Module org.jgrapht.core
Package org.jgrapht.alg.connectivity

Class TreeDynamicConnectivity<T>

java.lang.Object
org.jgrapht.alg.connectivity.TreeDynamicConnectivity<T>
Type Parameters:
T - element type
public class TreeDynamicConnectivity<T> extends Object
Data structure for storing dynamic trees and querying node connectivity

This data structure supports the following operations:

  • Adding an element in $\mathcal{O}(\log 1)$
  • Checking if an element in present in $\mathcal{O}(1)$
  • Connecting two elements in $\mathcal{O}(\log n)$
  • Checking if two elements are connected in $\mathcal{O}(\log n)$
  • Removing connection between two nodes in $\mathcal{O}(\log n)$
  • Removing an element in $\mathcal{O}(deg(element)\cdot\log n + 1)$

This data structure doesn't allow to store graphs with cycles. Also, the edges are considered to be undirected. The memory complexity is linear in the number of inserted elements. The implementation is based on the Euler tour technique.

For the description of the Euler tour data structure, we refer to the Monika Rauch Henzinger, Valerie King: Randomized dynamic graph algorithms with polylogarithmic time per operation. STOC 1995: 519-527

Author:
Timofey Chudakov

  • Constructor Summary

    Constructors
    Constructor
    Description
    TreeDynamicConnectivity()
    Constructs a new TreeDynamicConnectivity instance

  • Method Summary

    Modifier and Type
    Method
    Description
    boolean
    add(T element)
    Adds an element to this data structure.
    boolean
    connected(T first, T second)
    Checks if the first and second belong to the same tree.
    boolean
    contains(T element)
    Checks if this data structure contains the element.
    boolean
    cut(T first, T second)
    Removes an edge between the first and second.
    boolean
    link(T first, T second)
    Adds an edge between the first and second elements.
    boolean
    remove(T element)
    Removes the element from this data structure.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • TreeDynamicConnectivity

      public TreeDynamicConnectivity()
      Constructs a new TreeDynamicConnectivity instance

  • Method Details

    • add

      public boolean add(T element)
      Adds an element to this data structure. If the element has been added before, this method returns false and has no effect.

      This method has $\mathcal{O}(\log 1)$ running time complexity

      Parameters:
      element - an element to add
      Returns:
      true upon successful modification, false otherwise

    • remove

      public boolean remove(T element)
      Removes the element from this data structure. This method has no effect if the element hasn't been added to this data structure

      This method has $\mathcal{O}(deg(element)\cdot\log n + 1)$ running time complexity

      Parameters:
      element - an element to remove
      Returns:
      true upon successful modification, false otherwise

    • contains

      public boolean contains(T element)
      Checks if this data structure contains the element.

      This method has expected $\mathcal{O}(1)$ running time complexity

      Parameters:
      element - an element to check presence of
      Returns:
      true if the element is stored in this data structure, false otherwise

    • link

      public boolean link(T first, T second)
      Adds an edge between the first and second elements. The method has no effect if the elements are already connected by some path, i.e. belong to the same tree. In the case some of the nodes haven't been added before, they're added to this data structure.

      This method has $\mathcal{O}(\log n)$ running time complexity

      Parameters:
      first - an element
      second - an element
      Returns:
      true upon successful modification, false otherwise

    • connected

      public boolean connected(T first, T second)
      Checks if the first and second belong to the same tree. The method will return false if either of the elements hasn't been added to this data structure

      This method has $\mathcal{O}(\log n)$ running time complexity

      Parameters:
      first - an element
      second - an element
      Returns:
      true if the elements belong to the same tree, false otherwise

    • cut

      public boolean cut(T first, T second)
      Removes an edge between the first and second. This method doesn't have any effect if there's no edge between these elements

      This method has $\mathcal{O}(\log n)$ running time complexity

      Parameters:
      first - an element
      second - an element
      Returns:
      true upon successful modification, false otherwise