiveNodeContainer ()
	Initializes the container active_nodes_. More...

NodeIndex	GetAndRemoveFirstActiveNode ()
	Get the first element from the active node container. More...

void	PushActiveNode (const NodeIndex &node)
	Push element to the active node container. More...

bool	IsEmptyActiveNodeContainer ()
	Check the emptiness of the container. More...

void	Refine ()
	Performs optimization step. More...

void	RefineWithGlobalUpdate ()

void	Discharge (NodeIndex node)
	Discharges an active node node by saturating its admissible adjacent arcs, if any, and by relabelling it when it becomes inactive. More...

void	InitializePreflow ()
	Initializes the preflow to a state that enables to run Refine. More...

void	PushFlowExcessBackToSource ()
	Clears the flow excess at each node by pushing the flow back to the source: More...

void	GlobalUpdate ()
	Computes the best possible node potential given the current flow using a reverse breadth-first search from the sink in the reverse residual graph. More...

bool	SaturateOutgoingArcsFromSource ()
	Tries to saturate all the outgoing arcs from the source that can reach the sink. More...

void	PushFlow (FlowQuantity flow, ArcIndex arc)
	Pushes flow on arc, i.e. More...

void	Relabel (NodeIndex node)
	Relabels a node, i.e. More...

NodeIndex	Head (ArcIndex arc) const
	Handy member functions to make the code more compact. More...

NodeIndex	Tail (ArcIndex arc) const

ArcIndex	Opposite (ArcIndex arc) const

bool	IsArcDirect (ArcIndex arc) const

bool	IsArcValid (ArcIndex arc) const

template<bool reverse>
void	ComputeReachableNodes (NodeIndex start, std::vector< NodeIndex > *result)
	Returns the set of nodes reachable from start in the residual graph or in the reverse residual graph (if reverse is true). More...

Protected Attributes
const Graph *	graph_
	A pointer to the graph passed as argument. More...

QuantityArray	node_excess_
	An array representing the excess for each node in graph_. More...

NodeHeightArray	node_potential_
	An array representing the height function for each node in graph_. More...

QuantityArray	residual_arc_capacity_
	An array representing the residual_capacity for each arc in graph_. More...

ArcIndexArray	first_admissible_arc_
	An array representing the first admissible arc for each node in graph_. More...

std::vector< NodeIndex >	active_nodes_
	A stack used for managing active nodes in the algorithm. More...

PriorityQueueWithRestrictedPush< NodeIndex, NodeHeight >	active_node_by_height_
	A priority queue used for managing active nodes in the algorithm. More...

NodeIndex	source_
	The index of the source node in graph_. More...

NodeIndex	sink_
	The index of the sink node in graph_. More...

Status	status_
	The status of the problem. More...

std::vector< bool >	node_in_bfs_queue_
	BFS queue used by the GlobalUpdate() function. More...

std::vector< NodeIndex >	bfs_queue_

bool	use_global_update_
	Whether or not to use GlobalUpdate(). More...

bool	use_two_phase_algorithm_
	Whether or not we use a two-phase algorithm: 1/ Only deal with nodes that can reach the sink. More...

bool	process_node_by_height_
	Whether or not we use the PriorityQueueWithRestrictedPush to process the active nodes rather than a simple queue. More...

bool	check_input_
	Whether or not we check the input, this is a small price to pay for robustness. More...

bool	check_result_
	Whether or not we check the result. More...

StatsGroup	stats_
	Statistics about this class. More...

Static Protected Attributes
static const FlowQuantity	kMaxFlowQuantity
	Maximum manageable flow. More...

Member Typedef Documentation

◆ ArcIndex

template<typename Graph>

typedef Graph::ArcIndex operations_research::GenericMaxFlow< Graph >::ArcIndex

Definition at line 318 of file max_flow.h.

◆ ArcIndexArray

template<typename Graph>

typedef ZVector<ArcIndex> operations_research::GenericMaxFlow< Graph >::ArcIndexArray

Definition at line 323 of file max_flow.h.

◆ IncomingArcIterator

template<typename Graph>

typedef Graph::IncomingArcIterator operations_research::GenericMaxFlow< Graph >::IncomingArcIterator

Definition at line 322 of file max_flow.h.

◆ NodeHeight

template<typename Graph>

typedef NodeIndex operations_research::GenericMaxFlow< Graph >::NodeHeight

The height of a node never excess 2 times the number of node, so we use the same type as a Node index.

Definition at line 327 of file max_flow.h.

◆ NodeHeightArray

template<typename Graph>

typedef ZVector<NodeHeight> operations_research::GenericMaxFlow< Graph >::NodeHeightArray

Definition at line 328 of file max_flow.h.

◆ NodeIndex

template<typename Graph>

typedef Graph::NodeIndex operations_research::GenericMaxFlow< Graph >::NodeIndex

Definition at line 317 of file max_flow.h.

◆ OutgoingArcIterator

template<typename Graph>

typedef Graph::OutgoingArcIterator operations_research::GenericMaxFlow< Graph >::OutgoingArcIterator

Definition at line 319 of file max_flow.h.

◆ OutgoingOrOppositeIncomingArcIterator

template<typename Graph>

typedef Graph::OutgoingOrOppositeIncomingArcIterator operations_research::GenericMaxFlow< Graph >::OutgoingOrOppositeIncomingArcIterator

Definition at line 321 of file max_flow.h.

Member Enumeration Documentation

◆ Status

enum operations_research::MaxFlowStatusClass::Status

inherited

Enumerator
NOT_SOLVED
OPTIMAL
INT_OVERFLOW
BAD_INPUT
BAD_RESULT

Definition at line 302 of file max_flow.h.

Constructor & Destructor Documentation

◆ GenericMaxFlow()

template<typename Graph>

operations_research::GenericMaxFlow< Graph >::GenericMaxFlow	(	const Graph *	graph,
		NodeIndex	source,
		NodeIndex	sink
	)

Initialize a MaxFlow instance on the given graph.

The graph does not need to be fully built yet, but its capacity reservation are used to initialize the memory of this class. source and sink must also be valid node of graph.

◆ ~GenericMaxFlow()

template<typename Graph>

virtual operations_research::GenericMaxFlow< Graph >::~GenericMaxFlow ( )

inlinevirtual

Definition at line 335 of file max_flow.h.

Member Function Documentation

◆ AugmentingPathExists()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::AugmentingPathExists ( ) const

Returns true if there exists a path from the source to the sink with remaining capacity.

This allows us to easily check at the end that the flow we computed is indeed optimal (provided that all the conditions tested by CheckResult() also hold).

◆ Capacity()

template<typename Graph>

FlowQuantity operations_research::GenericMaxFlow< Graph >::Capacity ( ArcIndex arc ) const

inline

Returns the capacity of arc using the equations given in the comment on residual_arc_capacity_.

Definition at line 375 of file max_flow.h.

◆ CheckInputConsistency()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::CheckInputConsistency ( ) const

Checks the consistency of the input, i.e.

that capacities on the arcs are non-negative or null.

◆ CheckRelabelPrecondition()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::CheckRelabelPrecondition ( NodeIndex node ) const

protected

Returns true if a precondition for Relabel is met, i.e.

the outgoing arcs of node are all either saturated or the heights of their heads are greater or equal to the height of node.

◆ CheckResult()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::CheckResult ( ) const

Checks whether the result is valid, i.e.

that node excesses are all equal to zero (we have a flow) and that residual capacities are all non-negative or zero.

◆ ComputeReachableNodes()

template<typename Graph>

template<bool reverse>

void operations_research::GenericMaxFlow< Graph >::ComputeReachableNodes	(	NodeIndex	start,
		std::vector< NodeIndex > *	result
	)

protected

Returns the set of nodes reachable from start in the residual graph or in the reverse residual graph (if reverse is true).

◆ CreateFlowModel()

template<typename Graph>

FlowModel operations_research::GenericMaxFlow< Graph >::CreateFlowModel ( )

Returns the protocol buffer representation of the current problem.

◆ DebugString()

template<typename Graph>

std::string operations_research::GenericMaxFlow< Graph >::DebugString	(	const std::string &	context,
		ArcIndex	arc
	)		const

protected

Returns context concatenated with information about arc in a human-friendly way.

◆ Discharge()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::Discharge ( NodeIndex node )

protected

Discharges an active node node by saturating its admissible adjacent arcs, if any, and by relabelling it when it becomes inactive.

◆ Flow()

template<typename Graph>

FlowQuantity operations_research::GenericMaxFlow< Graph >::Flow ( ArcIndex arc ) const

inline

Returns the flow on arc using the equations given in the comment on residual_arc_capacity_.

Definition at line 365 of file max_flow.h.

◆ GetAndRemoveFirstActiveNode()

template<typename Graph>

NodeIndex operations_research::GenericMaxFlow< Graph >::GetAndRemoveFirstActiveNode ( )

inlineprotected

Get the first element from the active node container.

Definition at line 460 of file max_flow.h.

◆ GetOptimalFlow()

template<typename Graph>

FlowQuantity operations_research::GenericMaxFlow< Graph >::GetOptimalFlow ( ) const

inline

Returns the total flow found by the algorithm.

Definition at line 361 of file max_flow.h.

◆ GetSinkNodeIndex()

template<typename Graph>

NodeIndex operations_research::GenericMaxFlow< Graph >::GetSinkNodeIndex ( ) const

inline

Returns the index of the node corresponding to the sink of the network.

Definition at line 349 of file max_flow.h.

◆ GetSinkSideMinCut()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::GetSinkSideMinCut ( std::vector< NodeIndex > * result )

Returns the nodes that can reach the sink in the residual graph, the outgoing arcs of this set form a minimum cut.

Note that if this is the complement of GetNodeReachableFromSource(), then the min-cut is unique.

Todo:: (user): In the two-phases algorithm, we can get this minimum cut without doing the second phase. Add an option for this if there is a need to, note that the second phase is pretty fast so the gain will be small.

◆ GetSourceNodeIndex()

template<typename Graph>

NodeIndex operations_research::GenericMaxFlow< Graph >::GetSourceNodeIndex ( ) const

inline

Returns the index of the node corresponding to the source of the network.

Definition at line 346 of file max_flow.h.

◆ GetSourceSideMinCut()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::GetSourceSideMinCut ( std::vector< NodeIndex > * result )

Returns the nodes reachable from the source in the residual graph, the outgoing arcs of this set form a minimum cut.

◆ GlobalUpdate()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::GlobalUpdate ( )

protected

Computes the best possible node potential given the current flow using a reverse breadth-first search from the sink in the reverse residual graph.

This is an implementation of the global update heuristic mentioned in many max-flow papers. See for instance: B.V. Cherkassky, A.V. Goldberg, "On implementing push-relabel methods for the maximum flow problem", Algorithmica, 19:390-410, 1997. ftp://reports.stanford.edu/pub/cstr/reports/cs/tr/94/1523/CS-TR-94-1523.pdf

◆ graph()

template<typename Graph>

const Graph* operations_research::GenericMaxFlow< Graph >::graph ( ) const

inline

Returns the graph associated to the current object.

Definition at line 338 of file max_flow.h.

◆ Head()

template<typename Graph>

NodeIndex operations_research::GenericMaxFlow< Graph >::Head ( ArcIndex arc ) const

inlineprotected

Handy member functions to make the code more compact.

Definition at line 532 of file max_flow.h.

◆ InitializeActiveNodeContainer()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::InitializeActiveNodeContainer ( )

protected

Initializes the container active_nodes_.

◆ InitializePreflow()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::InitializePreflow ( )

protected

Initializes the preflow to a state that enables to run Refine.

◆ IsActive()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::IsActive ( NodeIndex node ) const

inlineprotected

Returns true if node is active, i.e.

if its excess is positive and it is neither the source or the sink of the graph.

Definition at line 437 of file max_flow.h.

◆ IsAdmissible()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::IsAdmissible ( ArcIndex arc ) const

inlineprotected

Returns true if arc is admissible.

Definition at line 430 of file max_flow.h.

◆ IsArcDirect()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::IsArcDirect ( ArcIndex arc ) const

protected

◆ IsArcValid()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::IsArcValid ( ArcIndex arc ) const

protected

◆ IsEmptyActiveNodeContainer()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::IsEmptyActiveNodeContainer ( )

inlineprotected

Check the emptiness of the container.

Definition at line 477 of file max_flow.h.

◆ Opposite()

template<typename Graph>

ArcIndex operations_research::GenericMaxFlow< Graph >::Opposite ( ArcIndex arc ) const

protected

◆ ProcessNodeByHeight()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::ProcessNodeByHeight ( bool value )

inline

Definition at line 421 of file max_flow.h.

◆ PushActiveNode()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::PushActiveNode ( const NodeIndex & node )

inlineprotected

Push element to the active node container.

Definition at line 468 of file max_flow.h.

◆ PushFlow()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::PushFlow	(	FlowQuantity	flow,
		ArcIndex	arc
	)

protected

Pushes flow on arc, i.e.

consumes flow on residual_arc_capacity_[arc], and consumes -flow on residual_arc_capacity_[Opposite(arc)]. Updates node_excess_ at the tail and head of arc accordingly.

◆ PushFlowExcessBackToSource()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::PushFlowExcessBackToSource ( )

protected

Clears the flow excess at each node by pushing the flow back to the source:

Do a depth-first search from the source in the direct graph to cancel flow cycles.
Then, return flow excess along the depth-first search tree (by pushing the flow in the reverse dfs topological order). The theoretical complexity is O(mn), but it is a lot faster in practice.

◆ Refine()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::Refine ( )

protected

Performs optimization step.

◆ RefineWithGlobalUpdate()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::RefineWithGlobalUpdate ( )

protected

◆ Relabel()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::Relabel ( NodeIndex node )

protected

Relabels a node, i.e.

increases its height by the minimum necessary amount. This version of Relabel is relaxed in a way such that if an admissible arc exists at the current node height, then the node is not relabeled. This enables us to deal with wrong values of first_admissible_arc_[node] when updating it is too costly.

◆ SaturateOutgoingArcsFromSource()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::SaturateOutgoingArcsFromSource ( )

protected

Tries to saturate all the outgoing arcs from the source that can reach the sink.

Most of the time, we can do that in one go, except when more flow than kMaxFlowQuantity can be pushed out of the source in which case we have to be careful. Returns true if some flow was pushed.

◆ SetArcCapacity()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::SetArcCapacity	(	ArcIndex	arc,
		FlowQuantity	new_capacity
	)

Sets the capacity for arc to new_capacity.

◆ SetArcFlow()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::SetArcFlow	(	ArcIndex	arc,
		FlowQuantity	new_flow
	)

Sets the flow for arc.

◆ SetCapacityAndClearFlow()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::SetCapacityAndClearFlow	(	ArcIndex	arc,
		FlowQuantity	capacity
	)

inlineprotected

Sets the capacity of arc to 'capacity' and clears the flow on arc.

Definition at line 442 of file max_flow.h.

◆ SetCheckInput()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::SetCheckInput ( bool value )

inline

Definition at line 419 of file max_flow.h.

◆ SetCheckResult()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::SetCheckResult ( bool value )

inline

Definition at line 420 of file max_flow.h.

◆ SetUseGlobalUpdate()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::SetUseGlobalUpdate ( bool value )

inline

Sets the different algorithm options.

All default to true. See the corresponding variable declaration below for more details.

Definition at line 414 of file max_flow.h.

◆ SetUseTwoPhaseAlgorithm()

template<typename Graph>

void operations_research::GenericMaxFlow< Graph >::SetUseTwoPhaseAlgorithm ( bool value )

inline

Definition at line 418 of file max_flow.h.

◆ Solve()

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::Solve ( )

Returns true if a maximum flow was solved.

◆ status()

template<typename Graph>

Status operations_research::GenericMaxFlow< Graph >::status ( ) const

inline

Returns the status of last call to Solve().

NOT_SOLVED is returned if Solve() has never been called or if the problem has been modified in such a way that the previous solution becomes invalid.

Definition at line 343 of file max_flow.h.

◆ Tail()

template<typename Graph>

NodeIndex operations_research::GenericMaxFlow< Graph >::Tail ( ArcIndex arc ) const

inlineprotected

Definition at line 533 of file max_flow.h.

Member Data Documentation

◆ active_node_by_height_

template<typename Graph>

PriorityQueueWithRestrictedPush<NodeIndex, NodeHeight> operations_research::GenericMaxFlow< Graph >::active_node_by_height_

protected

A priority queue used for managing active nodes in the algorithm.

It allows to select the active node with highest height before each Discharge(). Moreover, since all pushes from this node will be to nodes with height greater or equal to the initial discharged node height minus one, the PriorityQueueWithRestrictedPush is a perfect fit.

Definition at line 597 of file max_flow.h.

◆ active_nodes_

template<typename Graph>

std::vector<NodeIndex> operations_research::GenericMaxFlow< Graph >::active_nodes_

protected

A stack used for managing active nodes in the algorithm.

Note: the papers cited above recommend the use of a queue, but benchmarking so far has not proved it is better. In particular, processing nodes in LIFO order has better cache locality.

Definition at line 590 of file max_flow.h.

◆ bfs_queue_

template<typename Graph>

std::vector<NodeIndex> operations_research::GenericMaxFlow< Graph >::bfs_queue_

protected

Definition at line 611 of file max_flow.h.

◆ check_input_

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::check_input_

protected

Whether or not we check the input, this is a small price to pay for robustness.

Disable only if you know the input is valid because an invalid input can cause the algorithm to run into an infinite loop!

Definition at line 634 of file max_flow.h.

◆ check_result_

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::check_result_

protected

Whether or not we check the result.

Todo:: (user): Make the check more exhaustive by checking the optimality?

Definition at line 638 of file max_flow.h.

◆ first_admissible_arc_

template<typename Graph>

ArcIndexArray operations_research::GenericMaxFlow< Graph >::first_admissible_arc_

protected

An array representing the first admissible arc for each node in graph_.

Definition at line 584 of file max_flow.h.

◆ graph_

template<typename Graph>

const Graph* operations_research::GenericMaxFlow< Graph >::graph_

protected

A pointer to the graph passed as argument.

Definition at line 547 of file max_flow.h.

◆ kMaxFlowQuantity

template<typename Graph>

const FlowQuantity operations_research::GenericMaxFlow< Graph >::kMaxFlowQuantity

staticprotected

Maximum manageable flow.

Definition at line 544 of file max_flow.h.

◆ node_excess_

template<typename Graph>

QuantityArray operations_research::GenericMaxFlow< Graph >::node_excess_

protected

An array representing the excess for each node in graph_.

Definition at line 550 of file max_flow.h.

◆ node_in_bfs_queue_

template<typename Graph>

std::vector<bool> operations_research::GenericMaxFlow< Graph >::node_in_bfs_queue_

protected

BFS queue used by the GlobalUpdate() function.

We do not use a C++ queue because we need access to the vector for different optimizations.

Definition at line 610 of file max_flow.h.

◆ node_potential_

template<typename Graph>

NodeHeightArray operations_research::GenericMaxFlow< Graph >::node_potential_

protected

An array representing the height function for each node in graph_.

For a given node, this is a lower bound on the shortest path length from this node to the sink in the residual network. The height of a node always goes up during the course of a Solve().

Since initially we saturate all the outgoing arcs of the source, we can never reach the sink from the source in the residual graph. Initially we set the height of the source to n (the number of node of the graph) and it never changes. If a node as an height >= n, then this node can't reach the sink and its height minus n is a lower bound on the shortest path length from this node to the source in the residual graph.

Definition at line 563 of file max_flow.h.

◆ process_node_by_height_

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::process_node_by_height_

protected

Whether or not we use the PriorityQueueWithRestrictedPush to process the active nodes rather than a simple queue.

This can only be true if use_global_update_ is true.

Note(user): using a template will be slightly faster, but since we test this in a non-critical path, this only has a minor impact.

Definition at line 629 of file max_flow.h.

◆ residual_arc_capacity_

template<typename Graph>

QuantityArray operations_research::GenericMaxFlow< Graph >::residual_arc_capacity_

protected

An array representing the residual_capacity for each arc in graph_.

Residual capacities enable one to represent the capacity and flow for all arcs in the graph in the following manner. For all arc, residual_arc_capacity_[arc] = capacity[arc] - flow[arc] Moreover, for reverse arcs, capacity[arc] = 0 by definition, Also flow[Opposite(arc)] = -flow[arc] by definition. Therefore:

for a direct arc: flow[arc] = 0 - flow[Opposite(arc)] = capacity[Opposite(arc)] - flow[Opposite(arc)] = residual_arc_capacity_[Opposite(arc)]
for a reverse arc: flow[arc] = -residual_arc_capacity_[arc] Using these facts enables one to only maintain residual_arc_capacity_, instead of both capacity and flow, for each direct and indirect arc. This reduces the amount of memory for this information by a factor 2.

Definition at line 581 of file max_flow.h.

◆ sink_

template<typename Graph>

NodeIndex operations_research::GenericMaxFlow< Graph >::sink_

protected

The index of the sink node in graph_.

Definition at line 603 of file max_flow.h.

◆ source_

template<typename Graph>

NodeIndex operations_research::GenericMaxFlow< Graph >::source_

protected

The index of the source node in graph_.

Definition at line 600 of file max_flow.h.

◆ stats_

template<typename Graph>

StatsGroup operations_research::GenericMaxFlow< Graph >::stats_

mutableprotected

Statistics about this class.

Definition at line 641 of file max_flow.h.

◆ status_

template<typename Graph>

Status operations_research::GenericMaxFlow< Graph >::status_

protected

The status of the problem.

Definition at line 606 of file max_flow.h.

◆ use_global_update_

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::use_global_update_

protected

Whether or not to use GlobalUpdate().

Definition at line 614 of file max_flow.h.

◆ use_two_phase_algorithm_

template<typename Graph>

bool operations_research::GenericMaxFlow< Graph >::use_two_phase_algorithm_

protected

Whether or not we use a two-phase algorithm: 1/ Only deal with nodes that can reach the sink.

At the end we know the value of the maximum flow and we have a min-cut. 2/ Call PushFlowExcessBackToSource() to obtain a max-flow. This is usually a lot faster than the first phase.

Definition at line 621 of file max_flow.h.

The documentation for this class was generated from the following file:

max_flow.h

Detailed Description

template<typename Graph> class operations_research::GenericMaxFlow< Graph >

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Member Typedef Documentation

◆ ArcIndex

◆ ArcIndexArray

◆ IncomingArcIterator

◆ NodeHeight

◆ NodeHeightArray

◆ NodeIndex

◆ OutgoingArcIterator

◆ OutgoingOrOppositeIncomingArcIterator

Member Enumeration Documentation

◆ Status

Constructor & Destructor Documentation

◆ GenericMaxFlow()

◆ ~GenericMaxFlow()

Member Function Documentation

◆ AugmentingPathExists()

◆ Capacity()

◆ CheckInputConsistency()

◆ CheckRelabelPrecondition()

◆ CheckResult()

◆ ComputeReachableNodes()

◆ CreateFlowModel()

◆ DebugString()

◆ Discharge()

◆ Flow()

◆ GetAndRemoveFirstActiveNode()

◆ GetOptimalFlow()

◆ GetSinkNodeIndex()

◆ GetSinkSideMinCut()

◆ GetSourceNodeIndex()

◆ GetSourceSideMinCut()

◆ GlobalUpdate()

◆ graph()

◆ Head()

◆ InitializeActiveNodeContainer()

◆ InitializePreflow()

◆ IsActive()

◆ IsAdmissible()

◆ IsArcDirect()

◆ IsArcValid()

◆ IsEmptyActiveNodeContainer()

◆ Opposite()

◆ ProcessNodeByHeight()

◆ PushActiveNode()

◆ PushFlow()

◆ PushFlowExcessBackToSource()

◆ Refine()

◆ RefineWithGlobalUpdate()

◆ Relabel()

◆ SaturateOutgoingArcsFromSource()

◆ SetArcCapacity()

◆ SetArcFlow()

◆ SetCapacityAndClearFlow()

◆ SetCheckInput()

◆ SetCheckResult()

◆ SetUseGlobalUpdate()

◆ SetUseTwoPhaseAlgorithm()

◆ Solve()

◆ status()

◆ Tail()

Member Data Documentation

◆ active_node_by_height_

◆ active_nodes_

◆ bfs_queue_

◆ check_input_

◆ check_result_

◆ first_admissible_arc_

◆ graph_

◆ kMaxFlowQuantity

◆ node_excess_

◆ node_in_bfs_queue_

◆ node_potential_

◆ process_node_by_height_

template<typename Graph>
class operations_research::GenericMaxFlow< Graph >