Interface MinimumVertexCutAllSt
- All Known Implementing Classes:
MinimumVertexCutAllStAbstract
,MinimumVertexCutAllStEdgeCut
Given a graph G=(V,E), a vertex cut (or separating set) is a set of vertices C whose removal transforms G
into a disconnected graph. In case the graph is a clique of size k, any vertex set of size k−1 is considered
by convention a vertex cut of the graph. Given a vertex weight function, the weight of a vertex-cut C is the
weight sum of all vertices in C. There are two variants of the problem to find a minimum weight vertex-cut: (1)
With terminal vertices, and (2) without terminal vertices. In the variant with terminal vertices, we are given two
special vertices source (S)
and sink (T)
and we need to find the minimum vertex-cut C such that
such that the source
and the sink
are not in the same connected components after the removal of the
vertices of C. In the variant without terminal vertices (also called 'global vertex-cut') we need to find the
minimal cut among all possible cuts, and the removal of the vertices of C should simply disconnect the graph (or
make it trivial, containing a single vertex).
Algorithms implementing this interface compute all minimum vertex-cuts given two terminal vertices,
source (S)
and sink (T)
. For a single minimum vertex-cut, use MinimumVertexCutSt
. For the
global variant (without terminal vertices), see MinimumVertexCutGlobal
.
The cardinality (unweighted) minimum vertex-cut between two vertices is equal to the (local) vertex connectivity of these two vertices. If the graph is directed, the vertex connectivity between u and v is the minimum of the minimum vertex-cut between u and v and the minimum vertex-cut between v and u.
Use newInstance()
to get a default implementation of this interface.
- Author:
- Barak Ugav
- See Also:
-
Method Summary
Modifier and TypeMethodDescriptionallMinimumCuts
(Graph<V, E> g, WeightFunction<V> w, V source, V sink) Compute all the minimum vertex-cuts in a graph between two terminal vertices.minimumCutsIter
(Graph<V, E> g, WeightFunction<V> w, V source, V sink) Iterate over all the minimum vertex-cuts in a graph between two terminal vertices.static MinimumVertexCutAllSt
Create a new minimum S-T all vertex-cuts algorithm object.
-
Method Details
-
minimumCutsIter
Iterate over all the minimum vertex-cuts in a graph between two terminal vertices.Given a graph G=(V,E), a vertex-cut is a set of vertices whose removal disconnect the source from the sink. Note that connectivity is with respect to direction from the source to the sink, and not the other way around. In undirected graphs the source and sink are interchangeable.
If the source and sink are the same vertex no vertex-cut exists and an exception will be thrown. If the source and sink and an edge exists between them, no vertex-cut exists and
null
will be returned.If
g
is anIntGraph
, an iterator ofIntSet
objects will be returned. In that case, its better to pass aIWeightFunction
asw
to avoid boxing/unboxing.- Type Parameters:
V
- the vertices typeE
- the edges type- Parameters:
g
- a graphw
- a vertex weight functionsource
- the source vertexsink
- the sink vertex- Returns:
- an iterator over the sets of vertices that form the minimum vertex-cuts, or
null
if an edge exists between the source and the sink and therefore no vertex-cut exists - Throws:
IllegalArgumentException
- if the source and the sink are the same vertex
-
allMinimumCuts
Compute all the minimum vertex-cuts in a graph between two terminal vertices.Given a graph G=(V,E), a vertex-cut is a set of vertices whose removal disconnect the source from the sink. Note that connectivity is with respect to direction from the source to the sink, and not the other way around. In undirected graphs the source and sink are interchangeable.
If the source and sink are the same vertex no vertex-cut exists and an exception will be thrown. If the source and sink and an edge exists between them, no vertex-cut exists and
null
will be returned.If
g
is anIntGraph
, a list ofIntSet
objects will be returned. In that case, its better to pass aIWeightFunction
asw
to avoid boxing/unboxing.- Type Parameters:
V
- the vertices typeE
- the edges type- Parameters:
g
- a graphw
- a vertex weight functionsource
- the source vertexsink
- the sink vertex- Returns:
- a list containing all the sets of vertices that form the minimum vertex-cuts, or
null
if an edge exists between the source and the sink and therefore no vertex-cut exists - Throws:
IllegalArgumentException
- if the source and the sink are the same vertex
-
newInstance
Create a new minimum S-T all vertex-cuts algorithm object.This is the recommended way to instantiate a new
MinimumVertexCutAllSt
object.- Returns:
- a default implementation of
MinimumVertexCutAllSt
-