Package com.jgalgo.alg.connect

Interface MinimumVertexCutSt

All Known Implementing Classes:
MinimumVertexCutStAbstract, MinimumVertexCutStEdgeCut
public interface MinimumVertexCutSt
Minimum Vertex-Cut algorithm with terminal vertices (source-sink, S-T).

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 the minimum vertex-cut given two terminal vertices, source (S) and sink (T).

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 Type
    Method
    Description
    <V, E> Set<V>
    computeMinimumCut(Graph<V,E> g, WeightFunction<V> w, V source, V sink)
    Compute the minimum vertex-cut in a graph between two terminal vertices.
    static MinimumVertexCutSt
    newInstance()
    Create a new minimum S-T vertex-cut algorithm object.

  • Method Details

    • computeMinimumCut

      <V, E> Set<V> computeMinimumCut(Graph<V,E> g, WeightFunction<V> w, V source, V sink)
      Compute the minimum vertex-cut 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 an IntGraph, a IntSet object will be returned. In that case, its better to pass a IWeightFunction as w to avoid boxing/unboxing.

      Type Parameters:
      V - the vertices type
      E - the edges type
      Parameters:
      g - a graph
      w - a vertex weight function
      source - the source vertex
      sink - the sink vertex
      Returns:
      a set of vertices that form the minimum vertex-cut, 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

      static MinimumVertexCutSt newInstance()
      Create a new minimum S-T vertex-cut algorithm object.

      This is the recommended way to instantiate a new MinimumVertexCutSt object.

      Returns:
      a default implementation of MinimumVertexCutSt