Package it.unimi.dsi.webgraph.algo

Class SumSweepUndirectedDiameterRadius

java.lang.Object
it.unimi.dsi.webgraph.algo.SumSweepUndirectedDiameterRadius
public class SumSweepUndirectedDiameterRadius
extends Object
Computes the radius and/or the diameter and/or all eccentricities of an undirected graph, using the SumSweep algorithm described by Michele Borassi, Pierluigi Crescenzi, Michel Habib, Walter A. Kosters, Andrea Marino, and Frank W. Takes in “Fast diameter and radius BFS-based computation in (weakly connected) real-world graphs—With an application to the six degrees of separation games ”, Theoretical Computer Science, 586:59−80, 2015.

We define the eccentricity of a node v in a graph G=(V,E) as ecc(v)=max w reachable from v d(v ,w), where d(v,w) is the number of edges in a shortest path from v to w. The diameter is maxv∈V ecc(v), and the radius is min v∈ V ecc(v).

This algorithm performs some BFSs from "clever" vertices, and uses these BFSs to bound the eccentricity of all vertices. More specifically, for each vertex v, this algorithm keeps a lower and an upper bound on the eccentricity of v, named l[v], u[ v]. Furthermore, it keeps a lower bound dL on the diameter and an upper bound rU on the radius. At each step, the algorithm performs a BFS, and it updates all these bounds: the radius is found as soon as rU is smaller than the minimum value of l, and the diameter is found as soon as dL is bigger than the maximum value of u.

More specifically, the upper bound on the radius (resp., lower bound on the diameter) is defined as the minimum (resp., maximum) eccentricity of a vertex from which we performed a BFS. Moreover, if we perform a BFS from a vertex s, we update l[v]=max(l[ v], d(s, v)), and u[v ]=max(u[v], d(v, s) + ecc(s).

To use this class, it is enough to create an instance, and then invoke compute(). It is possible to choose between the following stopping conditions:

  • only the radius is found;
  • only the diameter is found;
  • radius and diameter are found;
  • all eccentricities are found.

After the method compute() is run, the output can be obtained through the methods getRadius() for the radius, getRadialVertex() for a radial vertex, getDiameter() for the diameter, getDiametralVertex() for a vertex whose (forward or backward) eccentricity equals the diameter, getEccentricity(int) for the eccentricity of a vertex. An exception is raised if the field has not been computed.

Performance issues

The algorithm is exact and, although the running-time is O( mn) in the worst-case, it is usually much faster on real-world networks.

Author:
Michele Borassi

  • Nested Class Summary

    Nested Classes
    Modifier and Type Class Description
    static class  SumSweepUndirectedDiameterRadius.OutputLevel
    The type of output requested: radius, diameter, radius and diameter, or all eccentricities.

  • Field Summary

    Fields
    Modifier and Type Field Description
    protected int[] ecc
    The array of eccentricity values.
    protected int[] l
    Lower bound on the eccentricity.
    protected int[] u
    Upper bound on the eccentricity.

  • Constructor Summary

    Constructors
    Constructor Description
    SumSweepUndirectedDiameterRadius​(ImmutableGraph graph, SumSweepUndirectedDiameterRadius.OutputLevel output, ProgressLogger pl)
    Creates a new class for computing diameter and/or radius and/or all eccentricities.

  • Method Summary

    Modifier and Type Method Description
    void compute()
    Computes diameter, radius, and/or all eccentricities.
    int getAllIterations()
    Returns the number of iteration needed to compute all eccentricities, if they have already been computed (otherwise, an exception is raised).
    int getDiameter()
    Returns the diameter, if it has already been computed (otherwise, an exception is raised).
    int getDiameterIterations()
    Returns the number of iteration needed to compute the diameter, if it has already been computed (otherwise, an exception is raised).
    int getDiametralVertex()
    Returns a diametral vertex, if it has already been computed (otherwise, an exception is raised).
    int getEccentricity​(int v)
    Returns the eccentricity of a vertex, if it has already been computed (otherwise, an exception is raised).
    int getRadialVertex()
    Returns a radial vertex, if it has already been computed (otherwise, an exception is raised).
    int getRadius()
    Returns the radius of the graph, if it has already been computed (otherwise, an exception is raised).
    int getRadiusIterations()
    Returns the number of iteration needed to compute the radius, if it has already been computed (otherwise, an exception is raised).
    static void main​(String[] arg)  
    void sumSweepHeuristic​(int start, int iter)
    Performs iter steps of the SumSweep heuristic, starting from vertex start.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • ecc

      protected final int[] ecc
      The array of eccentricity values.

    • l

      protected int[] l
      Lower bound on the eccentricity.

    • u

      protected int[] u
      Upper bound on the eccentricity.

  • Constructor Details

    • SumSweepUndirectedDiameterRadius

      public SumSweepUndirectedDiameterRadius​(ImmutableGraph graph, SumSweepUndirectedDiameterRadius.OutputLevel output, ProgressLogger pl)
      Creates a new class for computing diameter and/or radius and/or all eccentricities.
      Parameters:
      graph - a graph.
      pl - a progress logger, or null.
      output - which output is requested: radius, diameter, radius and diameter, or all eccentricities.

  • Method Details

    • getRadius

      public int getRadius()
      Returns the radius of the graph, if it has already been computed (otherwise, an exception is raised).
      Returns:
      the radius

    • getDiameter

      public int getDiameter()
      Returns the diameter, if it has already been computed (otherwise, an exception is raised).
      Returns:
      the diameter

    • getRadialVertex

      public int getRadialVertex()
      Returns a radial vertex, if it has already been computed (otherwise, an exception is raised).
      Returns:
      a radial vertex

    • getDiametralVertex

      public int getDiametralVertex()
      Returns a diametral vertex, if it has already been computed (otherwise, an exception is raised).
      Returns:
      a diametral vertex

    • getEccentricity

      public int getEccentricity​(int v)
      Returns the eccentricity of a vertex, if it has already been computed (otherwise, an exception is raised).
      Parameters:
      v - the vertex

    • getRadiusIterations

      public int getRadiusIterations()
      Returns the number of iteration needed to compute the radius, if it has already been computed (otherwise, an exception is raised).
      Returns:
      the number of iterations before the radius is found

    • getDiameterIterations

      public int getDiameterIterations()
      Returns the number of iteration needed to compute the diameter, if it has already been computed (otherwise, an exception is raised).
      Returns:
      the number of iterations before the diameter is found

    • getAllIterations

      public int getAllIterations()
      Returns the number of iteration needed to compute all eccentricities, if they have already been computed (otherwise, an exception is raised).
      Returns:
      the number of iterations before all eccentricities are found

    • sumSweepHeuristic

      public void sumSweepHeuristic​(int start, int iter)
      Performs iter steps of the SumSweep heuristic, starting from vertex start. The SumSweep heuristic performs BFSes from vertices maximizing the sum of the distance from the starting vertices of previous BFSes, and should be considered "peripheral". This way, after few iterations, usually most lower bounds on the eccentricities are tight.
      Parameters:
      start - the starting vertex
      iter - the number of iterations

    • compute

      public void compute()
      Computes diameter, radius, and/or all eccentricities. Results can be accessed by methods such as getDiameter(), getRadialVertex() and getEccentricity(int).

    • main

      public static void main​(String[] arg) throws IOException, JSAPException
      Throws:
      IOException
      JSAPException