Module org.jgrapht.core
Package org.jgrapht.alg.clique

Class PivotBronKerboschCliqueFinder<V,E>

java.lang.Object
org.jgrapht.alg.clique.PivotBronKerboschCliqueFinder<V,E>
Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:
Iterable<Set<V>>, MaximalCliqueEnumerationAlgorithm<V,E>
Direct Known Subclasses:
DegeneracyBronKerboschCliqueFinder
public class PivotBronKerboschCliqueFinder<V,E> extends 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:

  • Field Details

    • 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 List<Set<V>> allMaximalCliques
      The result

    • maxSize

      protected int maxSize
      Size of biggest maximal clique found.

  • Constructor Details

    • 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, 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 Details

    • lazyRun

      protected void lazyRun()
      Lazily execute the enumeration algorithm.

    • findCliques

      protected void findCliques(Set<V> p, Set<V> r, 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

    • iterator

      public Iterator<Set<V>> iterator()
      Description copied from interface: MaximalCliqueEnumerationAlgorithm
      Returns an iterator over all maximal cliques.
      Specified by:
      iterator in interface Iterable<V>
      Specified by:
      iterator in interface MaximalCliqueEnumerationAlgorithm<V,E>
      Returns:
      an iterator over all maximal cliques

    • maximumIterator

      public Iterator<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