Class PivotBronKerboschCliqueFinder<V,​E>

  • Type Parameters:
    V - the graph vertex type
    E - the graph edge type
    All Implemented Interfaces:
    java.lang.Iterable<java.util.Set<V>>, MaximalCliqueEnumerationAlgorithm<V,​E>
    Direct Known Subclasses:
    DegeneracyBronKerboschCliqueFinder

    public class PivotBronKerboschCliqueFinder<V,​E>
    extends java.lang.Object
    Bron-Kerbosch maximal clique enumeration algorithm with pivot.

    The pivoting follows the rule from the paper

    • E. Tomita, A. Tanaka, and H. Takahashi. The worst-case time complexity for generating all maximal cliques and computational experiments. Theor. Comput. Sci. 363(1):28–42, 2006.

    where the authors show that using that rule guarantees that the Bron-Kerbosch algorithm has worst-case running time $O(3^{n/3})$ where $n$ is the number of vertices of the graph, excluding time to write the output, which is worst-case optimal.

    The algorithm first computes all maximal cliques and then returns the result to the user. A timeout can be set using the constructor parameters.

    Author:
    Dimitrios Michail
    See Also:
    BronKerboschCliqueFinder, DegeneracyBronKerboschCliqueFinder
    • Field Summary

      Fields 
      Modifier and Type Field Description
      protected java.util.List<java.util.Set<V>> allMaximalCliques
      The result
      protected Graph<V,​E> graph
      The underlying graph
      protected int maxSize
      Size of biggest maximal clique found.
      protected long nanos
      Timeout in nanoseconds
      protected boolean timeLimitReached
      Whether the last computation terminated due to a time limit.
    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      protected void findCliques​(java.util.Set<V> p, java.util.Set<V> r, java.util.Set<V> x, long nanosTimeLimit)
      Recursive implementation of the Bron-Kerbosch with pivot.
      boolean isTimeLimitReached()
      Check the computation has stopped due to a time limit or due to computing all maximal cliques.
      java.util.Iterator<java.util.Set<V>> iterator()
      Returns an iterator over all maximal cliques.
      protected void lazyRun()
      Lazily execute the enumeration algorithm.
      java.util.Iterator<java.util.Set<V>> maximumIterator()
      Create an iterator which returns only the maximum cliques of a graph.
      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
      • Methods inherited from interface java.lang.Iterable

        forEach, spliterator
    • Field Detail

      • graph

        protected final Graph<V,​E> graph
        The underlying graph
      • nanos

        protected final long nanos
        Timeout in nanoseconds
      • timeLimitReached

        protected boolean timeLimitReached
        Whether the last computation terminated due to a time limit.
      • allMaximalCliques

        protected java.util.List<java.util.Set<V>> allMaximalCliques
        The result
      • maxSize

        protected int maxSize
        Size of biggest maximal clique found.
    • Constructor Detail

      • PivotBronKerboschCliqueFinder

        public PivotBronKerboschCliqueFinder​(Graph<V,​E> graph)
        Constructs a new clique finder.
        Parameters:
        graph - the input graph; must be simple
      • PivotBronKerboschCliqueFinder

        public PivotBronKerboschCliqueFinder​(Graph<V,​E> graph,
                                             long timeout,
                                             java.util.concurrent.TimeUnit unit)
        Constructs a new clique finder.
        Parameters:
        graph - the input graph; must be simple
        timeout - the maximum time to wait, if zero no timeout
        unit - the time unit of the timeout argument
    • Method Detail

      • lazyRun

        protected void lazyRun()
        Lazily execute the enumeration algorithm.
      • findCliques

        protected void findCliques​(java.util.Set<V> p,
                                   java.util.Set<V> r,
                                   java.util.Set<V> x,
                                   long nanosTimeLimit)
        Recursive implementation of the Bron-Kerbosch with pivot.
        Parameters:
        p - vertices to consider adding to the clique
        r - a possibly non-maximal clique
        x - vertices which must be excluded from the clique
        nanosTimeLimit - time limit
      • maximumIterator

        public java.util.Iterator<java.util.Set<V>> maximumIterator()
        Create an iterator which returns only the maximum cliques of a graph. The iterator computes all maximal cliques and then filters them by the size of the maximum found clique.
        Returns:
        an iterator which returns only the maximum cliques of a graph
      • isTimeLimitReached

        public boolean isTimeLimitReached()
        Check the computation has stopped due to a time limit or due to computing all maximal cliques.
        Returns:
        true if the computation has stopped due to a time limit, false otherwise