Class GusfieldGomoryHuCutTree<V,E>
- java.lang.Object
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- org.jgrapht.alg.flow.GusfieldGomoryHuCutTree<V,E>
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- Type Parameters:
V
- the graph vertex typeE
- the graph edge type
- All Implemented Interfaces:
FlowAlgorithm<V,E>
,MaximumFlowAlgorithm<V,E>
,MinimumSTCutAlgorithm<V,E>
public class GusfieldGomoryHuCutTree<V,E> extends java.lang.Object implements MaximumFlowAlgorithm<V,E>, MinimumSTCutAlgorithm<V,E>
This class computes a Gomory-Hu tree (GHT) using the algorithm proposed by Dan Gusfield. For a definition of GHTs, refer to: Gomory, R., Hu, T. Multi-terminal network flows. Journal of the Socieity for Industrial and Applied mathematics, 9(4), p551-570, 1961. GHTs can be used to efficiently query the maximum flows and minimum cuts for all pairs of vertices. The algorithm is described in: Gusfield, D, Very simple methods for all pairs network flow analysis. SIAM Journal on Computing, 19(1), p142-155, 1990
In an undirected graph, there exist $\frac{n(n-1)}{2}$ different vertex pairs. This class computes the maximum flow/minimum cut between each of these pairs efficiently by performing exactly $(n-1)$ minimum $s-t$ cut computations. If your application needs fewer than $n-1$ flow/cut computations, consider computing the maximum flows/minimum cuts manually throughMaximumFlowAlgorithm
/MinimumSTCutAlgorithm
.The runtime complexity of this class is $O((V-1)Q)$, where $Q$ is the runtime complexity of the algorithm used to compute $s-t$ cuts in the graph. By default, this class uses the
PushRelabelMFImpl
implementation to calculate minimum s-t cuts. This class has a runtime complexity of $O(V^3)$, resulting in a $O(V^4)$ runtime complexity for the overall algorithm.Note: this class performs calculations in a lazy manner. The GHT is not calculated until the first invocation of
getMaximumFlowValue(Object, Object)
orgetGomoryHuTree()
. Moreover, this class only calculates the value of the maximum flow between a source-destination pair; it does not calculate the corresponding flow per edge. If you need to know the exact flow through an edge, use one of the alternativeMaximumFlowAlgorithm
implementations.In contrast to an Equivalent Flow Tree (
GusfieldEquivalentFlowTree
), Gomory-Hu trees also provide all minimum cuts for all pairs of vertices!This class does not support changes to the underlying graph. The behavior of this class is undefined when the graph is modified after instantiating this class.
- Author:
- Joris Kinable
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Nested Class Summary
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Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.FlowAlgorithm
FlowAlgorithm.Flow<E>, FlowAlgorithm.FlowImpl<E>
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Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.MaximumFlowAlgorithm
MaximumFlowAlgorithm.MaximumFlow<E>, MaximumFlowAlgorithm.MaximumFlowImpl<E>
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Constructor Summary
Constructors Constructor Description GusfieldGomoryHuCutTree(Graph<V,E> network)
Constructs a new GusfieldEquivalentFlowTree instance.GusfieldGomoryHuCutTree(Graph<V,E> network, double epsilon)
Constructs a new GusfieldEquivalentFlowTree instance.GusfieldGomoryHuCutTree(Graph<V,E> network, MinimumSTCutAlgorithm<V,E> minimumSTCutAlgorithm)
Constructs a new GusfieldEquivalentFlowTree instance.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
calculateMinCut()
Calculates the minimum cut in the graph, that is, the minimum cut over all $s-t$ pairs.double
calculateMinCut(V source, V sink)
Computes a minimum capacity $s-t$ cut.double
getCutCapacity()
Returns the capacity of the cut obtained after the last invocation ofMinimumSTCutAlgorithm.calculateMinCut(Object, Object)
java.util.Set<E>
getCutEdges()
Returns the set of edges which run from $S$ to $T$, in the $s-t$ cut obtained after the last invocation ofMinimumSTCutAlgorithm.calculateMinCut(Object, Object)
In case of a directed graph, only the edges with their tail in $S$ and their head in $T$ are returned.V
getFlowDirection(E e)
Unsupported operationjava.util.Map<E,java.lang.Double>
getFlowMap()
Unsupported operationSimpleWeightedGraph<V,DefaultWeightedEdge>
getGomoryHuTree()
Returns the Gomory-Hu Tree as an actual tree (graph).MaximumFlowAlgorithm.MaximumFlow<E>
getMaximumFlow(V source, V sink)
Unsupported operationdouble
getMaximumFlowValue(V source, V sink)
Returns the Maximum flow between source and sink.java.util.Set<V>
getSinkPartition()
Returns the sink partition $T$, $t \in T$, of the cut obtained after the last invocation ofMinimumSTCutAlgorithm.calculateMinCut(Object, Object)
java.util.Set<V>
getSourcePartition()
Returns the source partition $S$, $s \in S$, of the cut obtained after the last invocation ofMinimumSTCutAlgorithm.calculateMinCut(Object, Object)
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface org.jgrapht.alg.interfaces.FlowAlgorithm
getFlow
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Constructor Detail
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GusfieldGomoryHuCutTree
public GusfieldGomoryHuCutTree(Graph<V,E> network)
Constructs a new GusfieldEquivalentFlowTree instance.- Parameters:
network
- input graph
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GusfieldGomoryHuCutTree
public GusfieldGomoryHuCutTree(Graph<V,E> network, double epsilon)
Constructs a new GusfieldEquivalentFlowTree instance.- Parameters:
network
- input graphepsilon
- precision
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Method Detail
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getGomoryHuTree
public SimpleWeightedGraph<V,DefaultWeightedEdge> getGomoryHuTree()
Returns the Gomory-Hu Tree as an actual tree (graph). Note that this tree is not necessarily unique. The edge weights represent the flow values/cut weights. This method runs in $O(n)$ time.- Returns:
- Gomory-Hu Tree
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getMaximumFlow
public MaximumFlowAlgorithm.MaximumFlow<E> getMaximumFlow(V source, V sink)
Unsupported operation- Specified by:
getMaximumFlow
in interfaceMaximumFlowAlgorithm<V,E>
- Parameters:
source
- source of the flow inside the networksink
- sink of the flow inside the network- Returns:
- nothing
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getMaximumFlowValue
public double getMaximumFlowValue(V source, V sink)
Returns the Maximum flow between source and sink. The algorithm is only executed once; successive invocations of this method will return in $O(1)$ time.- Specified by:
getMaximumFlowValue
in interfaceMaximumFlowAlgorithm<V,E>
- Parameters:
source
- source vertexsink
- sink vertex- Returns:
- the Maximum flow between source and sink.
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getFlowMap
public java.util.Map<E,java.lang.Double> getFlowMap()
Unsupported operation- Specified by:
getFlowMap
in interfaceFlowAlgorithm<V,E>
- Returns:
- nothing
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getFlowDirection
public V getFlowDirection(E e)
Unsupported operation- Specified by:
getFlowDirection
in interfaceFlowAlgorithm<V,E>
- Parameters:
e
- edge- Returns:
- nothing
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calculateMinCut
public double calculateMinCut(V source, V sink)
Description copied from interface:MinimumSTCutAlgorithm
Computes a minimum capacity $s-t$ cut.- Specified by:
calculateMinCut
in interfaceMinimumSTCutAlgorithm<V,E>
- Parameters:
source
- ssink
- t- Returns:
- capacity of the cut
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calculateMinCut
public double calculateMinCut()
Calculates the minimum cut in the graph, that is, the minimum cut over all $s-t$ pairs. The same result can be obtained with theStoerWagnerMinimumCut
implementation. After invoking this method, the source/sink partitions corresponding to the minimum cut can be queried through thegetSourcePartition()
andgetSinkPartition()
methods. After computing the Gomory-Hu Cut tree, this method runs in $O(N)$ time.- Returns:
- weight of the minimum cut in the graph
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getCutCapacity
public double getCutCapacity()
Description copied from interface:MinimumSTCutAlgorithm
Returns the capacity of the cut obtained after the last invocation ofMinimumSTCutAlgorithm.calculateMinCut(Object, Object)
- Specified by:
getCutCapacity
in interfaceMinimumSTCutAlgorithm<V,E>
- Returns:
- capacity of the cut
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getSourcePartition
public java.util.Set<V> getSourcePartition()
Description copied from interface:MinimumSTCutAlgorithm
Returns the source partition $S$, $s \in S$, of the cut obtained after the last invocation ofMinimumSTCutAlgorithm.calculateMinCut(Object, Object)
- Specified by:
getSourcePartition
in interfaceMinimumSTCutAlgorithm<V,E>
- Returns:
- source partition S
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getSinkPartition
public java.util.Set<V> getSinkPartition()
Description copied from interface:MinimumSTCutAlgorithm
Returns the sink partition $T$, $t \in T$, of the cut obtained after the last invocation ofMinimumSTCutAlgorithm.calculateMinCut(Object, Object)
- Specified by:
getSinkPartition
in interfaceMinimumSTCutAlgorithm<V,E>
- Returns:
- source partition T
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getCutEdges
public java.util.Set<E> getCutEdges()
Description copied from interface:MinimumSTCutAlgorithm
Returns the set of edges which run from $S$ to $T$, in the $s-t$ cut obtained after the last invocation ofMinimumSTCutAlgorithm.calculateMinCut(Object, Object)
In case of a directed graph, only the edges with their tail in $S$ and their head in $T$ are returned. In cased of a undirected graph, all edges with one endpoint in $S$ and one endpoint in $T$ are returned.- Specified by:
getCutEdges
in interfaceMinimumSTCutAlgorithm<V,E>
- Returns:
- set of edges which run from $S$ to $T$
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