Module org.jgrapht.core
Package org.jgrapht.alg.densesubgraph

Class GoldbergMaximumDensitySubgraphAlgorithm<V,E>

java.lang.Object
org.jgrapht.alg.densesubgraph.GoldbergMaximumDensitySubgraphAlgorithmBase<V,E>
org.jgrapht.alg.densesubgraph.GoldbergMaximumDensitySubgraphAlgorithm<V,E>
Type Parameters:
V - Type of vertices
E - Type of edges
All Implemented Interfaces:
MaximumDensitySubgraphAlgorithm<V,E>
public class GoldbergMaximumDensitySubgraphAlgorithm<V,E> extends GoldbergMaximumDensitySubgraphAlgorithmBase<V,E>
This class computes a maximum density subgraph based on the algorithm described by Andrew Vladislav Goldberg in Finding Maximum Density Subgraphs, 1984, University of Berkley.
The basic concept is to construct a network that can be used to compute the maximum density subgraph using a binary search approach. See GoldbergMaximumDensitySubgraphAlgorithmBase for further details

This variant of the algorithm assumes the density of a positive real-weighted graph G=(V,E) to be defined as \[\frac{\sum\limits_{e \in E} w(e)}{\left|{V}\right|}\] and sets the weights of the network from GoldbergMaximumDensitySubgraphAlgorithmBase as proposed in the above paper. For this case the weights of the network must be chosen to be: \[c_{ij}=w(ij)\,\forall \{i,j\}\in E\] \[c_{it}=m+2g-d_i\,\forall i \in V\] \[c_{si}=m\,\forall i \in V\] where $m=\left|{E}\right|$ and $d_i$ is the degree of vertex $i$.
All the math to prove the correctness of these weights is the same as in GoldbergMaximumDensitySubgraphAlgorithmBase.

Because the density is per definition guaranteed to be rational, the distance of 2 possible solutions for the maximum density can't be smaller than $\frac{1}{W(W-1)}$. This means shrinking the binary search interval to this size, the correct solution is found. The runtime can in this case be given by $O(M(n,n+m)\log{W})$, where $M(n,m)$ is the runtime of the internally used MinimumSTCutAlgorithm and $W$ is the sum of all weights from $G$.

Author:
Andre Immig

  • Constructor Details

    • GoldbergMaximumDensitySubgraphAlgorithm

      public GoldbergMaximumDensitySubgraphAlgorithm(Graph<V,E> graph, V s, V t, double epsilon, Function<Graph<V,DefaultWeightedEdge>,MinimumSTCutAlgorithm<V,DefaultWeightedEdge>> algFactory)
      Constructor
      Parameters:
      algFactory - factory to construct the algorithm to use
      graph - input for computation
      s - additional source vertex
      t - additional target vertex
      epsilon - to use for internal computation

    • GoldbergMaximumDensitySubgraphAlgorithm

      public GoldbergMaximumDensitySubgraphAlgorithm(Graph<V,E> graph, V s, V t, double epsilon)
      Convenience constructor that uses PushRelabel as default MinimumSTCutAlgorithm
      Parameters:
      graph - input for computation
      s - additional source vertex
      t - additional target vertex
      epsilon - to use for internal computation

  • Method Details