Module org.jgrapht.core
Package org.jgrapht.alg.lca

Class TarjanLCAFinder<V,E>

java.lang.Object
org.jgrapht.alg.lca.TarjanLCAFinder<V,E>
Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:
LowestCommonAncestorAlgorithm<V>
public class TarjanLCAFinder<V,E> extends Object implements LowestCommonAncestorAlgorithm<V>
Tarjan's offline algorithm for computing lowest common ancestors in rooted trees and forests.

See the article on wikipedia for more information on the algorithm.

The original algorithm can be found in Gabow, H. N.; Tarjan, R. E. (1983), "A linear-time algorithm for a special case of disjoint set union", Proceedings of the 15th ACM Symposium on Theory of Computing (STOC), pp. 246–251, doi:10.1145/800061.808753

Preprocessing Time complexity: $O(1)$
Preprocessing Space complexity: $O(1)$
Query Time complexity: $O(|V| log^{*}(|V|) + |Q|)$ where $|Q|$ is the number of queries
Query Space complexity: $O(|V| + |Q|)$ where $|Q|$ is the number of queries

For small (i.e. less than 100 vertices) trees or forests, all implementations behave similarly. For larger trees/forests with less than 50,000 queries you can use either BinaryLiftingLCAFinder, HeavyPathLCAFinder or EulerTourRMQLCAFinder. Fo more than that use EulerTourRMQLCAFinder since it provides $O(1)$ per query.
Space-wise, HeavyPathLCAFinder and TarjanLCAFinder only use a linear amount while BinaryLiftingLCAFinder and EulerTourRMQLCAFinder require linearithmic space.
For DAGs, use NaiveLCAFinder.

Author:
Alexandru Valeanu

  • Constructor Details

    • TarjanLCAFinder

      public TarjanLCAFinder(Graph<V,E> graph, V root)
      Construct a new instance of the algorithm.

      Note: The constructor will NOT check if the input graph is a valid tree.

      Parameters:
      graph - the input graph
      root - the root of the graph

    • TarjanLCAFinder

      public TarjanLCAFinder(Graph<V,E> graph, Set<V> roots)
      Construct a new instance of the algorithm.

      Note: If two roots appear in the same tree, an error will be thrown.

      Note: The constructor will NOT check if the input graph is a valid forest.

      Parameters:
      graph - the input graph
      roots - the set of roots of the graph

  • Method Details

    • getLCA

      public V getLCA(V a, V b)
      Return the LCA of a and b
      Specified by:
      getLCA in interface LowestCommonAncestorAlgorithm<V>
      Parameters:
      a - the first element to find LCA for
      b - the other element to find the LCA for
      Returns:
      the LCA of a and b, or null if there is no LCA.

    • getBatchLCA

      public List<V> getBatchLCA(List<Pair<V,V>> queries)
      Return a list of LCAs for a batch of queries
      Specified by:
      getBatchLCA in interface LowestCommonAncestorAlgorithm<V>
      Parameters:
      queries - a list of pairs of vertices
      Returns:
      a list L of LCAs where L(i) is the LCA for pair queries(i)

    • getLCASet

      public Set<V> getLCASet(V a, V b)
      Note: This operation is not supported.
      Return the computed set of LCAs of a and b
      Specified by:
      getLCASet in interface LowestCommonAncestorAlgorithm<V>
      Parameters:
      a - the first element to find LCA for
      b - the other element to find the LCA for
      Returns:
      the set LCAs of a and b, or empty set if there is no LCA computed.
      Throws:
      UnsupportedOperationException - if the method is called