Class SumSweepUndirectedDiameterRadius


  • public class SumSweepUndirectedDiameterRadius
    extends java.lang.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 maxvV 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.
    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      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​(java.lang.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 Detail

      • 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 Detail

      • SumSweepUndirectedDiameterRadius

        public SumSweepUndirectedDiameterRadius​(ImmutableGraph graph,
                                                SumSweepUndirectedDiameterRadius.OutputLevel output,
                                                it.unimi.dsi.logging.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 Detail

      • 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
      • main

        public static void main​(java.lang.String[] arg)
                         throws java.io.IOException,
                                com.martiansoftware.jsap.JSAPException
        Throws:
        java.io.IOException
        com.martiansoftware.jsap.JSAPException