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 java.lang.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